LEPTONS - Institute of Physics · 7 × 10 23 68 REUSSER 91 CNTR Ge K-shell disapprance ea > 2 × 10...

LEPTONS

e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713µ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714τ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724Heavy Charged Lepton Searches . . . . . . . . . . . . . . . 756Neutrino Properties . . . . . . . . . . . . . . . . . . . . . 757Number of Neutrino Types . . . . . . . . . . . . . . . . . . 765Double-β Decay . . . . . . . . . . . . . . . . . . . . . . 767Neutrino Mixing . . . . . . . . . . . . . . . . . . . . . . 772Heavy Neutral Leptons, Searches for . . . . . . . . . . . . . . 787

Notes in the Lepton Listings

Muon anomalous magnetic moment . . . . . . . . . . . . . . . . 715Muon decay parameters . . . . . . . . . . . . . . . . . . . . . 719τ branching fractions (rev.) . . . . . . . . . . . . . . . . . . . . 729τ -lepton decay parameters . . . . . . . . . . . . . . . . . . . . 752Introduction to the neutrino properties listings . . . . . . . . . . . 757Sum of neutrino masses (rev.) . . . . . . . . . . . . . . . . . . . 760Number of light neutrino types . . . . . . . . . . . . . . . . . . 765Neutrinoless double-β decay (rev.) . . . . . . . . . . . . . . . . . 767Introduction to three-neutrino mixing parameters (rev.) . . . . . . . 772

713713713713See key on page 601 LeptonParti le ListingseLEPTONSLEPTONSLEPTONSLEPTONSe J = 12e MASS (atomi mass units u)e MASS (atomi mass units u)e MASS (atomi mass units u)e MASS (atomi mass units u)The primary determination of an ele tron's mass omes from measuringthe ratio of the mass to that of a nu leus, so that the result is obtained inu (atomi mass units). The onversion fa tor to MeV is more un ertainthan the mass of the ele tron in u; indeed, the re ent improvements inthe mass determination are not evident when the result is given in MeV.In this datablo k we give the result in u, and in the following datablo k inMeV.VALUE (10−6 u) DOCUMENT ID TECN COMMENT548.579909070±0.000000016548.579909070±0.000000016548.579909070±0.000000016548.579909070±0.000000016 MOHR 16 RVUE 2014 CODATA value• • • We do not use the following data for averages, ts, limits, et . • • •548.57990946 ±0.00000022 MOHR 12 RVUE 2010 CODATA value548.57990943 ±0.00000023 MOHR 08 RVUE 2006 CODATA value548.57990945 ±0.00000024 MOHR 05 RVUE 2002 CODATA value548.5799092 ±0.0000004 1 BEIER 02 CNTR Penning trap548.5799110 ±0.0000012 MOHR 99 RVUE 1998 CODATA value548.5799111 ±0.0000012 2 FARNHAM 95 CNTR Penning trap548.579903 ±0.000013 COHEN 87 RVUE 1986 CODATA value1BEIER 02 ompares Larmor frequen y of the ele tron bound in a 12C5+ ion with the y lotron frequen y of a single trapped 12C5+ ion.2 FARNHAM 95 ompares y lotron frequen y of trapped ele trons with that of a singletrapped 12C6+ ion. e MASSe MASSe MASSe MASS2010 CODATA (MOHR 12) gives the onversion fa tor from u (atomi mass units, see the above datablo k) to MeV as 931.494 061 (21). Ear-lier values use the then- urrent onversion fa tor. The onversion errordominates the un ertainty of the masses given below.VALUE (MeV) DOCUMENT ID TECN COMMENT0.5109989461±0.00000000310.5109989461±0.00000000310.5109989461±0.00000000310.5109989461±0.0000000031 MOHR 16 RVUE 2014 CODATA value• • • We do not use the following data for averages, ts, limits, et . • • •0.510998928 ±0.000000011 MOHR 12 RVUE 2010 CODATA value0.510998910 ±0.000000013 MOHR 08 RVUE 2006 CODATA value0.510998918 ±0.000000044 MOHR 05 RVUE 2002 CODATA value0.510998901 ±0.000000020 1,2 BEIER 02 CNTR Penning trap0.510998902 ±0.000000021 MOHR 99 RVUE 1998 CODATA value0.510998903 ±0.000000020 1,3 FARNHAM 95 CNTR Penning trap0.510998895 ±0.000000024 1 COHEN 87 RVUE 1986 CODATA value0.5110034 ±0.0000014 COHEN 73 RVUE 1973 CODATA value1Converted to MeV using the 1998 CODATA value of the onversion onstant,931.494013 ± 0.000037 MeV/u.2BEIER 02 ompares Larmor frequen y of the ele tron bound in a 12C5+ ion with the y lotron frequen y of a single trapped 12C5+ ion.3 FARNHAM 95 ompares y lotron frequen y of trapped ele trons with that of a singletrapped 12C6+ ion. (me+ − me−) / maverage(me+ − me−) / maverage(me+ − me−) / maverage(me+ − me−) / maverageA test of CPT invarian e.VALUE CL% DOCUMENT ID TECN COMMENT<8× 10−9<8× 10−9<8× 10−9<8× 10−9 90 1 FEE 93 CNTR Positronium spe tros opy• • • We do not use the following data for averages, ts, limits, et . • • •<4× 10−23 90 2 DOLGOV 14 From photon mass limit<4× 10−8 90 CHU 84 CNTR Positronium spe tros opy1FEE 93 value is obtained under the assumption that the positronium Rydberg onstantis exa tly half the hydrogen one.2DOLGOV 14 result is obtained under the assumption that any mass dieren e betweenele tron and positron would lead to a non-zero photon mass. The PDG 12 limit of1× 10−18 eV on the photon mass is in turn used to derive the value quoted here.

∣∣qe+ + qe− ∣∣/e∣∣qe+ + qe− ∣∣/e∣∣qe+ + qe− ∣∣/e∣∣qe+ + qe− ∣∣/eA test of CPT invarian e. See also similar tests involving the proton.VALUE DOCUMENT ID TECN COMMENT<4× 10−8<4× 10−8<4× 10−8<4× 10−8 1 HUGHES 92 RVUE• • • We do not use the following data for averages, ts, limits, et . • • •<2× 10−18 2 SCHAEFER 95 THEO Va uum polarization<1× 10−18 3 MUELLER 92 THEO Va uum polarization1HUGHES 92 uses re ent measurements of Rydberg-energy and y lotron-frequen y ra-tios.2 SCHAEFER 95 removes model dependen y of MUELLER 92.3MUELLER 92 argues that an inequality of the harge magnitudes would, through higher-order va uum polarization, ontribute to the net harge of atoms.

e MAGNETIC MOMENT ANOMALYe MAGNETIC MOMENT ANOMALYe MAGNETIC MOMENT ANOMALYe MAGNETIC MOMENT ANOMALYµe/µB − 1 = (g−2)/2µe/µB − 1 = (g−2)/2µe/µB − 1 = (g−2)/2µe/µB − 1 = (g−2)/2VALUE (units 10−6) DOCUMENT ID TECN CHG COMMENT1159.65218091±0.000000261159.65218091±0.000000261159.65218091±0.000000261159.65218091±0.00000026 MOHR 16 RVUE 2014 CODATA value• • • We do not use the following data for averages, ts, limits, et . • • •1159.65218076±0.00000027 MOHR 12 RVUE 2010 CODATA value1159.65218073±0.00000028 HANNEKE 08 MRS Single ele tron1159.65218111±0.00000074 1 MOHR 08 RVUE 2006 CODATA value1159.65218085±0.00000076 2 ODOM 06 MRS − Single ele tron1159.6521859 ±0.0000038 MOHR 05 RVUE 2002 CODATA value1159.6521869 ±0.0000041 MOHR 99 RVUE 1998 CODATA value1159.652193 ±0.000010 COHEN 87 RVUE 1986 CODATA value1159.6521884 ±0.0000043 VANDYCK 87 MRS − Single ele tron1159.6521879 ±0.0000043 VANDYCK 87 MRS + Single positron1MOHR 08 average is dominated by ODOM 06.2 Superseded by HANNEKE 08 per private ommuni ation with Gerald Gabrielse.(ge+ − ge−) / gaverage(ge+ − ge−) / gaverage(ge+ − ge−) / gaverage(ge+ − ge−) / gaverageA test of CPT invarian e.VALUE (units 10−12) CL% DOCUMENT ID TECN COMMENT

− 0.5± 2.1− 0.5± 2.1− 0.5± 2.1− 0.5± 2.1 1 VANDYCK 87 MRS Penning trap• • • We do not use the following data for averages, ts, limits, et . • • •< 12 95 2 VASSERMAN 87 CNTR Assumes me+ = me−22 ±64 SCHWINBERG 81 MRS Penning trap1VANDYCK 87 measured (g−/g+)−1 and we onverted it.2VASSERMAN 87 measured (g+ − g−)/(g−2). We multiplied by (g−2)/g = 1.2 ×10−3. e ELECTRIC DIPOLE MOMENT (d)e ELECTRIC DIPOLE MOMENT (d)e ELECTRIC DIPOLE MOMENT (d)e ELECTRIC DIPOLE MOMENT (d)A nonzero value is forbidden by both T invarian e and P invarian e.VALUE (10−28 e m) CL% DOCUMENT ID TECN COMMENT< 0.87< 0.87< 0.87< 0.87 90 1 BARON 14 CNTR ThO mole ules• • • We do not use the following data for averages, ts, limits, et . • • •

− 5570 ± 7980 ±120 KIM 15 CNTR Gd3Ga5O12mole ules< 6050 90 2 ECKEL 12 CNTR Eu0.5Ba0.5TiO3mole ules< 10.5 90 3 HUDSON 11 NMR YbF mole ules6.9 ± 7.4 REGAN 02 MRS 205Tl beams18 ± 12 ± 10 4 COMMINS 94 MRS 205Tl beams− 27 ± 83 4 ABDULLAH 90 MRS 205Tl beams− 1400 ± 2400 CHO 89 NMR TlF mole ules− 150 ± 550 ±150 MURTHY 89 Cs, no B eld− 5000 ±11000 LAMOREAUX 87 NMR 199Hg19000 ±34000 90 SANDARS 75 MRS Thallium7000 ±22000 90 PLAYER 70 MRS Xenon

< 30000 90 WEISSKOPF 68 MRS Cesium1BARON 14 gives a measurement orresponding to this limit as (−0.21 ± 0.37 ± 0.25)×10−28 e m.2ECKEL 12 gives a measurement orresponding to this limit as (−1.07 ± 3.06 ± 1.74)×10−25 e m.3HUDSON 11 gives a measurement orresponding to this limit as (−2.4 ± 5.7 ± 1.5)×10−28 e m.4ABDULLAH 90, COMMINS 94, and REGAN 02 use the relativisti enhan ement of avalen e ele tron's ele tri dipole moment in a high-Z atom.e− MEAN LIFE / BRANCHING FRACTIONe− MEAN LIFE / BRANCHING FRACTIONe− MEAN LIFE / BRANCHING FRACTIONe− MEAN LIFE / BRANCHING FRACTIONA test of harge onservation. See the \Note on Testing Charge Conserva-tion and the Pauli Ex lusion Prin iple" following this se tion in our 1992edition (Physi al Review D45D45D45D45 S1 (1992), p. VI.10).Most of these experiments are one of three kinds: Attempts to observe(a) the 255.5 keV gamma ray produ ed in e− → νe γ, (b) the (K) shellx ray produ ed when an ele tron de ays without additional energy deposit,e.g., e− → νe νe νe (\disappearan e" experiments), and ( ) nu lear de-ex itation gamma rays after the ele tron disappears from an atomi shelland the nu leus is left in an ex ited state. The last an in lude both weakboson and photon mediating pro esses. We use the best e− → νe γ limitfor the Summary Tables.Note that we use the mean life rather than the half life, whi h is oftenreported.e → νe γ and astrophysi al limitse → νe γ and astrophysi al limitse → νe γ and astrophysi al limitse → νe γ and astrophysi al limitsVALUE (yr) CL% DOCUMENT ID TECN COMMENT>6.6 × 1028>6.6 × 1028>6.6 × 1028>6.6 × 1028 90 AGOSTINI 15B BORX e− → ν γ

714714714714LeptonParti le Listingse,µ• • • We do not use the following data for averages, ts, limits, et . • • •>1.22× 1026 68 1 KLAPDOR-K... 07 CNTR e− → ν γ

>4.6 × 1026 90 BACK 02 BORX e− → ν γ

>3.4 × 1026 68 BELLI 00B DAMA e− → ν γ, liquid Xe>3.7 × 1025 68 AHARONOV 95B CNTR e− → ν γ

>2.35× 1025 68 BALYSH 93 CNTR e− → ν γ, 76Ge dete tor>1.5 × 1025 68 AVIGNONE 86 CNTR e− → ν γ

>1 × 1039 2 ORITO 85 ASTR Astrophysi al argument>3 × 1023 68 BELLOTTI 83B CNTR e− → ν γ1The authors of A. Derbin et al, arXiv:0704.2047v1 argue that this limit is overestimatedby at least a fa tor of 5.2ORITO 85 assumes that ele tromagneti for es extend out to large enough distan es andthat the age of our galaxy is 1010 years.Disappearan e and nu lear-de-ex itation experimentsDisappearan e and nu lear-de-ex itation experimentsDisappearan e and nu lear-de-ex itation experimentsDisappearan e and nu lear-de-ex itation experimentsVALUE (yr) CL% DOCUMENT ID TECN COMMENT>6.4× 1024>6.4× 1024>6.4× 1024>6.4× 1024 68 1 BELLI 99B DAMA De-ex itation of 129Xe• • • We do not use the following data for averages, ts, limits, et . • • •>4.2× 1024 68 BELLI 99 DAMA Iodine L-shell disappearan e>2.4× 1023 90 2 BELLI 99D DAMA De-ex itation of 127I (in NaI)>4.3× 1023 68 AHARONOV 95B CNTR Ge K-shell disappearan e>2.7× 1023 68 REUSSER 91 CNTR Ge K-shell disappearan e>2 × 1022 68 BELLOTTI 83B CNTR Ge K-shell disappearan e1BELLI 99B limit on harge non onserving e− apture involving ex itation of the 236.1keV nu lear state of 129Xe; the 90% CL limit is 3.7× 1024 yr. Less stringent limits forother states are also given.2BELLI 99D limit on harge non onserving e− apture involving ex itation of the 57.6keV nu lear state of 127I. Less stringent limits for the other states and for the state of23Na are also given.LIMITS ON LEPTON-FLAVOR VIOLATION IN PRODUCTIONLIMITS ON LEPTON-FLAVOR VIOLATION IN PRODUCTIONLIMITS ON LEPTON-FLAVOR VIOLATION IN PRODUCTIONLIMITS ON LEPTON-FLAVOR VIOLATION IN PRODUCTIONForbidden by lepton family number onservation.This se tion was added for the 2008 edition of this Review and is not omplete. For a list of further measurements see referen es in the paperslisted below.σ(e+ e− → e± τ∓) / σ(e+ e− → µ+µ−)σ(e+ e− → e± τ∓) / σ(e+ e− → µ+µ−)σ(e+ e− → e± τ∓) / σ(e+ e− → µ+µ−)σ(e+ e− → e± τ∓) / σ(e+ e− → µ+µ−)VALUE CL% DOCUMENT ID TECN COMMENT<8.9× 10−6<8.9× 10−6<8.9× 10−6<8.9× 10−6 95 AUBERT 07P BABR e+ e− at E m = 10.58 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.8× 10−3 95 GOMEZ-CAD... 91 MRK2 e+ e− at E m = 29 GeVσ(e+ e− → µ± τ∓) / σ(e+ e− → µ+µ−)σ(e+ e− → µ± τ∓) / σ(e+ e− → µ+µ−)σ(e+ e− → µ± τ∓) / σ(e+ e− → µ+µ−)σ(e+ e− → µ± τ∓) / σ(e+ e− → µ+µ−)VALUE CL% DOCUMENT ID TECN COMMENT<4.0× 10−6<4.0× 10−6<4.0× 10−6<4.0× 10−6 95 AUBERT 07P BABR e+ e− at E m = 10.58 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<6.1× 10−3 95 GOMEZ-CAD... 91 MRK2 e+ e− at E m = 29 GeVe REFERENCESe REFERENCESe REFERENCESe REFERENCESMOHR 16 arXiv:1507.07956 P.J. Mohr, D.B. Newell, B.N. Taylor (NIST)A epted for publi ation in RMPAGOSTINI 15B PRL 115 231802 M. Agostini et al. (BOREXINO Collab.)KIM 15 PR D91 102004 Y.J. Kim et al. (IND, YALE, LANL)BARON 14 SCIENCE 343 269 J. Baron et al. (ACME Collab.)DOLGOV 14 PL B732 244 A.D. Dolgov, V.A. NovikovECKEL 12 PRL 109 193003 S. E kel, A.O. Sushkov, S.K. Lamoreaux (YALE)MOHR 12 RMP 84 1527 P.J. Mohr, B.N. Taylor, D.B. Newell (NIST)PDG 12 PR D86 010001 J. Beringer et al. (PDG Collab.)HUDSON 11 NAT 473 493 J.J. Hadson et al. (LOIC)HANNEKE 08 PRL 100 120801 D. Hanneke, S. Fogwell, G. Gabrielse (HARV)MOHR 08 RMP 80 633 P.J. Mohr, B.N. Taylor, D.B. Newell (NIST)AUBERT 07P PR D75 031103 B. Aubert et al. (BABAR Collab.)KLAPDOR-K... 07 PL B644 109 H.V. Klapdor-Kleingrothaus, I.V. Krivosheina, I.V. TitkovaODOM 06 PRL 97 030801 B. Odom et al. (HARV)MOHR 05 RMP 77 1 P.J. Mohr, B.N. Taylor (NIST)BACK 02 PL B525 29 H.O. Ba k et al. (BOREXINO/SASSO Collab.)BEIER 02 PRL 88 011603 T. Beier et al.REGAN 02 PRL 88 071805 B.C. Regan et al.BELLI 00B PR D61 117301 P. Belli et al. (DAMA Collab.)BELLI 99 PL B460 236 P. Belli et al. (DAMA Collab.)BELLI 99B PL B465 315 P. Belli et al. (DAMA Collab.)BELLI 99D PR C60 065501 P. Belli et al. (DAMA Collab.)MOHR 99 JPCRD 28 1713 P.J. Mohr, B.N. Taylor (NIST)Also RMP 72 351 P.J. Mohr, B.N. Taylor (NIST)AHARONOV 95B PR D52 3785 Y. Aharonov et al. (SCUC, PNL, ZARA+)Also PL B353 168 Y. Aharonov et al. (SCUC, PNL, ZARA+)FARNHAM 95 PRL 75 3598 D.L. Farnham, R.S. van Dy k, P.B. S hwinberg (WASH)SCHAEFER 95 PR A51 838 A. S haefer, J. Reinhardt (FRAN)COMMINS 94 PR A50 2960 E.D. Commins et al.BALYSH 93 PL B298 278 A. Balysh et al. (KIAE, MPIH, SASSO)FEE 93 PR A48 192 M.S. Fee et al.HUGHES 92 PRL 69 578 R.J. Hughes, B.I. Deut h (LANL, AARH)MUELLER 92 PRL 69 3432 B. Muller, M.H. Thoma (DUKE)PDG 92 PR D45 S1 K. Hikasa et al. (KEK, LBL, BOST+)GOMEZ-CAD... 91 PRL 66 1007 J.J. Gomez-Cadenas et al. (SLAC MARK-2 Collab.)REUSSER 91 PL B255 143 D. Reusser et al. (NEUC, CIT, PSI)ABDULLAH 90 PRL 65 2347 K. Abdullah et al. (LBL, UCB)CHO 89 PRL 63 2559 D. Cho, K. Sangster, E.A. Hinds (YALE)MURTHY 89 PRL 63 965 S.A. Murthy et al. (AMHT)COHEN 87 RMP 59 1121 E.R. Cohen, B.N. Taylor (RISC, NBS)LAMOREAUX 87 PRL 59 2275 S.K. Lamoreaux et al. (WASH)VANDYCK 87 PRL 59 26 R.S. van Dy k, P.B. S hwinberg, H.G. Dehmelt (WASH)VASSERMAN 87 PL B198 302 I.B. Vasserman et al. (NOVO)Also PL B187 172 I.B. Vasserman et al. (NOVO)

AVIGNONE 86 PR D34 97 F.T. Avignone et al. (PNL, SCUC)ORITO 85 PRL 54 2457 S. Orito, M. Yoshimura (TOKY, KEK)CHU 84 PRL 52 1689 S. Chu, A.P. Mills, J.L. Hall (BELL, NBS, COLO)BELLOTTI 83B PL 124B 435 E. Bellotti et al. (MILA)SCHWINBERG 81 PRL 47 1679 P.B. S hwinberg, R.S. van Dy k, H.G. Dehmelt (WASH)SANDARS 75 PR A11 473 P.G.H. Sandars, D.M. Sternheimer (OXF, BNL)COHEN 73 JPCRD 2 664 E.R. Cohen, B.N. Taylor (RISC, NBS)PLAYER 70 JP B3 1620 M.A. Player, P.G.H. Sandars (OXF)WEISSKOPF 68 PRL 21 1645 M.C. Weisskopf et al. (BRAN)µ J = 12

µ MASS (atomi mass units u)µ MASS (atomi mass units u)µ MASS (atomi mass units u)µ MASS (atomi mass units u)The muon's mass is obtained from the muon-ele tron mass ratio as deter-mined from the measurement of Zeeman transition frequen ies in muonium(µ+ e− atom). Sin e the ele tron's mass is most a urately known in u,the muon's mass is also most a urately known in u. The onversion fa -tor to MeV has approximately the same relative un ertainty as the massof the muon in u. In this datablo k we give the result in u, and in thefollowing datablo k in MeV.VALUE (u) DOCUMENT ID TECN COMMENT0.1134289257±0.00000000250.1134289257±0.00000000250.1134289257±0.00000000250.1134289257±0.0000000025 MOHR 16 RVUE 2014 CODATA value• • • We do not use the following data for averages, ts, limits, et . • • •0.1134289267±0.0000000029 MOHR 12 RVUE 2010 CODATA value0.1134289256±0.0000000029 MOHR 08 RVUE 2006 CODATA value0.1134289264±0.0000000030 MOHR 05 RVUE 2002 CODATA value0.1134289168±0.0000000034 1 MOHR 99 RVUE 1998 CODATA value0.113428913 ±0.000000017 2 COHEN 87 RVUE 1986 CODATA value1MOHR 99 make use of other 1998 CODATA entries below.2COHEN 87 make use of other 1986 CODATA entries below.

µ MASSµ MASSµ MASSµ MASS2010 CODATA (MOHR 12) gives the onversion fa tor from u (atomi mass units, see the above datablo k) to MeV as 931.494 061 (21). Ear-lier values use the then- urrent onversion fa tor. The onversion error ontributes signi antly to the un ertainty of the masses given below.VALUE (MeV) DOCUMENT ID TECN CHG COMMENT105.6583745±0.0000024105.6583745±0.0000024105.6583745±0.0000024105.6583745±0.0000024 MOHR 16 RVUE 2014 CODATA value• • • We do not use the following data for averages, ts, limits, et . • • •105.6583715±0.0000035 MOHR 12 RVUE 2010 CODATA value105.6583668±0.0000038 MOHR 08 RVUE 2006 CODATA value105.6583692±0.0000094 MOHR 05 RVUE 2002 CODATA value105.6583568±0.0000052 MOHR 99 RVUE 1998 CODATA value105.658353 ±0.000016 1 COHEN 87 RVUE 1986 CODATA value105.658386 ±0.000044 2 MARIAM 82 CNTR +105.65836 ±0.00026 3 CROWE 72 CNTR105.65865 ±0.00044 4 CRANE 71 CNTR1Converted to MeV using the 1998 CODATA value of the onversion onstant,931.494013 ± 0.000037 MeV/u.2MARIAM 82 give mµ/me = 206.768259(62).3CROWE 72 give mµ/me = 206.7682(5).4CRANE 71 give mµ/me = 206.76878(85).

µ MEAN LIFE τµ MEAN LIFE τµ MEAN LIFE τµ MEAN LIFE τMeasurements with an error > 0.001× 10−6 s have been omitted.VALUE (10−6 s) DOCUMENT ID TECN CHG COMMENT2.1969811±0.0000022 OUR AVERAGE2.1969811±0.0000022 OUR AVERAGE2.1969811±0.0000022 OUR AVERAGE2.1969811±0.0000022 OUR AVERAGE2.1969803±0.0000021±0.0000007 1 TISHCHENKO 13 CNTR + Surfa e µ+ at PSI2.197083 ±0.000032 ±0.000015 BARCZYK 08 CNTR + Muons from π+de ay at rest2.197013 ±0.000021 ±0.000011 CHITWOOD 07 CNTR + Surfa e µ+ at PSI2.197078 ±0.000073 BARDIN 84 CNTR +2.197025 ±0.000155 BARDIN 84 CNTR −2.19695 ±0.00006 GIOVANETTI 84 CNTR +2.19711 ±0.00008 BALANDIN 74 CNTR +2.1973 ±0.0003 DUCLOS 73 CNTR +• • • We do not use the following data for averages, ts, limits, et . • • •2.1969803±0.0000022 WEBBER 11 CNTR + Surfa e µ+ at PSI1TISHCHENKO 13 uses 1.6× 1012 µ+ events and supersedes WEBBER 11.

τ µ+/τ µ− MEAN LIFE RATIOτ µ+/τ µ− MEAN LIFE RATIOτ µ+/τ µ− MEAN LIFE RATIOτ µ+/τ µ− MEAN LIFE RATIOA test of CPT invarian e.VALUE DOCUMENT ID TECN COMMENT1.000024±0.0000781.000024±0.0000781.000024±0.0000781.000024±0.000078 BARDIN 84 CNTR• • • We do not use the following data for averages, ts, limits, et . • • •

715715715715See key on page 601 Lepton Parti le Listingsµ1.0008 ±0.0010 BAILEY 79 CNTR Storage ring1.000 ±0.001 MEYER 63 CNTR Mean life µ+/ µ−(τ µ+ − τ µ−) / τ average(τ µ+ − τ µ−) / τ average(τ µ+ − τ µ−) / τ average(τ µ+ − τ µ−) / τ averageA test of CPT invarian e. Cal ulated from the mean-life ratio, above.VALUE DOCUMENT ID(2±8)× 10−5 OUR EVALUATION(2±8)× 10−5 OUR EVALUATION(2±8)× 10−5 OUR EVALUATION(2±8)× 10−5 OUR EVALUATION

µ/p MAGNETIC MOMENT RATIOµ/p MAGNETIC MOMENT RATIOµ/p MAGNETIC MOMENT RATIOµ/p MAGNETIC MOMENT RATIOThis ratio is used to obtain a pre ise value of the muon mass and toredu e experimental muon Larmor frequen y measurements to the muonmagneti moment anomaly. Measurements with an error > 0.00001 havebeen omitted. By onvention, the minus sign on this ratio is omitted.CODATA values were tted using their sele tion of data, plus other datafrom multiparameter ts.VALUE DOCUMENT ID TECN CHG COMMENT3.183345142±0.0000000713.183345142±0.0000000713.183345142±0.0000000713.183345142±0.000000071 MOHR 16 RVUE 2014 CODATA value• • • We do not use the following data for averages, ts, limits, et . • • •3.183345107±0.000000084 MOHR 12 RVUE 2010 CODATA value3.183345137±0.000000085 MOHR 08 RVUE 2006 CODATA value3.183345118±0.000000089 MOHR 05 RVUE 2002 CODATA value3.18334513 ±0.00000039 LIU 99 CNTR + HFS in muonium3.18334539 ±0.00000010 MOHR 99 RVUE 1998 CODATA value3.18334547 ±0.00000047 COHEN 87 RVUE 1986 CODATA value3.1833441 ±0.0000017 KLEMPT 82 CNTR + Pre ession strob3.1833461 ±0.0000011 MARIAM 82 CNTR + HFS splitting3.1833448 ±0.0000029 CAMANI 78 CNTR + See KLEMPT 823.1833403 ±0.0000044 CASPERSON 77 CNTR + HFS splitting3.1833402 ±0.0000072 COHEN 73 RVUE 1973 CODATA value3.1833467 ±0.0000082 CROWE 72 CNTR + Pre ession phaseTHE MUON ANOMALOUS MAGNETIC MOMENT

Updated August 2013 by A. Hoecker (CERN), and W.J. Mar-ciano (BNL).

The Dirac equation predicts a muon magnetic moment,~M = gµ

e

2mµ

~S, with gyromagnetic ratio gµ = 2. Quantum

loop effects lead to a small calculable deviation from gµ = 2,

parameterized by the anomalous magnetic moment

aµ ≡ gµ − 2

2. (1)

That quantity can be accurately measured and, within the

Standard Model (SM) framework, precisely predicted. Hence,

comparison of experiment and theory tests the SM at its quan-

tum loop level. A deviation in aexpµ from the SM expectation

would signal effects of new physics, with current sensitivity

reaching up to mass scales of O(TeV) [1,2]. For recent and

very thorough muon g − 2 reviews, see Refs. [3–5].

The E821 experiment at Brookhaven National Lab (BNL)

studied the precession of µ+ and µ− in a constant external

magnetic field as they circulated in a confining storage ring. It

found [7] 1

aexpµ+ = 11 659 204(6)(5)× 10−10 ,

aexpµ− = 11 659 215(8)(3)× 10−10 , (2)

1 The original results reported by the experiment have been

updated in Eq. (2) and Eq. (3) to the newest value for the ab-

solute muon-to-proton magnetic ratio λ = 3.183 345 107(84) [6].

The change induced in aexpµ with respect to the value of λ =

3.183 345 39(10) used in Ref. 7 amounts to +1.12 × 10−10.

γ

γ

µ µ

γ

Z

µ µ

γ

W W

ν

µ µ

γ

γ γ

µ µhad

where the first errors are statistical and the second system-

atic. Assuming CPT invariance and taking into account cor-

relations between systematic uncertainties, one finds for their

average [6,7]

aexpµ = 11 659 209.1(5.4)(3.3)× 10−10 . (3)

These results represent about a factor of 14 improvement over

the classic CERN experiments of the 1970’s [8]. Improvement

of the measurement in Eq. (3) by a factor of four by moving the

E821 storage ring to Fermilab, and utilizing a cleaner and more

intense muon beam is in progress. An even more ambitious

precision goal is set by an experiment based on a beam of

ultra-cold muons proposed at the Japan Proton Accelerator

Research Complex.

The SM prediction for aSMµ is generally divided into three

parts (see Fig. 1 for representative Feynman diagrams)

aSMµ = aQED

µ + aEWµ + aHad

µ . (4)

The QED part includes all photonic and leptonic (e, µ, τ) loops

starting with the classic α/2π Schwinger contribution. It has

been computed through 5 loops [9]

aQEDµ =

α

2π+ 0.765 857 425(17)

(α

π

)2+ 24.050 509 96(32)

(α

π

)3

+ 130.879 6(6 3)(α

π

)4+ 753.3(1.0)

(α

π

)5+ · · · (5)

with a few significant changes in the coefficients since our

previous update of this review in 2011. Employing2 α−1 =

137.035 999 049(90), obtained [6] from the precise measure-

ments of h/mRb [11], the Rydberg constant and mRb/me [6],

leads to [9]

aQEDµ = 116 584 718.95(0.08)× 10−11 , (6)

where the small error results mainly from the uncertainty in α.

Loop contributions involving heavy W±, Z or Higgs parti-

cles are collectively labeled as aEWµ . They are suppressed by at

least a factor ofα

π

m2µ

m2W

≃ 4 × 10−9. At 1-loop order [12]

aEWµ [1-loop] =

Gµm2µ

8√

2π2

[5

3+

1

3

(1 − 4 sin2θW

)2

+ O(

m2µ

M2W

)+ O

(m2

µ

m2H

)],

= 194.8 × 10−11 , (7)

2 In the previous versions of this review we used the precise

α value determined from the electron ae measurement [9,10].

With the new measurement [11] of the recoil velocity of Rubid-

ium, h/mRb, an ae-independent determination of α with suffi-

cient precision is available and preferred.

716716716716Lepton Parti le Listingsµ

for sin2θW ≡ 1 − M2W/M2

Z ≃ 0.223, and where Gµ ≃1.166 × 10−5 GeV−2 is the Fermi coupling constant. Two-loop

corrections are relatively large and negative [13]. For a Higgs

boson mass of ≃126 GeV [13]

aEWµ [2-loop] = −41.2(1.0) × 10−11 , (8)

where the uncertainty stems from quark triangle loops. The

3-loop leading logarithms are negligible [13,14], O(10−12),

implying in total

aEWµ = 153.6(1.0)× 10−11 . (9)

Hadronic (quark and gluon) loop contributions to aSMµ give rise

to its main theoretical uncertainties. At present, those effects

are not calculable from first principles, but such an approach,

at least partially, may become possible as lattice QCD matures.

Instead, one currently relies on a dispersion relation approach

to evaluate the lowest-order (i.e., O(α2)) hadronic vacuum

polarization contribution aHadµ [LO] from corresponding cross

section measurements [15]

aHadµ [LO] =

1

3

(α

π

)2 ∞∫

m2π

dsK(s)

sR(0)(s) , (10)

where K(s) is a QED kernel function [16], and where R(0)(s)

denotes the ratio of the bare3 cross section for e+e− annihilation

into hadrons to the pointlike muon-pair cross section at center-

of-mass energy√

s. The function K(s) ∼ 1/s in Eq. (10) gives

a strong weight to the low-energy part of the integral. Hence,

aHadµ [LO] is dominated by the ρ(770) resonance.

Currently, the available σ(e+e− → hadrons) data give a

leading-order hadronic vacuum polarization (representative)

contribution of [17]

aHadµ [LO] = 6 923(42)(3)× 10−11 , (11)

where the first error is experimental (dominated by system-

atic uncertainties), and the second due to perturbative QCD,

which is used at intermediate and large energies to predict the

contribution from the quark-antiquark continuum. New multi-

hadron data from the BABAR experiment have increased the

constraints on unmeasured exclusive final states and led to a

small reduction in the hadronic contribution compared to the

2009 PDG value.

Alternatively, one can use precise vector spectral functions

from τ → ντ + hadrons decays [18] that can be related to

isovector e+e− → hadrons cross sections by isospin symmetry.

Replacing e+e− data in the two-pion and four-pion channels

by the corresponding isospin-transformed τ data, and applying

3 The bare cross section is defined as the measured cross sec-

tion corrected for initial-state radiation, electron-vertex loop

contributions and vacuum-polarization effects in the photon pro-

pagator. However, QED effects in the hadron vertex and final

state, as photon radiation, are included.

isospin-violating corrections (from QED and md−mu 6= 0), one

finds [17]

aHadµ [LO] = 7 015(42)(19)(3)× 10−11 (τ) , (12)

where the first error is experimental, the second estimates the

uncertainty in the isospin-breaking corrections applied to the

τ data, and the third error is due to perturbative QCD. The

current discrepancy between the e+e− and τ -based determina-

tions of aHadµ [LO] has been reduced to 1.8σ with respect to

earlier evaluations. New e+e− and τ data from the B-factory

experiments BABAR and Belle have increased the experimental

information. Reevaluated isospin-breaking corrections have also

contributed to this improvement [19]. BABAR reported good

agreement with the τ data in the most important two-pion

channel [20]. The remaining discrepancy with the older e+e−

and τ datasets may be indicative of problems with one or

both data sets. It may also suggest the need for additional

isospin-violating corrections to the τ data. Several evaluations

of aHadµ [LO] have been published leading to similar results (see

Fig. 2). The low-energy contribution to aHadµ [LO] has also been

evaluated with the use of additional theory or model constraints

in Refs. [22] and [23], respectively.

Higher order, O(α3), hadronic contributions are obtained

from dispersion relations using the same e+e− → hadrons

data [18,21,24], giving aHad,Dispµ [NLO] = (−98.4± 0.6)× 10−11,

along with model-dependent estimates of the hadronic light-

by-light scattering contribution, aHad,LBLµ [NLO], motivated by

large-NC QCD [25–31]. 4 Following [29], one finds for the sum

of the two terms

aHadµ [NLO] = 7(26) × 10−11 , (13)

where the error is dominated by hadronic light-by-light uncer-

tainties.

Adding Eqs. (6), (9), (11) and (13) gives the representative

e+e− data based SM prediction

aSMµ = 116 591 803(1)(42)(26)× 10−11 , (14)

where the errors are due to the electroweak, lowest-order

hadronic, and higher-order hadronic contributions, respectively.

The difference between experiment and theory

∆aµ = aexpµ − aSM

µ = 288(63)(49)× 10−11 , (15)

(with all errors combined in quadrature) represents an inter-

esting but not yet conclusive discrepancy of 3.6 times the

estimated 1σ error. All the recent estimates for the hadronic

contribution compiled in Fig. 2 exhibit similar discrepancies.

Switching to τ data reduces the discrepancy to 2.4σ, assuming

the isospin-violating corrections are under control within the

4 Some representative recent estimates of the hadronic light-

by-light scattering contribution, aHad,LBLµ [NLO], that followed

after the sign correction of [27], are: 105(26) × 10−11 [29],

110(40) × 10−11 [25], 136(25) × 10−11 [26].

717717717717See key on page 601 Lepton Parti le Listingsµ

-700 -600 -500 -400 -300 -200 -100 0

aµ – aµ exp × 10–11

BN

L-E821 2004

JN 09 (e+e–-based)

DHMZ 10 (τ-based)

DHMZ 10 (e+e–)

HLMNT 11 (e+e–)

BNL-E821 (world average)

–301 ± 65

–197 ± 54

–289 ± 49

–263 ± 49

0 ± 63

Figure 2: Compilation of recent published re-sults for aµ (in units of 10−11), subtracted by thecentral value of the experimental average (3).The shaded band indicates the size of the ex-perimental uncertainty. The SM predictions aretaken from: JN [4], DHMZ [17], HMNT [21].Note that the quoted errors in the figure donot include the uncertainty on the subtractedexperimental value. To obtain for each theorycalculation a result equivalent to Eq. (15), theerrors from theory and experiment must beadded in quadrature.

estimated uncertainties (see Ref. 32 for an analysis leading to a

different conclusion).

An alternate interpretation is that ∆aµ may be a new

physics signal with supersymmetric particle loops as the leading

candidate explanation. Such a scenario is quite natural, since

generically, supersymmetric models predict [1] an additional

contribution to aSMµ

aSUSYµ ≃ sign(µ) · 130 × 10−11 ·

(100 GeV

mSUSY

)2

tanβ , (16)

where mSUSY is a representative supersymmetric mass scale,

tanβ ≃ 3–40 a potential enhancement factor, and sign(µ) = ±1.

Supersymmetric particles in the mass range 100–500 GeV could

be the source of the deviation ∆aµ. If so, those particles should

be directly observed at the Large Hadron Collider at CERN.

New physics effects [1] other than supersymmetry could also

explain a non-vanishing ∆aµ. A recent popular scenario involves

the “dark photon”, a relatively light hypothetical vector boson

from the dark matter sector that couples to our world of particle

physics through mixing with the ordinary photon [33–35]. As

a result, it couples to ordinary charged particles with strength

ε · e and gives rise to an additional muon anomalous magnetic

moment contribution

adark photonµ =

α

2πε2F (mV /mµ) , (17)

where F (x) =∫ 10 2z(1 − z)2/[(1 − z)2 + x2z] dz. For values of

ε ∼ 1–2 · 10−3 and mV ∼ 10–100 MeV, the dark photon, which

was originally motivated by cosmology, can provide a viable

solution to the muon g − 2 discrepancy. Searches for the dark

photon in that mass range are currently underway at Jefferson

Lab, USA, and MAMI in Mainz, Germany.

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µ MAGNETIC MOMENT ANOMALYµ MAGNETIC MOMENT ANOMALYµ MAGNETIC MOMENT ANOMALYµ MAGNETIC MOMENT ANOMALYThe parity-violating de ay of muons in a storage ring is observed. Thedieren e frequen y ωa between the muon spin pre ision and the orbitalangular frequen y (e/mµ )⟨B⟩ is measured, as is the free proton NMRfrequen y ωp , thus determining the ratio R=ωa/ωp . Given the magneti moment ratio λ=µµ/µp (from hyperne stru ture in muonium), (g−2)/2= R/(λ−R).µµ/(eh/2mµ)−1 = (gµ−2)/2µµ/(eh/2mµ)−1 = (gµ−2)/2µµ/(eh/2mµ)−1 = (gµ−2)/2µµ/(eh/2mµ)−1 = (gµ−2)/2VALUE (units 10−10) DOCUMENT ID TECN CHG COMMENT11659208.9± 5.4±3.311659208.9± 5.4±3.311659208.9± 5.4±3.311659208.9± 5.4±3.3 1 BENNETT 06 MUG2 Average µ+ and µ−• • • We do not use the following data for averages, ts, limits, et . • • •11659208 ± 6 BENNETT 04 MUG2 Average µ+ and µ−11659214 ± 8 ±3 BENNETT 04 MUG2 − Storage ring11659203 ± 6 ±5 BENNETT 04 MUG2 + Storage ring11659204 ± 7 ±5 BENNETT 02 MUG2 + Storage ring11659202 ± 14 ±6 BROWN 01 MUG2 + Storage ring11659191 ± 59 BROWN 00 MUG2 +11659100 ± 110 2 BAILEY 79 CNTR + Storage ring11659360 ± 120 2 BAILEY 79 CNTR − Storage ring11659230 ± 85 2 BAILEY 79 CNTR ± Storage ring11620000 ±5000 CHARPAK 62 CNTR +1BENNETT 06 reports (gµ−2)/2 = (11659208.0 ± 5.4 ± 3.3) × 10−10. We res aledthis value using µ/p magneti moment ratio of 3.183345137(85) from MOHR 08.2BAILEY 79 values re al ulated by HUGHES 99 using the COHEN 87 µ/p magneti moment. The improved MOHR 99 value does not hange the result.

(gµ+ − gµ−) / gaverage(gµ+ − gµ−) / gaverage(gµ+ − gµ−) / gaverage(gµ+ − gµ−) / gaverageA test of CPT invarian e.VALUE (units 10−8) DOCUMENT ID TECN−0.11±0.12−0.11±0.12−0.11±0.12−0.11±0.12 BENNETT 04 MUG2• • • We do not use the following data for averages, ts, limits, et . • • •−2.6 ±1.6 BAILEY 79 CNTR

µ ELECTRIC DIPOLE MOMENT (d)µ ELECTRIC DIPOLE MOMENT (d)µ ELECTRIC DIPOLE MOMENT (d)µ ELECTRIC DIPOLE MOMENT (d)A nonzero value is forbidden by both T invarian e and P invarian e.VALUE (10−19 e m) DOCUMENT ID TECN CHG COMMENT−0.1±0.9−0.1±0.9−0.1±0.9−0.1±0.9 1 BENNETT 09 MUG2 ± Storage ring• • • We do not use the following data for averages, ts, limits, et . • • •−0.1±1.0 BENNETT 09 MUG2 + Storage ring−0.1±0.7 BENNETT 09 MUG2 − Storage ring−3.7±3.4 2 BAILEY 78 CNTR ± Storage ring8.6±4.5 BAILEY 78 CNTR + Storage ring0.8±4.3 BAILEY 78 CNTR − Storage ring1This is the ombination of the two BENNETT 09 results quoted here separately for µ+and µ−. BENNETT 09 uses the onvention d = 1/2 · (d

µ−− dµ+ ).2This is the ombination of the two BAILEY 78 results quoted here separately for µ+ and

µ−. BAILEY 78 uses the onvention d = 1/2 · (dµ+− d

µ− ) and reports 3.7 ± 3.4. We onvert their result to use the same onvention as BENNETT 09.MUON-ELECTRON CHARGE RATIO ANOMALY qµ+/qe− + 1MUON-ELECTRON CHARGE RATIO ANOMALY qµ+/qe− + 1MUON-ELECTRON CHARGE RATIO ANOMALY qµ+/qe− + 1MUON-ELECTRON CHARGE RATIO ANOMALY qµ+/qe− + 1VALUE DOCUMENT ID TECN CHG COMMENT(1.1±2.1)× 10−9(1.1±2.1)× 10−9(1.1±2.1)× 10−9(1.1±2.1)× 10−9 1 MEYER 00 CNTR + 1s2s muoniuminterval1MEYER 00 measure the 1s2s muonium interval, and then interpret the result in termsof muon-ele tron harge ratio qµ+/qe− .

µ− DECAY MODESµ− DECAY MODESµ− DECAY MODESµ− DECAY MODESµ+ modes are harge onjugates of the modes below.Mode Fra tion (i /) Conden e level1 e−νe νµ ≈ 100%2 e−νe νµ γ [a (1.4±0.4) %3 e−νe νµ e+ e− [b (3.4±0.4)× 10−5Lepton Family number (LF ) violating modesLepton Family number (LF ) violating modesLepton Family number (LF ) violating modesLepton Family number (LF ) violating modes4 e−νe νµ LF [ < 1.2 % 90%5 e−γ LF < 5.7 × 10−13 90%6 e− e+ e− LF < 1.0 × 10−12 90%7 e−2γ LF < 7.2 × 10−11 90%[a This only in ludes events with the γ energy > 10 MeV. Sin e the e−νe νµand e−νe νµ γ modes annot be learly separated, we regard the lattermode as a subset of the former.[b See the Parti le Listings below for the energy limits used in this mea-surement.[ A test of additive vs. multipli ative lepton family number onservation.

µ− BRANCHING RATIOSµ− BRANCHING RATIOSµ− BRANCHING RATIOSµ− BRANCHING RATIOS(e− νe νµ γ)/total 2/(e− νe νµ γ)/total 2/(e− νe νµ γ)/total 2/(e− νe νµ γ)/total 2/VALUE EVTS DOCUMENT ID TECN COMMENT0.014 ±0.0040.014 ±0.0040.014 ±0.0040.014 ±0.004 CRITTENDEN 61 CNTR γ KE > 10 MeV

• • • We do not use the following data for averages, ts, limits, et . • • •862 BOGART 67 CNTR γ KE > 14.5 MeV0.0033±0.0013 CRITTENDEN 61 CNTR γ KE > 20 MeV27 ASHKIN 59 CNTR(e− νe νµ e+ e−)/total 3/(e− νe νµ e+ e−)/total 3/(e− νe νµ e+ e−)/total 3/(e− νe νµ e+ e−)/total 3/VALUE (units 10−5) EVTS DOCUMENT ID TECN CHG COMMENT3.4±0.2±0.33.4±0.2±0.33.4±0.2±0.33.4±0.2±0.3 7443 1 BERTL 85 SPEC + SINDRUM• • • We do not use the following data for averages, ts, limits, et . • • •2.2±1.5 7 2 CRITTENDEN 61 HLBC + E(e+e−) > 10 MeV2 1 3 GUREVICH 60 EMUL +1.5±1.0 3 4 LEE 59 HBC +1BERTL 85 has transverse momentum ut pT > 17 MeV/ . Systemati error wasin reased by us.2CRITTENDEN 61 ount only those de ays where total energy of either (e+, e−) om-bination is >10 MeV.3GUREVICH 60 interpret their event as either virtual or real photon onversion. e+ ande− energies not measured.4 In the three LEE 59 events, the sum of energies E(e+) + E(e−) + E(e+) was 51 MeV,55 MeV, and 33 MeV.

719719719719See key on page 601 Lepton Parti le Listingsµ(e− νe νµ

)/total 4/(e− νe νµ



)/total 4/Forbidden by the additive onservation law for lepton family number. A multipli ativelaw predi ts this bran hing ratio to be 1/2. For a review see NEMETHY 81.VALUE CL% DOCUMENT ID TECN CHG COMMENT< 0.012< 0.012< 0.012< 0.012 90 1 FREEDMAN 93 CNTR + ν os illation sear h• • • We do not use the following data for averages, ts, limits, et . • • •< 0.018 90 KRAKAUER 91B CALO +< 0.05 90 2 BERGSMA 83 CALO νµ e → µ− νe< 0.09 90 JONKER 80 CALO See BERGSMA 83−0.001±0.061 WILLIS 80 CNTR +0.13 ±0.15 BLIETSCHAU 78 HLBC ± Avg. of 4 values

< 0.25 90 EICHTEN 73 HLBC +1FREEDMAN 93 limit on νe observation is here interpreted as a limit on lepton familynumber violation.2BERGSMA 83 gives a limit on the inverse muon de ay ross-se tion ratio σ(νµ e− →µ− νe )/σ(νµ e− → µ− νe ), whi h is essentially equivalent to (e− νe νµ

)/total forsmall values like that quoted.(e− γ)/total 5/(e− γ)/total 5/(e− γ)/total 5/(e− γ)/total 5/Forbidden by lepton family number onservation.VALUE (units 10−11) CL% DOCUMENT ID TECN CHG COMMENT

< 0.057< 0.057< 0.057< 0.057 90 ADAM 13B SPEC + MEG at PSI• • • We do not use the following data for averages, ts, limits, et . • • •< 0.24 90 ADAM 11 SPEC + MEG at PSI< 2.8 90 ADAM 10 SPEC + MEG at PSI< 1.2 90 AHMED 02 SPEC + MEGA< 1.2 90 BROOKS 99 SPEC + LAMPF< 4.9 90 BOLTON 88 CBOX + LAMPF<100 90 AZUELOS 83 CNTR + TRIUMF< 17 90 KINNISON 82 SPEC + LAMPF<100 90 SCHAAF 80 ELEC + SIN(e− e+ e−)/total 6/(e− e+ e−)/total 6/(e− e+ e−)/total 6/(e− e+ e−)/total 6/Forbidden by lepton family number onservation.VALUE (units 10−12) CL% DOCUMENT ID TECN CHG COMMENT< 1.0< 1.0< 1.0< 1.0 90 1 BELLGARDT 88 SPEC + SINDRUM• • • We do not use the following data for averages, ts, limits, et . • • •< 36 90 BARANOV 91 SPEC + ARES< 35 90 BOLTON 88 CBOX + LAMPF< 2.4 90 1 BERTL 85 SPEC + SINDRUM<160 90 1 BERTL 84 SPEC + SINDRUM<130 90 1 BOLTON 84 CNTR LAMPF1These experiments assume a onstant matrix element.(e− 2γ)/total 7/(e− 2γ)/total 7/(e− 2γ)/total 7/(e− 2γ)/total 7/Forbidden by lepton family number onservation.VALUE (units 10−11) CL% DOCUMENT ID TECN CHG COMMENT< 7.2< 7.2< 7.2< 7.2 90 BOLTON 88 CBOX + LAMPF• • • We do not use the following data for averages, ts, limits, et . • • •< 840 90 1 AZUELOS 83 CNTR + TRIUMF<5000 90 2 BOWMAN 78 CNTR DEPOMMIER 77 data1AZUELOS 83 uses the phase spa e distribution of BOWMAN 78.2BOWMAN 78 assumes an intera tion Lagrangian lo al on the s ale of the inverse µmass. LIMIT ON µ− → e− CONVERSIONLIMIT ON µ− → e− CONVERSIONLIMIT ON µ− → e− CONVERSIONLIMIT ON µ− → e− CONVERSIONForbidden by lepton family number onservation.σ(µ− 32S → e− 32S) / σ(µ− 32S → νµ

32P∗)σ(µ− 32S → e− 32S) / σ(µ− 32S → νµ32P∗)σ(µ− 32S → e− 32S) / σ(µ− 32S → νµ32P∗)σ(µ− 32S → e− 32S) / σ(µ− 32S → νµ32P∗)VALUE CL% DOCUMENT ID TECN COMMENT

<7× 10−11<7× 10−11<7× 10−11<7× 10−11 90 BADERT... 80 STRC SIN• • • We do not use the following data for averages, ts, limits, et . • • •<4× 10−10 90 BADERT... 77 STRC SINσ(µ−Cu → e−Cu) / σ(µ−Cu → apture)σ(µ−Cu → e−Cu) / σ(µ−Cu → apture)σ(µ−Cu → e−Cu) / σ(µ−Cu → apture)σ(µ−Cu → e−Cu) / σ(µ−Cu → apture)VALUE CL% DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •<1.6× 10−8 90 BRYMAN 72 SPECσ(µ−Ti → e−Ti) / σ(µ−Ti → apture)σ(µ−Ti → e−Ti) / σ(µ−Ti → apture)σ(µ−Ti → e−Ti) / σ(µ−Ti → apture)σ(µ−Ti → e−Ti) / σ(µ−Ti → apture)VALUE CL% DOCUMENT ID TECN COMMENT<4.3× 10−12<4.3× 10−12<4.3× 10−12<4.3× 10−12 90 1 DOHMEN 93 SPEC SINDRUM II• • • We do not use the following data for averages, ts, limits, et . • • •<4.6× 10−12 90 AHMAD 88 TPC TRIUMF<1.6× 10−11 90 BRYMAN 85 TPC TRIUMF1DOHMEN 93 assumes µ− → e− onversion leaves the nu leus in its ground state, apro ess enhan ed by oheren e and expe ted to dominate.σ(µ−Pb → e−Pb) / σ(µ−Pb → apture)σ(µ−Pb → e−Pb) / σ(µ−Pb → apture)σ(µ−Pb → e−Pb) / σ(µ−Pb → apture)σ(µ−Pb → e−Pb) / σ(µ−Pb → apture)VALUE CL% DOCUMENT ID TECN COMMENT<4.6× 10−11<4.6× 10−11<4.6× 10−11<4.6× 10−11 90 HONECKER 96 SPEC SINDRUM II• • • We do not use the following data for averages, ts, limits, et . • • •<4.9× 10−10 90 AHMAD 88 TPC TRIUMF

σ(µ−Au → e−Au) / σ(µ−Au → apture)σ(µ−Au → e−Au) / σ(µ−Au → apture)σ(µ−Au → e−Au) / σ(µ−Au → apture)σ(µ−Au → e−Au) / σ(µ−Au → apture)VALUE CL% DOCUMENT ID TECN CHG COMMENT<7× 10−13<7× 10−13<7× 10−13<7× 10−13 90 BERTL 06 SPEC − SINDRUM IILIMIT ON µ− → e+ CONVERSIONLIMIT ON µ− → e+ CONVERSIONLIMIT ON µ− → e+ CONVERSIONLIMIT ON µ− → e+ CONVERSIONForbidden by total lepton number onservation.σ(µ− 32S → e+32Si∗) / σ(µ− 32S → νµ

32P∗)σ(µ− 32S → e+32Si∗) / σ(µ− 32S → νµ32P∗)σ(µ− 32S → e+32Si∗) / σ(µ− 32S → νµ32P∗)σ(µ− 32S → e+32Si∗) / σ(µ− 32S → νµ32P∗)VALUE CL% DOCUMENT ID TECN COMMENT

<9 × 10−10<9 × 10−10<9 × 10−10<9 × 10−10 90 BADERT... 80 STRC SIN• • • We do not use the following data for averages, ts, limits, et . • • •<1.5× 10−9 90 BADERT... 78 STRC SINσ(µ− 127I → e+127Sb∗) / σ(µ− 127I → anything)σ(µ− 127I → e+127Sb∗) / σ(µ− 127I → anything)σ(µ− 127I → e+127Sb∗) / σ(µ− 127I → anything)σ(µ− 127I → e+127Sb∗) / σ(µ− 127I → anything)VALUE CL% DOCUMENT ID TECN COMMENT<3× 10−10<3× 10−10<3× 10−10<3× 10−10 90 1 ABELA 80 CNTR Radio hemi al te h.1ABELA 80 is upper limit for µ− e+ onversion leading to parti le-stable states of 127Sb.Limit for total onversion rate is higher by a fa tor less than 4 (G. Ba kenstoss, private ommuni ation).σ(µ−Cu → e+Co) / σ(µ−Cu → νµNi)σ(µ−Cu → e+Co) / σ(µ−Cu → νµNi)σ(µ−Cu → e+Co) / σ(µ−Cu → νµNi)σ(µ−Cu → e+Co) / σ(µ−Cu → νµNi)VALUE CL% DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •<2.6× 10−8 90 BRYMAN 72 SPEC<2.2× 10−7 90 CONFORTO 62 OSPKσ(µ−Ti → e+Ca) / σ(µ−Ti → apture)σ(µ−Ti → e+Ca) / σ(µ−Ti → apture)σ(µ−Ti → e+Ca) / σ(µ−Ti → apture)σ(µ−Ti → e+Ca) / σ(µ−Ti → apture)VALUE CL% EVTS DOCUMENT ID TECN CHG COMMENT<3.6× 10−11<3.6× 10−11<3.6× 10−11<3.6× 10−11 90 1 1,2 KAULARD 98 SPEC − SINDRUM II• • • We do not use the following data for averages, ts, limits, et . • • •<1.7× 10−12 90 1 2,3 KAULARD 98 SPEC − SINDRUM II<4.3× 10−12 90 3 DOHMEN 93 SPEC SINDRUM II<8.9× 10−11 90 1 DOHMEN 93 SPEC SINDRUM II<1.7× 10−10 90 4 AHMAD 88 TPC TRIUMF1This limit assumes a giant resonan e ex itation of the daughter Ca nu leus (mean energyand width both 20 MeV).2KAULARD 98 obtained these same limits using the unied lassi al analysis of FELD-MAN 98.3This limit assumes the daughter Ca nu leus is left in the ground state. However, theprobability of this is unknown.4Assuming a giant-resonan e-ex itation model.LIMIT ON MUONIUM → ANTIMUONIUM CONVERSIONLIMIT ON MUONIUM → ANTIMUONIUM CONVERSIONLIMIT ON MUONIUM → ANTIMUONIUM CONVERSIONLIMIT ON MUONIUM → ANTIMUONIUM CONVERSIONForbidden by lepton family number onservation.Rg = GC / GFRg = GC / GFRg = GC / GFRg = GC / GFThe ee tive Lagrangian for the µ+ e− → µ− e+ onversion is assumed to be

L = 2−1/2 GC [ψµγλ (1 − γ5) ψe [ψµγλ (1 − γ5) ψe + h. .The experimental result is then an upper limit on GC /GF , where GF is the Fermi oupling onstant.VALUE CL% EVTS DOCUMENT ID TECN CHG COMMENT< 0.0030< 0.0030< 0.0030< 0.0030 90 1 1 WILLMANN 99 SPEC + µ+ at 26 GeV/ • • • We do not use the following data for averages, ts, limits, et . • • •< 0.14 90 1 2 GORDEEV 97 SPEC + JINR phasotron< 0.018 90 0 3 ABELA 96 SPEC + µ+ at 24 MeV< 6.9 90 NI 93 CBOX LAMPF< 0.16 90 MATTHIAS 91 SPEC LAMPF< 0.29 90 HUBER 90B CNTR TRIUMF<20 95 BEER 86 CNTR TRIUMF<42 95 MARSHALL 82 CNTR1WILLMANN 99 quote both probability PMM < 8.3× 10−11 at 90%CL in a 0.1 T eldand Rg= GC /GF .2GORDEEV 97 quote limits on both f=GMM/GF and the probability WMM < 4.7 ×10−7 (90% CL).3ABELA 96 quote both probability PMM < 8× 10−9 at 90% CL and Rg = GC /GF .MUON DECAY PARAMETERS

Revised September 2013 by W. Fetscher and H.-J. Gerber (ETHZurich).

Introduction: All measurements in direct muon decay, µ− →e− + 2 neutrals, and its inverse, νµ + e− → µ− + neutral, are

successfully described by the “V -A interaction,” which is a par-

ticular case of a local, derivative-free, lepton-number-conserving,


four-fermion interaction [1]. As shown below, within this frame-

work, the Standard Model assumptions, such as the V -A form

and the nature of the neutrals (νµ and νe), and hence the dou-

blet assignments (νe e−)L and (νµ µ−)L, have been determined

from experiments [2,3]. All considerations on muon decay are

valid for the leptonic tau decays τ → ℓ + ντ + νe with the

replacements mµ → mτ , me → mℓ.

Parameters: The differential decay probability to obtain an

e± with (reduced) energy between x and x + dx, emitted in the

direction x3 at an angle between ϑ and ϑ + dϑ with respect

to the muon polarization vector P µ, and with its spin parallel

to the arbitrary direction ζ, neglecting radiative corrections, is

given by

d2Γ

dx d cos ϑ=

mµ

4π3W 4

eµ G2F

√x2 − x2

0

× (FIS(x) ± Pµ cos ϑ FAS(x))

×[1 + ζ · P e(x, ϑ)

]. (1)

Here, Weµ = max(Ee) = (m2µ + m2

e)/2mµ is the maximum e±

energy, x = Ee/Weµ is the reduced energy, x0 = me/Weµ =

9.67 × 10−3, and Pµ = |P µ| is the degree of muon polarization.

ζ is the direction in which a perfect polarization-sensitive

electron detector is most sensitive. The isotropic part of the

spectrum, FIS(x), the anisotropic part FAS(x), and the electron

polarization, P e(x, ϑ), may be parametrized by the Michel

parameter ρ [1], by η [4], by ξ and δ [5,6], etc. These are

bilinear combinations of the coupling constants gγεµ, which occur

in the matrix element (given below).

If the masses of the neutrinos as well as x20 are neglected,

the energy and angular distribution of the electron in the rest

frame of a muon (µ±) measured by a polarization insensitive

detector, is given by

d2Γ

dx d cos ϑ∼ x2 ·

3(1 − x) +

2ρ

3(4x − 3) + 3η x0(1 − x)/x

± Pµ · ξ · cos ϑ

[1 − x +

2δ

3(4x − 3)

]. (2)

Here, ϑ is the angle between the electron momentum and the

muon spin, and x ≡ 2Ee/mµ. For the Standard Model coupling,

we obtain ρ = ξδ = 3/4, ξ = 1, η = 0 and the differential decay

rate is

d2Γ

dx d cos ϑ=

G2Fm5

µ

192π3[3 − 2x ± Pµ cos ϑ(2x − 1)] x2 . (3)

The coefficient in front of the square bracket is the total decay

rate.

If only the neutrino masses are neglected, and if the e±

polarization is detected, then the functions in Eq. (1) become

FIS(x) = x(1 − x) + 29

ρ(4x2 − 3x − x20) + η · x0(1 − x)

FAS(x) = 13ξ

√x2 − x2

0

× [1 − x + 23δ(4x − 3 + (

√1 − x2

0 − 1))]

P e(x, ϑ) = PT1· x1 + PT2

· x2 + PL · x3 . (4)

Here x1, x2, and x3 are orthogonal unit vectors defined as

follows:

x3 is along the e momentum pe

x3 × P µ

|x2 × P µ|= x2 is transverse to pe and perpendicular

to the “decay plane”x2 × x3 = x1 is transverse to the pe and in the

“decay plane.”

The components of P e then are given by

PT1(x, ϑ) = Pµ sin ϑ · FT1

(x)/ (FIS(x) ± Pµ cos ϑ · FAS(x))

PT2(x, ϑ) = Pµ sin ϑ · FT2

(x)/ (FIS(x) ± Pµ cos ϑ · FAS(x))

PL(x, ϑ) =(±FIP(x) + Pµ cos ϑ

× FAP(x))/ (FIS(x) ± Pµ cos ϑ · FAS(x)) ,

where

FT1(x) = 1

12

−2

[ξ′′ + 12(ρ − 3

4)](1 − x)x0

−3η(x2 − x20) + η′′(−3x2 + 4x − x2

0)

FT2(x) = 1

3

√x2 − x2

0

3α′

A(1 − x) + 2

β′

A

√1 − x2

0

FIP(x) = 154

√x2 − x2

0

9ξ′

(−2x + 2 +

√1 − x2

0

)

+ 4ξ(δ − 34)(4x − 4 +

√1 − x2

0)

FAP(x) = 16

ξ′′(2x2 − x − x2

0) + 4(ρ − 34)(4x2 − 3x − x2

0

)

+2η′′(1 − x)x0

. (5)

For the experimental values of the parameters ρ, ξ, ξ ′, ξ′′, δ,

η, η′′, α/A, β/A, α′/A, β′/A, which are not all independent,

see the Data Listings below. Experiments in the past have also

been analyzed using the parameters a, b, c, a′, b′, c′, α/A, β/A,

α′/A, β′/A (and η = (α − 2β)/2A), as defined by Kinoshita

and Sirlin [5,6]. They serve as a model-independent summary

of all possible measurements on the decay electron (see Listings

below). The relations between the two sets of parameters are

ρ − 34

= 34(−a + 2c)/A ,

η = (α − 2β)/A ,

η ′′ = (3α + 2β)/A ,

δ − 34

= 94

· (a′ − 2c′)/A

1 − [a + 3a′ + 4(b + b′) + 6c − 14c′]/A,

1 − ξδ

ρ= 4

[(b + b′) + 2(c − c′)]/A

1 − (a − 2c)/A,

1 − ξ′ = [(a + a′) + 4(b + b′) + 6(c + c′)]/A ,

1 − ξ ′′ = (−2a + 20c)/A ,

where

A = a + 4b + 6c . (6)

The differential decay probability to obtain a left-handed νe with

(reduced) energy between y and y + dy, neglecting radiative

721721721721See key on page 601 Lepton Parti le Listingsµ

corrections as well as the masses of the electron and of the

neutrinos, is given by [7]

dΓ

dy=

m5µ G2

F

16π3· Qνe

L · y2

(1 − y) − ωL · (y − 34)

. (7)

Here, y = 2 Eνe/mµ. Qνe

L and ωL are parameters. ωL is the

neutrino analog of the spectral shape parameter ρ of Michel.

Since in the Standard Model, Qνe

L = 1, ωL = 0, the measure-

ment of dΓ/dy has allowed a null-test of the Standard Model

(see Listings below).

Matrix element: All results in direct muon decay (energy

spectra of the electron and of the neutrinos, polarizations,

and angular distributions), and in inverse muon decay (the

reaction cross section) at energies well below mW c2, may be

parametrized in terms of amplitudes gγεµ and the Fermi coupling

constant GF , using the matrix element

4GF√2

∑

γ=S,V,Tε,µ=R,L

gγεµ〈eε|Γγ |(νe)n〉〈(νµ)m|Γγ |µµ〉. (8)

We use the notation of Fetscher et al. [2], who in turn use the

sign conventions and definitions of Scheck [8]. Here, γ = S, V, T

indicates a scalar, vector, or tensor interaction; and ε, µ = R, L

indicate a right- or left-handed chirality of the electron or muon.

The chiralities n and m of the νe and νµ are then determined

by the values of γ, ε, and µ. The particles are represented by

fields of definite chirality [9].

As shown by Langacker and London [10], explicit lepton-

number nonconservation still leads to a matrix element equiv-

alent to Eq. (8). They conclude that it is not possible, even in

principle, to test lepton-number conservation in (leptonic) muon

decay if the final neutrinos are massless and are not observed.

The ten complex amplitudes gγεµ (gT

RR and gTLL are identi-

cally zero) and GF constitute 19 independent (real) parameters

to be determined by experiment. The Standard Model interac-

tion corresponds to one single amplitude gVLL being unity and

all the others being zero.

The (direct) muon decay experiments are compatible with

an arbitrary mix of the scalar and vector amplitudes gSLL and

gVLL – in the extreme even with purely scalar gS

LL = 2, gVLL = 0.

The decision in favour of the Standard Model comes from the

quantitative observation of inverse muon decay, which would be

forbidden for pure gSLL [2].

Experimental determination of V –A: In order to deter-

mine the amplitudes gγεµ uniquely from experiment, the fol-

lowing set of equations, where the left-hand sides represent

experimental results, has to be solved.

a = 16(|gVRL|2 + |gV

LR|2) + |gSRL + 6gT

RL|2 + |gSLR + 6gT

LR|2

a′ = 16(|gVRL|2 − |gV

LR|2) + |gSRL + 6gT

RL|2 − |gSLR + 6gT

LR|2

α = 8Re

gVRL(gS∗

LR + 6gT∗LR) + gV

LR(gS∗RL + 6gT∗

RL)

α′ = 8ImgVLR(gS∗

RL + 6gT∗RL) − gV

RL(gS∗LR + 6gT∗

LR)

b = 4(|gVRR|2 + |gV

LL|2) + |gSRR|2 + |gS

LL|2

b′ = 4(|gVRR|2 − |gV

LL|2) + |gSRR|2 − |gS

LL|2

β = −4RegVRRgS∗

LL + gVLLgS∗

RR

β′ = 4ImgVRRgS∗

LL − gVLLgS∗

RR

c = 12

|gS

RL − 2gTRL|2 + |gS

LR − 2gTLR|2

c′ = 12

|gS

RL − 2gTRL|2 − |gS

LR − 2gTLR|2

and

Qνe

L = 1 −

14|gS

LR|2 + 14|gS

LL|2 + |gVRR|2 + |gV

RL|2 + 3|gTLR|2

ωL = 34

|gSRR|2 + 4|gV

LR|2 + |gSRL + 2gT

RL|2|gS

RL|2 + |gSRR|2 + 4|gV

LL|2 + 4|gVLR|2 + 12|gT

RL|2.

It has been noted earlier by C. Jarlskog [11], that certain exper-

iments observing the decay electron are especially informative

if they yield the V -A values. The complete solution is now

found as follows. Fetscher et al. [2] introduced four probabilities

Qεµ(ε, µ = R, L) for the decay of a µ-handed muon into an

ε-handed electron, and showed that there exist upper bounds

on QRR, QLR, and QRL, and a lower bound on QLL. These

probabilities are given in terms of the gγεµ’s by

Qεµ = 14|gS

εµ|2 + |gVεµ|2 + 3(1 − δεµ)|gT

εµ|2 , (9)

where δεµ = 1 for ε = µ, and δεµ = 0 for ε 6= µ. They are

related to the parameters a, b, c, a′, b′, and c′ by

QRR = 2(b + b′)/A ,

QLR = [(a − a′) + 6(c − c′)]/2A ,

QRL = [(a + a′) + 6(c + c′)]/2A ,

QLL = 2(b − b′)/A , (10)

with A = 16. In the Standard Model, QLL = 1 and the others

are zero.

Since the upper bounds on QRR, QLR, and QRL are found

to be small, and since the helicity of the νµ in pion decay is

known from experiment [12,13] to very high precision to be

−1 [14], the cross section S of inverse muon decay, normalized

to the V -A value, yields [2]

|gSLL|2 ≤ 4(1 − S) (11)

and

|gVLL|2 = S . (12)

Thus the Standard Model assumption of a pure V -A leptonic

charged weak interaction of e and µ is derived (within errors)

from experiments at energies far below mass of the W±: Eq. (12)

gives a lower limit for V -A, and Eqs. (9) and (11) give upper

limits for the other four-fermion interactions. The existence of

such upper limits may also be seen from QRR+QRL = (1−ξ′)/2

and QRR + QLR = 12(1 + ξ/3 − 16 ξδ/9). Table 1 gives the

current experimental limits on the magnitudes of the gγεµ’s.

More stringent limits on the six coupling constants gSLR, gV

LR,

722722722722LeptonParti le Listingsµ

gTLR, gS

RL, gVRL, and gT

RL have been derived from upper limits

on the neutrino mass [18]. Limits on the “charge retention”

coordinates, as used in the older literature (e.g., Ref. 19), are

given by Burkard et al. [20].

Table 1. Coupling constants gγεµ and some combina-

tions of them. Ninety-percent confidence level experi-mental limits. The limits on |gS

LL| and |gVLL| are from

Ref. 15, and the others from a general analysis ofmuon decay measurements. Top three rows: Ref. 22,fourth row: Ref. 16, next three rows: Ref. 17, last row:Ref. 21. The experimental uncertainty on the muonpolarization in pion decay is included. Note that, bydefinition, |gS

εµ| ≤ 2, |gVεµ| ≤ 1 and |gT

εµ| ≤ 1/√

3.

|gSRR| < 0.035 |gV

RR| < 0.017 |gTRR| ≡ 0

|gSLR| < 0.050 |gV

LR| < 0.023 |gTLR| < 0.015

|gSRL| < 0.420 |gV

RL| < 0.105 |gTRL| < 0.105

|gSLL| < 0.550 |gV

LL| > 0.960 |gTLL| ≡ 0

|gSLR + 6gT

LR| < 0.143 |gSRL + 6gT

RL| < 0.418

|gSLR + 2gT

LR| < 0.108 |gSRL + 2gT

RL| < 0.417

|gSLR − 2gT

LR| < 0.070 |gSRL − 2gT

RL| < 0.418

QRR + QLR < 8.2 × 10−4

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21. R. Bayes et al., Phys. Rev. Lett. 106, 041804 (2011).

22. A. Hillairet et al., Phys. Rev. D85, 092013 (2012).

µ DECAY PARAMETERSµ DECAY PARAMETERSµ DECAY PARAMETERSµ DECAY PARAMETERSρ PARAMETERρ PARAMETERρ PARAMETERρ PARAMETER(V−A) theory predi ts ρ = 0.75.VALUE EVTS DOCUMENT ID TECN CHG COMMENT0.74979±0.00026 OUR AVERAGE0.74979±0.00026 OUR AVERAGE0.74979±0.00026 OUR AVERAGE0.74979±0.00026 OUR AVERAGE0.74977±0.00012±0.00023 1 BAYES 11 TWST + Surfa e µ+0.7518 ±0.0026 DERENZO 69 RVUE• • • We do not use the following data for averages, ts, limits, et . • • •0.75014±0.00017±0.00045 2 MACDONALD 08 TWST + Surfa e µ+0.75080±0.00032±0.00100 6G 3 MUSSER 05 TWST + Surfa e µ+0.72 ±0.06 ±0.08 AMORUSO 04 ICAR Liquid Ar TPC0.762 ±0.008 170k 4 FRYBERGER 68 ASPK + 2553 MeV e+0.760 ±0.009 280k 4 SHERWOOD 67 ASPK + 2553 MeV e+0.7503 ±0.0026 800k 4 PEOPLES 66 ASPK + 2053 MeV e+1The quoted systemati error in ludes a ontribution of 0.00013 (added in quadrature)from un ertainties on radiative orre tions and on the Mi hel parameter η.2The quoted systemati error in ludes a ontribution of 0.00011 (added in quadrature)from the dependen e on the Mi hel parameter η.3The quoted systemati error in ludes a ontribution of 0.00023 (added in quadrature)from the dependen e on the Mi hel parameter η.4 η onstrained = 0. These values in orporated into a two parameter t to ρ and η byDERENZO 69.η PARAMETERη PARAMETERη PARAMETERη PARAMETER(V−A) theory predi ts η = 0.VALUE EVTS DOCUMENT ID TECN CHG COMMENT0.057 ±0.034 OUR AVERAGE0.057 ±0.034 OUR AVERAGE0.057 ±0.034 OUR AVERAGE0.057 ±0.034 OUR AVERAGE0.071 ±0.037 ±0.005 30M DANNEBERG 05 CNTR + 753 MeV e+0.011 ±0.081 ±0.026 5.3M 1 BURKARD 85BCNTR + 953 MeV e+−0.12 ±0.21 6346 DERENZO 69 HBC + 1.66.8 MeV e+• • • We do not use the following data for averages, ts, limits, et . • • •−0.0021±0.0070±0.0010 30M 2 DANNEBERG 05 CNTR + 753 MeV e+−0.012 ±0.015 ±0.003 5.3M 2 BURKARD 85BCNTR + 953 MeV e+−0.007 ±0.013 5.3M 3 BURKARD 85BFIT + 953 MeV e+−0.7 ±0.5 170k 4 FRYBERGER 68 ASPK + 2553 MeV e+−0.7 ±0.6 280k 4 SHERWOOD 67 ASPK + 2553 MeV e+0.05 ±0.5 800k 4 PEOPLES 66 ASPK + 2053 MeV e+−2.0 ±0.9 9213 5 PLANO 60 HBC + Whole spe trum1Previously we used the global t result from BURKARD 85B in OUR AVERAGE, we nowonly in lude their a tual measurement.2α = α′ = 0 assumed.3Global t to all measured parameters. The t orrelation oeÆ ients are given inBURKARD 85B.4 ρ onstrained = 0.75.5Two parameter t to ρ and η; PLANO 60 dis ounts value for η.δ PARAMETERδ PARAMETERδ PARAMETERδ PARAMETER(V−A) theory predi ts δ = 0.75.VALUE EVTS DOCUMENT ID TECN CHG COMMENT0.75047±0.00034 OUR AVERAGE0.75047±0.00034 OUR AVERAGE0.75047±0.00034 OUR AVERAGE0.75047±0.00034 OUR AVERAGE0.75049±0.00021±0.00027 1 BAYES 11 TWST + Surfa e µ+0.7486 ±0.0026 ±0.0028 2 BALKE 88 SPEC + Surfa e µ+• • • We do not use the following data for averages, ts, limits, et . • • •0.75067±0.00030±0.00067 MACDONALD 08 TWST + Surfa e µ+0.74964±0.00066±0.00112 6G GAPONENKO 05 TWST + Surfa e µ+3 VOSSLER 690.752 ±0.009 490k FRYBERGER 68 ASPK + 2553 MeV e+0.782 ±0.031 KRUGER 610.78 ±0.05 8354 PLANO 60 HBC + Whole spe trum1The quoted systemati error in ludes a ontribution of 0.00006 (added in quadrature)from un ertainties on radiative orre tions and on the Mi hel parameter η.2BALKE 88 uses ρ = 0.752 ± 0.003.3VOSSLER 69 has measured the asymmetry below 10 MeV. See omments about radiative orre tions in VOSSLER 69.∣∣(ξ PARAMETER)×(µ LONGITUDINAL POLARIZATION)∣∣∣∣(ξ PARAMETER)×(µ LONGITUDINAL POLARIZATION)∣∣∣∣(ξ PARAMETER)×(µ LONGITUDINAL POLARIZATION)∣∣∣∣(ξ PARAMETER)×(µ LONGITUDINAL POLARIZATION)∣∣(V−A) theory predi ts ξ = 1, longitudinal polarization = 1.VALUE DOCUMENT ID TECN CHG COMMENT1.0009 +0.0016

−0.0007 OUR AVERAGE1.0009 +0.0016−0.0007 OUR AVERAGE1.0009 +0.0016−0.0007 OUR AVERAGE1.0009 +0.0016−0.0007 OUR AVERAGE1.00084±0.00029+0.00165

−0.00063 BUENO 11 TWST Surfa e µ+ beam1.0027 ±0.0079 ±0.0030 BELTRAMI 87 CNTR SIN, π de ay in ight• • • We do not use the following data for averages, ts, limits, et . • • •1.0003 ±0.0006 ±0.0038 JAMIESON 06 TWST + surfa e µ+ beam1.0013 ±0.0030 ±0.0053 1 IMAZATO 92 SPEC + K+ → µ+ νµ0.975 ±0.015 AKHMANOV 68 EMUL 140 kG0.975 ±0.030 GUREVICH 64 EMUL See AKHMANOV 680.903 ±0.027 2 ALI-ZADE 61 EMUL + 27 kG0.93 ±0.06 PLANO 60 HBC + 8.8 kG0.97 ±0.05 BARDON 59 CNTR Bromoform target1The orresponding 90% onden e limit from IMAZATO 92 is ∣∣ξPµ

∣∣ > 0.990. Thismeasurement is of K+ de ay, not π+ de ay, so we do not in lude it in an average, nordo we yet set up a separate data blo k for K results.2Depolarization by medium not known suÆ iently well.

723723723723See key on page 601 LeptonParti le Listingsµ

ξ × (µ LONGITUDINAL POLARIZATION) × δ / ρξ × (µ LONGITUDINAL POLARIZATION) × δ / ρξ × (µ LONGITUDINAL POLARIZATION) × δ / ρξ × (µ LONGITUDINAL POLARIZATION) × δ / ρVALUE CL% DOCUMENT ID TECN CHG COMMENT1.00179+0.00156−0.000711.00179+0.00156−0.000711.00179+0.00156−0.000711.00179+0.00156−0.00071 1 BAYES 11 TWST + Surfa e µ+ beam

• • • We do not use the following data for averages, ts, limits, et . • • •>0.99682 90 2 JODIDIO 86 SPEC + TRIUMF>0.9966 90 3 STOKER 85 SPEC + µ-spin rotation>0.9959 90 CARR 83 SPEC + 11 kG1BAYES 11 obtains the limit > 0.99909 (90% CL) with the onstraint that ξ×(µ LON-GITUDINAL POLARIZATION)× δ/ρ ≤ 1.0.2 JODIDIO 86 in ludes data from CARR 83 and STOKER 85. The value here is from theerratum.3 STOKER 85 nd (ξPµδ/ρ) >0.9955 and >0.9966, where the rst limit is from new µspin-rotation data and the se ond is from ombination with CARR 83 data. In V−Atheory, (δ/ρ) = 1.0.ξ′ = LONGITUDINAL POLARIZATION OF e+ξ′ = LONGITUDINAL POLARIZATION OF e+ξ′ = LONGITUDINAL POLARIZATION OF e+ξ′ = LONGITUDINAL POLARIZATION OF e+(V−A) theory predi ts the longitudinal polarization = ±1 for e±, respe tively. Wehave ipped the sign for e− so our programs an average.VALUE EVTS DOCUMENT ID TECN CHG COMMENT1.00 ±0.04 OUR AVERAGE1.00 ±0.04 OUR AVERAGE1.00 ±0.04 OUR AVERAGE1.00 ±0.04 OUR AVERAGE0.998±0.045 1M BURKARD 85 CNTR + Bhabha + annihil0.89 ±0.28 29k SCHWARTZ 67 OSPK − Moller s attering0.94 ±0.38 BLOOM 64 CNTR + Brems. transmiss.1.04 ±0.18 DUCLOS 64 CNTR + Bhabha s attering1.05 ±0.30 BUHLER 63 CNTR + Annihilationξ′′ PARAMETERξ′′ PARAMETERξ′′ PARAMETERξ′′ PARAMETERVALUE EVTS DOCUMENT ID TECN CHG COMMENT0.98 ±0.04 OUR AVERAGE0.98 ±0.04 OUR AVERAGE0.98 ±0.04 OUR AVERAGE0.98 ±0.04 OUR AVERAGE0.981±0.045±0.003 3.87M PRIEELS 14 CNTR + Bhabha + annihil0.65 ±0.36 326k 1 BURKARD 85 CNTR + Bhabha + annihil1BURKARD 85 measure (ξ′′-ξξ′)/ξ and ξ′ and set ξ = 1.TRANSVERSE e+ POLARIZATION IN PLANE OF µ SPIN, e+ MOMEN-TUMTRANSVERSE e+ POLARIZATION IN PLANE OF µ SPIN, e+ MOMEN-TUMTRANSVERSE e+ POLARIZATION IN PLANE OF µ SPIN, e+ MOMEN-TUMTRANSVERSE e+ POLARIZATION IN PLANE OF µ SPIN, e+ MOMEN-TUMVALUE (units 10−3) EVTS DOCUMENT ID TECN CHG COMMENT7 ± 8 OUR AVERAGE7 ± 8 OUR AVERAGE7 ± 8 OUR AVERAGE7 ± 8 OUR AVERAGE6.3± 7.7± 3.4 30M DANNEBERG 05 CNTR + 753 MeV e+16 ±21 ±10 5.3M BURKARD 85B CNTR + Annihil 953 MeVTRANSVERSE e+ POLARIZATION NORMAL TO PLANE OF µ SPIN, e+MOMENTUMTRANSVERSE e+ POLARIZATION NORMAL TO PLANE OF µ SPIN, e+MOMENTUMTRANSVERSE e+ POLARIZATION NORMAL TO PLANE OF µ SPIN, e+MOMENTUMTRANSVERSE e+ POLARIZATION NORMAL TO PLANE OF µ SPIN, e+MOMENTUMZero if T invarian e holds.VALUE (units 10−3) EVTS DOCUMENT ID TECN CHG COMMENT−2 ± 8 OUR AVERAGE−2 ± 8 OUR AVERAGE−2 ± 8 OUR AVERAGE−2 ± 8 OUR AVERAGE−3.7± 7.7±3.4 30M DANNEBERG 05 CNTR + 753 MeV e+7 ±22 ±7 5.3M BURKARD 85B CNTR + Annihil 953 MeVα/Aα/Aα/Aα/AVALUE (units 10−3) EVTS DOCUMENT ID TECN CHG COMMENT0.4± 4.30.4± 4.30.4± 4.30.4± 4.3 1 BURKARD 85B FIT• • • We do not use the following data for averages, ts, limits, et . • • •15 ±50 ±14 5.3M BURKARD 85B CNTR + 953 MeV e+1Global t to all measured parameters. Correlation oeÆ ients are given inBURKARD 85B.α′/Aα′/Aα′/Aα′/AZero if T invarian e holds.VALUE (units 10−3) EVTS DOCUMENT ID TECN CHG COMMENT−10 ±20 OUR AVERAGE−10 ±20 OUR AVERAGE−10 ±20 OUR AVERAGE−10 ±20 OUR AVERAGE− 3.4±21.3± 4.9 30M DANNEBERG 05 CNTR + 753 MeV e+−47 ±50 ±14 5.3M 1 BURKARD 85B CNTR + 953 MeV e+• • • We do not use the following data for averages, ts, limits, et . • • •− 0.2± 4.3 2 BURKARD 85B FIT1Previously we used the global t result from BURKARD 85B in OUR AVERAGE, we nowonly in lude their a tual measurement. BURKARD 85B measure e+ polarizations PT 1and PT 2 versus e+ energy.2Global t to all measured parameters. The t orrelation oeÆ ients are given inBURKARD 85B.β/Aβ/Aβ/Aβ/AVALUE (units 10−3) EVTS DOCUMENT ID TECN CHG COMMENT3.9± 6.23.9± 6.23.9± 6.23.9± 6.2 1 BURKARD 85B FIT• • • We do not use the following data for averages, ts, limits, et . • • •2 ±17 ±6 5.3M BURKARD 85B CNTR + 953 MeV e+1Global t to all measured parameters. The t orrelation oeÆ ients are given inBURKARD 85B.

β′/Aβ′/Aβ′/Aβ′/AZero if T invarian e holds.VALUE (units 10−3) EVTS DOCUMENT ID TECN CHG COMMENT2 ± 7 OUR AVERAGE2 ± 7 OUR AVERAGE2 ± 7 OUR AVERAGE2 ± 7 OUR AVERAGE− 0.5± 7.8±1.8 30M DANNEBERG 05 CNTR + 753 MeV e+17 ±17 ±6 5.3M 1 BURKARD 85B CNTR + 953 MeV e+• • • We do not use the following data for averages, ts, limits, et . • • •− 1.3± 3.5±0.6 30M 2 DANNEBERG 05 CNTR + 753 MeV e+1.5± 6.3 3 BURKARD 85B FIT1Previously we used the global t result from BURKARD 85B in OUR AVERAGE, we nowonly in lude their a tual measurement. BURKARD 85B measure e+ polarizations PT 1and PT 2 versus e+ energy.2α = α′ = 0 assumed.3Global t to all measured parameters. The t orrelation oeÆ ients are given inBURKARD 85B.a/Aa/Aa/Aa/A This omes from an alternative parameterization to that used in the Summary Table(see the \Note on Muon De ay Parameters" above).VALUE (units 10−3) CL% DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •<15.9 90 1 BURKARD 85B FIT1Global t to all measured parameters. Correlation oeÆ ients are given inBURKARD 85B.a′/Aa′/Aa′/Aa′/A This omes from an alternative parameterization to that used in the Summary Table(see the \Note on Muon De ay Parameters" above).VALUE (units 10−3) DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •5.3±4.1 1 BURKARD 85B FIT1Global t to all measured parameters. Correlation oeÆ ients are given inBURKARD 85B.(b′+b)/A(b′+b)/A(b′+b)/A(b′+b)/AThis omes from an alternative parameterization to that used in the Summary Table(see the \Note on Muon De ay Parameters" above).VALUE (units 10−3) CL% DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •<1.04 90 1 BURKARD 85B FIT1Global t to all measured parameters. Correlation oeÆ ients are given inBURKARD 85B. /A /A /A /A This omes from an alternative parameterization to that used in the Summary Table(see the \Note on Muon De ay Parameters" above).VALUE (units 10−3) CL% DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •<6.4 90 1 BURKARD 85B FIT1Global t to all measured parameters. Correlation oeÆ ients are given inBURKARD 85B. ′/A ′/A ′/A ′/A This omes from an alternative parameterization to that used in the Summary Table(see the \Note on Muon De ay Parameters" above).VALUE (units 10−3) DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •3.5±2.0 1 BURKARD 85B FIT1Global t to all measured parameters. Correlation oeÆ ients are given inBURKARD 85B.η PARAMETERη PARAMETERη PARAMETERη PARAMETER(V−A) theory predi ts η = 0. η ae ts spe trum of radiative muon de ay.VALUE DOCUMENT ID TECN CHG COMMENT0.02 ±0.08 OUR AVERAGE0.02 ±0.08 OUR AVERAGE0.02 ±0.08 OUR AVERAGE0.02 ±0.08 OUR AVERAGE−0.014±0.090 EICHENBER... 84 ELEC + ρ free+0.09 ±0.14 BOGART 67 CNTR +• • • We do not use the following data for averages, ts, limits, et . • • •−0.035±0.098 EICHENBER... 84 ELEC + ρ=0.75 assumed

µ REFERENCESµ REFERENCESµ REFERENCESµ REFERENCESMOHR 16 arXiv:1507.07956 P.J. Mohr, D.B. Newell, B.N. Taylor (NIST)A epted for publi ation in RMPPRIEELS 14 PR D90 112003 R. Prieels et al. (LOUV, ETH, PSI+)ADAM 13B PRL 110 201801 J. Adam et al. (MEG Collab.)TISHCHENKO 13 PR D87 052003 V. Tish henko et al. (MuLan Collab.)MOHR 12 RMP 84 1527 P.J. Mohr, B.N. Taylor, D.B. Newell (NIST)ADAM 11 PRL 107 171801 J. Adam et al. (MEG Collab.)BAYES 11 PRL 106 041804 R. Bayes et al. (TWIST Collab.)Also PR D85 092013 A. Hillairet et al. (TWIST Collab.)BUENO 11 PR D84 032005 J.F. Bueno et al. (TWIST Collab.)Also PR D85 039908 (errat.) J.F. Bueno et al. (TWIST Collab.)WEBBER 11 PRL 106 041803 D.M. Webber et al. (MuLan Collab.)Also PRL 106 079901 (errat.) D.M. Webber et al. (MuLan Collab.)ADAM 10 NP B834 1 J. Adam et al. (MEG Collab.)BENNETT 09 PR D80 052008 G.W. Bennett et al. (MUG-2 Collab.)BARCZYK 08 PL B663 172 A. Bar zyk et al. (FAST Collab.)MACDONALD 08 PR D78 032010 R.P. Ma Donald et al. (TWIST Collab.)

724724724724LeptonParti le Listingsµ, τMOHR 08 RMP 80 633 P.J. Mohr, B.N. Taylor, D.B. Newell (NIST)CHITWOOD 07 PRL 99 032001 D.B. Chitwood et al. (MULAN Collab.)BENNETT 06 PR D73 072003 G.W. Bennett et al. (MUG-2 Collab.)BERTL 06 EPJ C47 337 W. Bertl et al. (SINDRUM II Collab.)JAMIESON 06 PR D74 072007 B. Jamieson et al. (TWIST Collab.)DANNEBERG 05 PRL 94 021802 N. Danneberg et al. (ETH, JAGL, PSI+)GAPONENKO 05 PR D71 071101 A. Gaponenko et al. (TWIST Collab.)MOHR 05 RMP 77 1 P.J. Mohr, B.N. Taylor (NIST)MUSSER 05 PRL 94 101805 J.R. Musser et al. (TWIST Collab.)AMORUSO 04 EPJ C33 233 S. Amoruso et al. (ICARUS Collab.)BENNETT 04 PRL 92 161802 G.W. Bennett et al. (Muon(g-2) Collab.)AHMED 02 PR D65 112002 M. Ahmed et al. (MEGA Collab.)BENNETT 02 PRL 89 101804 G.W. Bennett et al. (Muon(g-2) Collab.)BROWN 01 PRL 86 2227 H.N. Brown et al. (Muon(g-2) Collab.)BROWN 00 PR D62 091101 H.N. Brown et al. (BNL/G-2 Collab.)MEYER 00 PRL 84 1136 V. Meyer et al.BROOKS 99 PRL 83 1521 M.L. Brooks et al. (MEGA/LAMPF Collab.)HUGHES 99 RMP 71 S133 V.W. Hughes, T. KinoshitaLIU 99 PRL 82 711 W. Liu et al. (LAMPF Collab.)MOHR 99 JPCRD 28 1713 P.J. Mohr, B.N. Taylor (NIST)Also RMP 72 351 P.J. Mohr, B.N. Taylor (NIST)WILLMANN 99 PRL 82 49 L. Willmann et al.FELDMAN 98 PR D57 3873 G.J. Feldman, R.D. CousinsKAULARD 98 PL B422 334 J. Kaulard et al. (SINDRUM-II Collab.)GORDEEV 97 PAN 60 1164 V.A. Gordeev et al. (PNPI)Translated from YAF 60 1291.ABELA 96 PRL 77 1950 R. Abela et al. (PSI, ZURI, HEIDH, TBIL+)HONECKER 96 PRL 76 200 W. Hone ker et al. (SINDRUM II Collab.)DOHMEN 93 PL B317 631 C. Dohmen et al. (PSI SINDRUM-II Collab.)FREEDMAN 93 PR D47 811 S.J. Freedman et al. (LAMPF E645 Collab.)NI 93 PR D48 1976 B. Ni et al. (LAMPF Crystal-Box Collab.)IMAZATO 92 PRL 69 877 J. Imazato et al. (KEK, INUS, TOKY+)BARANOV 91 SJNP 53 802 V.A. Baranov et al. (JINR)Translated from YAF 53 1302.KRAKAUER 91B PL B263 534 D.A. Krakauer et al. (UMD, UCI, LANL)MATTHIAS 91 PRL 66 2716 B.E. Matthias et al. (YALE, HEIDP, WILL+)Also PRL 67 932 (erratum) B.E. Matthias et al. (YALE, HEIDP, WILL+)HUBER 90B PR D41 2709 T.M. Huber et al. (WYOM, VICT, ARIZ+)AHMAD 88 PR D38 2102 S. Ahmad et al. (TRIU, VICT, VPI, BRCO+)Also PRL 59 970 S. Ahmad et al. (TRIU, VPI, VICT, BRCO+)BALKE 88 PR D37 587 B. Balke et al. (LBL, UCB, COLO, NWES+)BELLGARDT 88 NP B299 1 U. Bellgardt et al. (SINDRUM Collab.)BOLTON 88 PR D38 2077 R.D. Bolton et al. (LANL, STAN, CHIC+)Also PRL 56 2461 R.D. Bolton et al. (LANL, STAN, CHIC+)Also PRL 57 3241 D. Grosni k et al. (CHIC, LANL, STAN+)BELTRAMI 87 PL B194 326 I. Beltrami et al. (ETH, SIN, MANZ)COHEN 87 RMP 59 1121 E.R. Cohen, B.N. Taylor (RISC, NBS)BEER 86 PRL 57 671 G.A. Beer et al. (VICT, TRIU, WYOM)JODIDIO 86 PR D34 1967 A. Jodidio et al. (LBL, NWES, TRIU)Also PR D37 237 (erratum) A. Jodidio et al. (LBL, NWES, TRIU)BERTL 85 NP B260 1 W. Bertl et al. (SINDRUM Collab.)BRYMAN 85 PRL 55 465 D.A. Bryman et al. (TRIU, CNRC, BRCO+)BURKARD 85 PL 150B 242 H. Burkhardt et al. (ETH, SIN, MANZ)BURKARD 85B PL 160B 343 H. Burkhardt et al. (ETH, SIN, MANZ)Also PR D24 2004 F. Corriveau et al. (ETH, SIN, MANZ)Also PL 129B 260 F. Corriveau et al. (ETH, SIN, MANZ)STOKER 85 PRL 54 1887 D.P. Stoker et al. (LBL, NWES, TRIU)BARDIN 84 PL 137B 135 G. Bardin et al. (SACL, CERN, BGNA, FIRZ)BERTL 84 PL 140B 299 W. Bertl et al. (SINDRUM Collab.)BOLTON 84 PRL 53 1415 R.D. Bolton et al. (LANL, CHIC, STAN+)EICHENBER... 84 NP A412 523 W. Ei henberger, R. Engfer, A. van der S haGIOVANETTI 84 PR D29 343 K.L. Giovanetti et al. (WILL)AZUELOS 83 PRL 51 164 G. Azuelos et al. (MONT, TRIU, BRCO)Also PRL 39 1113 P. Depommier et al. (MONT, BRCO, TRIU+)BERGSMA 83 PL 122B 465 F. Bergsma et al. (CHARM Collab.)CARR 83 PRL 51 627 J. Carr et al. (LBL, NWES, TRIU)KINNISON 82 PR D25 2846 W.W. Kinnison et al. (EFI, STAN, LANL)Also PRL 42 556 J.D. Bowman et al. (LASL, EFI, STAN)KLEMPT 82 PR D25 652 E. Klempt et al. (MANZ, ETH)MARIAM 82 PRL 49 993 F.G. Mariam et al. (YALE, HEIDH, BERN)MARSHALL 82 PR D25 1174 G.M. Marshall et al. (BRCO)NEMETHY 81 CNPP 10 147 P. Nemethy, V.W. Hughes (LBL, YALE)ABELA 80 PL 95B 318 R. Abela et al. (BASL, KARLK, KARLE)BADERT... 80 LNC 28 401 A. Baderts her et al. (BERN)Also NP A377 406 A. Baderts her et al. (BERN)JONKER 80 PL 93B 203 M. Jonker et al. (CHARM Collab.)SCHAAF 80 NP A340 249 A. van der S haaf et al. (ZURI, ETH+)Also PL 72B 183 H.P. Povel et al. (ZURI, ETH, SIN)WILLIS 80 PRL 44 522 S.E. Willis et al. (YALE, LBL, LASL+)Also PRL 45 1370 S.E. Willis et al. (YALE, LBL, LASL+)BAILEY 79 NP B150 1 J.M. Bailey (CERN, DARE, MANZ)BADERT... 78 PL 79B 371 A. Baderts her et al. (BERN)BAILEY 78 JP G4 345 J.M. Bailey (DARE, BERN, SHEF, MANZ, RMCS+)Also NP B150 1 J.M. Bailey (CERN, DARE, MANZ)BLIETSCHAU 78 NP B133 205 J. Bliets hau et al. (Gargamelle Collab.)BOWMAN 78 PRL 41 442 J.D. Bowman et al. (LASL, IAS, CMU+)CAMANI 78 PL 77B 326 M. Camani et al. (ETH, MANZ)BADERT... 77 PRL 39 1385 A. Baderts her et al. (BERN)CASPERSON 77 PRL 38 956 D.E. Casperson et al. (BERN, HEIDH, LASL+)DEPOMMIER 77 PRL 39 1113 P. Depommier et al. (MONT, BRCO, TRIU+)BALANDIN 74 JETP 40 811 M.P. Balandin et al. (JINR)Translated from ZETF 67 1631.COHEN 73 JPCRD 2 664 E.R. Cohen, B.N. Taylor (RISC, NBS)DUCLOS 73 PL 47B 491 J. Du los, A. Magnon, J. Pi ard (SACL)EICHTEN 73 PL 46B 281 T. Ei hten et al. (Gargamelle Collab.)BRYMAN 72 PRL 28 1469 D.A. Bryman et al. (VPI)CROWE 72 PR D5 2145 K.M. Crowe et al. (LBL, WASH)CRANE 71 PRL 27 474 T. Crane et al. (YALE)DERENZO 69 PR 181 1854 S.E. Derenzo (EFI)VOSSLER 69 NC 63A 423 C. Vossler (EFI)AKHMANOV 68 SJNP 6 230 V.V. Akhmanov et al. (KIAE)Translated from YAF 6 316.FRYBERGER 68 PR 166 1379 D. Fryberger (EFI)BOGART 67 PR 156 1405 E. Bogart et al. (COLU)SCHWARTZ 67 PR 162 1306 D.M. S hwartz (EFI)SHERWOOD 67 PR 156 1475 B.A. Sherwood (EFI)PEOPLES 66 Nevis 147 unpub. J. Peoples (COLU)BLOOM 64 PL 8 87 S. Bloom et al. (CERN)DUCLOS 64 PL 9 62 J. Du los et al. (CERN)GUREVICH 64 PL 11 185 I.I. Gurevi h et al. (KIAE)BUHLER 63 PL 7 368 A. Buhler-Broglin et al. (CERN)MEYER 63 PR 132 2693 S.L. Meyer et al. (COLU)CHARPAK 62 PL 1 16 G. Charpak et al. (CERN)CONFORTO 62 NC 26 261 G. Conforto et al. (INFN, ROMA, CERN)ALI-ZADE 61 JETP 13 313 S.A. Ali-Zade, I.I. Gurevi h, B.A. NikolskyTranslated from ZETF 40 452.CRITTENDEN 61 PR 121 1823 R.R. Crittenden, W.D. Walker, J. Ballam (WISC+)KRUGER 61 UCRL 9322 unpub. H. Kruger (LRL)GUREVICH 60 JETP 10 225 I.I. Gurevi h, B.A. Nikolsky, L.V. Surkova (ITEP)Translated from ZETF 37 318.

PLANO 60 PR 119 1400 R.J. Plano (COLU)ASHKIN 59 NC 14 1266 J. Ashkin et al. (CERN)BARDON 59 PRL 2 56 M. Bardon, D. Berley, L.M. Lederman (COLU)LEE 59 PRL 3 55 J. Lee, N.P. Samios (COLU)τ J = 12

τ dis overy paper was PERL 75. e+ e− → τ+ τ− ross-se tionthreshold behavior and magnitude are onsistent with pointlike spin-1/2 Dira parti le. BRANDELIK 78 ruled out pointlike spin-0 orspin-1 parti le. FELDMAN 78 ruled out J = 3/2. KIRKBY 79 alsoruled out J=integer, J = 3/2.τ MASSτ MASSτ MASSτ MASSVALUE (MeV) EVTS DOCUMENT ID TECN COMMENT1776.86±0.12 OUR AVERAGE1776.86±0.12 OUR AVERAGE1776.86±0.12 OUR AVERAGE1776.86±0.12 OUR AVERAGE1776.91±0.12+0.10

−0.13 1171 1 ABLIKIM 14D BES3 23.3 pb−1, Eee m=3.543.60 GeV1776.68±0.12±0.41 682k 2 AUBERT 09AK BABR 423 fb−1, Eee m=10.6 GeV1776.81+0.25−0.23±0.15 81 ANASHIN 07 KEDR 6.7 pb−1, Eee m=3.543.78 GeV1776.61±0.13±0.35 2 BELOUS 07 BELL 414 fb−1 Eee m=10.6 GeV1775.1 ±1.6 ±1.0 13.3k 3 ABBIENDI 00A OPAL 19901995 LEP runs1778.2 ±0.8 ±1.2 ANASTASSOV 97 CLEO Eee m= 10.6 GeV1776.96+0.18−0.21+0.25

−0.17 65 4 BAI 96 BES Eee m= 3.543.57 GeV1776.3 ±2.4 ±1.4 11k 5 ALBRECHT 92M ARG Eee m= 9.410.6 GeV1783 +3−4 692 6 BACINO 78B DLCO Eee m= 3.17.4 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •1777.8 ±0.7 ±1.7 35k 7 BALEST 93 CLEO Repl. by ANASTASSOV 971776.9 +0.4−0.5 ±0.2 14 8 BAI 92 BES Repl. by BAI 961ABLIKIM 14D t σ(e+ e− → τ+ τ−) at dierent energies near threshold.2AUBERT 09AK and BELOUS 07 t τ pseudomass spe trum in τ → ππ+π− ντ de ays.Result assumes mντ

= 0.3ABBIENDI 00A t τ pseudomass spe trum in τ → π± ≤ 2π0 ντ andτ → π±π+π− ≤ 1π0 ντ de ays. Result assumes mντ

=0.4BAI 96 t σ(e+ e− → τ+ τ−) at dierent energies near threshold.5ALBRECHT 92M t τ pseudomass spe trum in τ− → 2π−π+ ντ de ays. Resultassumes mντ=0.6BACINO 78B value omes from e±X∓ threshold. Published mass 1782 MeV in reasedby 1 MeV using the high pre ision ψ(2S) mass measurement of ZHOLENTZ 80 toeliminate the absolute SPEAR energy alibration un ertainty.7BALEST 93 t spe tra of minimum kinemati ally allowed τ mass in events of the typee+ e− → τ+ τ− → (π+ nπ0 ντ )(π−mπ0ντ ) n ≤ 2, m ≤ 2, 1 ≤ n+m ≤ 3. Ifmντ

6= 0, result in reases by (m2ντ

/1100 MeV).8BAI 92 t σ(e+ e− → τ+ τ−) near threshold using e µ events.(mτ+ − mτ−)/maverage(mτ+ − mτ−)/maverage(mτ+ − mτ−)/maverage(mτ+ − mτ−)/maverageA test of CPT invarian e.VALUE CL% DOCUMENT ID TECN COMMENT<2.8× 10−4<2.8× 10−4<2.8× 10−4<2.8× 10−4 90 BELOUS 07 BELL 414 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<5.5× 10−4 90 1 AUBERT 09AK BABR 423 fb−1, Eee m=10.6 GeV<3.0× 10−3 90 ABBIENDI 00A OPAL 19901995 LEP runs1AUBERT 09AK quote both the listed upper limit and (m

τ+ − mτ−)/maverage =(−3.4 ± 1.3 ± 0.3)× 10−4.

τ MEAN LIFEτ MEAN LIFEτ MEAN LIFEτ MEAN LIFEVALUE (10−15 s) EVTS DOCUMENT ID TECN COMMENT290.3 ± 0.5 OUR AVERAGE290.3 ± 0.5 OUR AVERAGE290.3 ± 0.5 OUR AVERAGE290.3 ± 0.5 OUR AVERAGE290.17± 0.53± 0.33 1.1M BELOUS 14 BELL 711 fb−1 Eee m=10.6 GeV290.9 ± 1.4 ± 1.0 ABDALLAH 04T DLPH 1991-1995 LEP runs293.2 ± 2.0 ± 1.5 ACCIARRI 00B L3 19911995 LEP runs290.1 ± 1.5 ± 1.1 BARATE 97R ALEP 19891994 LEP runs289.2 ± 1.7 ± 1.2 ALEXANDER 96E OPAL 19901994 LEP runs289.0 ± 2.8 ± 4.0 57.4k BALEST 96 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •291.2 ± 2.0 ± 1.2 BARATE 97I ALEP Repl. by BARATE 97R291.4 ± 3.0 ABREU 96B DLPH Repl. by ABDALLAH 04T290.1 ± 4.0 34k ACCIARRI 96K L3 Repl. by ACCIARRI 00B297 ± 9 ± 5 1671 ABE 95Y SLD 19921993 SLC runs304 ±14 ± 7 4100 BATTLE 92 CLEO Eee m= 10.6 GeV301 ±29 3780 KLEINWORT 89 JADE Eee m= 3546 GeV288 ±16 ±17 807 AMIDEI 88 MRK2 Eee m= 29 GeV

725725725725See key on page 601 Lepton Parti le Listingsτ306 ±20 ±14 695 BRAUNSCH... 88C TASS Eee m= 36 GeV299 ±15 ±10 1311 ABACHI 87C HRS Eee m= 29 GeV295 ±14 ±11 5696 ALBRECHT 87P ARG Eee m= 9.310.6 GeV309 ±17 ± 7 3788 BAND 87B MAC Eee m= 29 GeV325 ±14 ±18 8470 BEBEK 87C CLEO Eee m= 10.5 GeV460 ± 190 102 FELDMAN 82 MRK2 Eee m= 29 GeV(τ τ+ − τ τ−) / τ average(τ τ+ − τ τ−) / τ average(τ τ+ − τ τ−) / τ average(τ τ+ − τ τ−) / τ averageTest of CPT invarian e.VALUE CL% DOCUMENT ID TECN COMMENT

<7.0× 10−3<7.0× 10−3<7.0× 10−3<7.0× 10−3 90 1 BELOUS 14 BELL 711 fb−1 Eee m = 10.6 GeV1BELOUS 14 quote limit on the absolute value of the relative lifetime dieren e.τ MAGNETIC MOMENT ANOMALYτ MAGNETIC MOMENT ANOMALYτ MAGNETIC MOMENT ANOMALYτ MAGNETIC MOMENT ANOMALYThe q2 dependen e is expe ted to be small providing no thresholds arenearby.

µτ/(eh/2mτ )−1 = (gτ−2)/2µτ/(eh/2mτ )−1 = (gτ−2)/2µτ/(eh/2mτ )−1 = (gτ−2)/2µτ/(eh/2mτ )−1 = (gτ−2)/2For a theoreti al al ulation [(gτ−2)/2 = 117 721(5) × 10−8, see EIDELMAN 07.VALUE CL% DOCUMENT ID TECN COMMENT> −0.052 and < 0.013 (CL = 95%) OUR LIMIT> −0.052 and < 0.013 (CL = 95%) OUR LIMIT> −0.052 and < 0.013 (CL = 95%) OUR LIMIT> −0.052 and < 0.013 (CL = 95%) OUR LIMIT> −0.052 and < 0.013 95 1 ABDALLAH 04K DLPH e+ e− → e+ e− τ+ τ−at LEP2• • • We do not use the following data for averages, ts, limits, et . • • •<0.107 95 2 ACHARD 04G L3 e+ e− → e+ e− τ+ τ−at LEP2> −0.007 and < 0.005 95 3 GONZALEZ-S...00 RVUE e+ e− → τ+ τ− andW → τ ντ> −0.052 and < 0.058 95 4 ACCIARRI 98E L3 19911995 LEP runs> −0.068 and < 0.065 95 5 ACKERSTAFF 98N OPAL 19901995 LEP runs> −0.004 and < 0.006 95 6 ESCRIBANO 97 RVUE Z → τ+ τ− at LEP<0.01 95 7 ESCRIBANO 93 RVUE Z → τ+ τ− at LEP<0.12 90 GRIFOLS 91 RVUE Z → τ τ γ at LEP<0.023 95 8 SILVERMAN 83 RVUE e+ e− → τ+ τ− atPETRA1ABDALLAH 04K limit is derived from e+ e− → e+ e− τ+ τ− total ross-se tion mea-surements at √

s between 183 and 208 GeV. In addition to the limits, the authors alsoquote a value of −0.018 ± 0.017.2ACHARD 04G limit is derived from e+ e− → e+ e− τ+ τ− total ross-se tion mea-surements at √s between 189 and 206 GeV, and is on the absolute value of the magneti moment anomaly.3GONZALEZ-SPRINBERG 00 use data on tau lepton produ tion at LEP1, SLC, andLEP2, and data from olliders and LEP2 to determine limits. Assume imaginary ompo-nent is zero.4ACCIARRI 98E use Z → τ+ τ− γ events. In addition to the limits, the authors alsoquote a value of 0.004 ± 0.027 ± 0.023.5ACKERSTAFF 98N use Z → τ+ τ− γ events. The limit applies to an average of theform fa tor for o-shell τ 's having p2 ranging from m2τto (MZ mτ )2.6 ESCRIBANO 97 use preliminary experimental results.7 ESCRIBANO 93 limit derived from (Z → τ+ τ−), and is on the absolute value of themagneti moment anomaly.8 SILVERMAN 83 limit is derived from e+ e− → τ+ τ− total ross-se tion measurementsfor q2 up to (37 GeV)2.

τ ELECTRIC DIPOLE MOMENT (dτ )τ ELECTRIC DIPOLE MOMENT (dτ )τ ELECTRIC DIPOLE MOMENT (dτ )τ ELECTRIC DIPOLE MOMENT (dτ )A nonzero value is forbidden by both T invarian e and P invarian e.The q2 dependen e is expe ted to be small providing no thresholds arenearby.Re(dτ )Re(dτ )Re(dτ )Re(dτ )VALUE (10−16 e m) CL% DOCUMENT ID TECN COMMENT− 0.22 to 0.45− 0.22 to 0.45− 0.22 to 0.45− 0.22 to 0.45 95 1 INAMI 03 BELL Eee m= 10.6 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •< 2.3 90 2 GROZIN 09A RVUE From e EDM limit< 3.7 95 3 ABDALLAH 04K DLPH e+ e− → e+ e− τ+ τ−at LEP2< 11.4 95 4 ACHARD 04G L3 e+ e− → e+ e− τ+ τ−at LEP2< 4.6 95 5 ALBRECHT 00 ARG Eee m= 10.4 GeV> −3.1 and < 3.1 95 ACCIARRI 98E L3 19911995 LEP runs> −3.8 and < 3.6 95 6 ACKERSTAFF 98N OPAL 19901995 LEP runs< 0.11 95 7,8 ESCRIBANO 97 RVUE Z → τ+ τ− at LEP< 0.5 95 9 ESCRIBANO 93 RVUE Z → τ+ τ− at LEP< 7 90 GRIFOLS 91 RVUE Z → τ τ γ at LEP< 1.6 90 DELAGUILA 90 RVUE e+ e− → τ+ τ−Eee m= 35 GeV

1 INAMI 03 use e+ e− → τ+ τ− events.2GROZIN 09A al ulate the ontribution to the ele tron ele tri dipole moment from theτ ele tri dipole moment appearing in loops, whi h is de = 6.9× 10−12 dτ . Dividingthe REGAN 02 upper limit ∣∣de∣∣ ≤ 1.6× 10−27 e m at CL=90% by 6.9× 10−12 givesthis limit.3ABDALLAH 04K limit is derived from e+ e− → e+ e− τ+ τ− total ross-se tion mea-surements at √s between 183 and 208 GeV and is on the absolute value of dτ .4ACHARD 04G limit is derived from e+ e− → e+ e− τ+ τ− total ross-se tion mea-surements at √s between 189 and 206 GeV, and is on the absolute value of dτ .5ALBRECHT 00 use e+ e− → τ+ τ− events. Limit is on the absolute value of Re(dτ ).6ACKERSTAFF 98N use Z → τ+ τ− γ events. The limit applies to an average of theform fa tor for o-shell τ 's having p2 ranging from m2

τto (MZ mτ )2.7 ESCRIBANO 97 derive the relationship ∣∣dτ ∣∣ = ot θW ∣∣dWτ ∣∣ using ee tive Lagrangianmethods, and use a onferen e result ∣∣dW

τ

∣∣ < 5.8×10−18 e m at 95% CL (L. Silvestris,ICHEP96) to obtain this result.8 ESCRIBANO 97 use preliminary experimental results.9 ESCRIBANO 93 limit derived from (Z → τ+ τ−), and is on the absolute value of theele tri dipole moment.Im(dτ )Im(dτ )Im(dτ )Im(dτ )VALUE (10−16 e m) CL% DOCUMENT ID TECN COMMENT−0.25 to 0.008−0.25 to 0.008−0.25 to 0.008−0.25 to 0.008 95 1 INAMI 03 BELL Eee m= 10.6 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •< 1.8 95 2 ALBRECHT 00 ARG Eee m= 10.4 GeV1 INAMI 03 use e+ e− → τ+ τ− events.2ALBRECHT 00 use e+ e− → τ+ τ− events. Limit is on the absolute value of Im(dτ ).

τ WEAK DIPOLE MOMENT (dwτ )τ WEAK DIPOLE MOMENT (dwτ )τ WEAK DIPOLE MOMENT (dwτ )τ WEAK DIPOLE MOMENT (dwτ )A nonzero value is forbidden by CP invarian e.The q2 dependen e is expe ted to be small providing no thresholds arenearby.Re(dwτ )Re(dwτ )Re(dwτ )Re(dwτ )VALUE (10−17 e m) CL% DOCUMENT ID TECN COMMENT<0.50<0.50<0.50<0.50 95 1 HEISTER 03F ALEP 19901995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •<3.0 90 1 ACCIARRI 98C L3 19911995 LEP runs<0.56 95 ACKERSTAFF 97L OPAL 19911995 LEP runs<0.78 95 2 AKERS 95F OPAL Repl. by ACKERSTAFF 97L<1.5 95 2 BUSKULIC 95C ALEP Repl. by HEISTER 03F<7.0 95 2 ACTON 92F OPAL Z → τ+ τ− at LEP<3.7 95 2 BUSKULIC 92J ALEP Repl. by BUSKULIC 95C1 Limit is on the absolute value of the real part of the weak dipole moment.2 Limit is on the absolute value of the real part of the weak dipole moment, and appliesfor q2 = m2Z .Im(dwτ )Im(dwτ )Im(dwτ )Im(dwτ )VALUE (10−17 e m) CL% DOCUMENT ID TECN COMMENT<1.1<1.1<1.1<1.1 95 1 HEISTER 03F ALEP 19901995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •<1.5 95 ACKERSTAFF 97L OPAL 19911995 LEP runs<4.5 95 2 AKERS 95F OPAL Repl. by ACKERSTAFF 97L1HEISTER 03F limit is on the absolute value of the imaginary part of the weak dipolemoment.2 Limit is on the absolute value of the imaginary part of the weak dipole moment, andapplies for q2 = m2Z .

τ WEAK ANOMALOUS MAGNETIC DIPOLE MOMENT (αwτ )τ WEAK ANOMALOUS MAGNETIC DIPOLE MOMENT (αwτ )τ WEAK ANOMALOUS MAGNETIC DIPOLE MOMENT (αwτ )τ WEAK ANOMALOUS MAGNETIC DIPOLE MOMENT (αwτ )Ele troweak radiative orre tions are expe ted to ontribute at the 10−6level. See BERNABEU 95.The q2 dependen e is expe ted to be small providing no thresholds arenearby.Re(αwτ )Re(αwτ )Re(αwτ )Re(αwτ )VALUE CL% DOCUMENT ID TECN COMMENT<1.1× 10−3<1.1× 10−3<1.1× 10−3<1.1× 10−3 95 1 HEISTER 03F ALEP 19901995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •> −0.0024 and < 0.0025 95 2 GONZALEZ-S...00 RVUE e+ e− → τ+ τ−and W → τ ντ<4.5× 10−3 90 1 ACCIARRI 98C L3 19911995 LEP runs1 Limit is on the absolute value of the real part of the weak anomalous magneti dipolemoment.2GONZALEZ-SPRINBERG 00 use data on tau lepton produ tion at LEP1, SLC, andLEP2, and data from olliders and LEP2 to determine limits. Assume imaginary ompo-nent is zero.

726726726726LeptonParti le ListingsτIm(αwτ )Im(αwτ )Im(αwτ )Im(αwτ )VALUE CL% DOCUMENT ID TECN COMMENT<2.7× 10−3<2.7× 10−3<2.7× 10−3<2.7× 10−3 95 1 HEISTER 03F ALEP 19901995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •<9.9× 10−3 90 1 ACCIARRI 98C L3 19911995 LEP runs1 Limit is on the absolute value of the imaginary part of the weak anomalous magneti dipole moment.

τ− DECAY MODESτ− DECAY MODESτ− DECAY MODESτ− DECAY MODESτ+ modes are harge onjugates of the modes below. \h±" stands forπ± or K±. \ℓ" stands for e or µ. \Neutrals" stands for γ's and/or π0's.S ale fa tor/Mode Fra tion (i /) Conden e levelModes with one harged parti leModes with one harged parti leModes with one harged parti leModes with one harged parti le1 parti le− ≥ 0 neutrals ≥ 0K 0ντ(\1-prong") (85.24 ± 0.06 ) %2 parti le− ≥ 0 neutrals ≥ 0K 0Lντ (84.58 ± 0.06 ) %3 µ−νµ ντ [a (17.39 ± 0.04 ) %4 µ−νµ ντ γ [b ( 3.68 ± 0.10 )× 10−35 e−νe ντ [a (17.82 ± 0.04 ) %6 e−νe ντ γ [b ( 1.84 ± 0.05 ) %7 h− ≥ 0K0L ντ (12.03 ± 0.05 ) %8 h−ντ (11.51 ± 0.05 ) %9 π− ντ [a (10.82 ± 0.05 ) %10 K−ντ [a ( 6.96 ± 0.10 )× 10−311 h− ≥ 1 neutralsντ (37.00 ± 0.09 ) %12 h− ≥ 1π0 ντ (ex.K0) (36.51 ± 0.09 ) %13 h−π0 ντ (25.93 ± 0.09 ) %14 π−π0 ντ [a (25.49 ± 0.09 ) %15 π−π0 non-ρ(770)ντ ( 3.0 ± 3.2 )× 10−316 K−π0 ντ [a ( 4.33 ± 0.15 )× 10−317 h− ≥ 2π0 ντ (10.81 ± 0.09 ) %18 h−2π0 ντ ( 9.48 ± 0.10 ) %19 h−2π0 ντ (ex.K0) ( 9.32 ± 0.10 ) %20 π− 2π0ντ (ex.K0) [a ( 9.26 ± 0.10 ) %21 π− 2π0ντ (ex.K0),s alar < 9 × 10−3 CL=95%22 π− 2π0ντ (ex.K0),ve tor < 7 × 10−3 CL=95%23 K−2π0 ντ (ex.K0) [a ( 6.5 ± 2.2 )× 10−424 h− ≥ 3π0 ντ ( 1.34 ± 0.07 ) %25 h− ≥ 3π0 ντ (ex. K0) ( 1.25 ± 0.07 ) %26 h−3π0 ντ ( 1.18 ± 0.07 ) %27 π− 3π0ντ (ex.K0) [a ( 1.04 ± 0.07 ) %28 K−3π0 ντ (ex.K0, η) [a ( 4.8 ± 2.1 )× 10−429 h−4π0 ντ (ex.K0) ( 1.6 ± 0.4 )× 10−330 h−4π0 ντ (ex.K0,η) [a ( 1.1 ± 0.4 )× 10−331 a1(1260)ντ → π− γ ντ ( 3.8 ± 1.5 )× 10−432 K− ≥ 0π0 ≥ 0K0 ≥ 0γ ντ ( 1.552± 0.029) %33 K− ≥ 1 (π0 or K0 or γ) ντ ( 8.59 ± 0.28 )× 10−3Modes with K0'sModes with K0'sModes with K0'sModes with K0's34 K0S (parti les)− ντ ( 9.44 ± 0.28 )× 10−335 h−K0 ντ ( 9.87 ± 0.14 )× 10−336 π−K0 ντ [a ( 8.40 ± 0.14 )× 10−337 π−K0 (non-K∗(892)−)ντ ( 5.4 ± 2.1 )× 10−438 K−K0ντ [a ( 1.48 ± 0.05 )× 10−339 K−K0 ≥ 0π0 ντ ( 2.98 ± 0.08 )× 10−340 h−K0π0 ντ ( 5.32 ± 0.13 )× 10−341 π−K0π0 ντ [a ( 3.82 ± 0.13 )× 10−342 K0ρ− ντ ( 2.2 ± 0.5 )× 10−343 K−K0π0 ντ [a ( 1.50 ± 0.07 )× 10−344 π−K0 ≥ 1π0 ντ ( 4.08 ± 0.25 )× 10−345 π−K0π0π0 ντ (ex.K0) [a ( 2.6 ± 2.3 )× 10−446 K−K0π0π0 ντ < 1.6 × 10−4 CL=95%47 π−K0K0ντ ( 1.55 ± 0.24 )× 10−348 π−K0S K0S ντ [a ( 2.33 ± 0.07 )× 10−449 π−K0S K0Lντ [a ( 1.08 ± 0.24 )× 10−350 π−K0LK0L ντ ( 2.33 ± 0.07 )× 10−451 π−K0K0π0 ντ ( 3.6 ± 1.2 )× 10−452 π−K0S K0S π0 ντ [a ( 1.82 ± 0.21 )× 10−553 K∗−K0π0 ντ →

π−K0S K0S π0 ντ

( 1.08 ± 0.21 )× 10−5

54 f1(1285)π−ντ →π−K0S K0S π0 ντ

( 6.8 ± 1.5 )× 10−655 f1(1420)π−ντ →π−K0S K0S π0 ντ

( 2.4 ± 0.8 )× 10−656 π−K0S K0Lπ0 ντ [a ( 3.2 ± 1.2 )× 10−457 π−K0LK0Lπ0 ντ ( 1.82 ± 0.21 )× 10−558 K−K0S K0S ντ < 6.3 × 10−7 CL=90%59 K−K0S K0S π0 ντ < 4.0 × 10−7 CL=90%60 K0h+ h−h− ≥ 0 neutrals ντ < 1.7 × 10−3 CL=95%61 K0h+ h−h−ντ [a ( 2.5 ± 2.0 )× 10−4Modes with three harged parti lesModes with three harged parti lesModes with three harged parti lesModes with three harged parti les62 h−h− h+ ≥ 0 neutrals ≥ 0K 0Lντ (15.21 ± 0.06 ) %63 h− h−h+ ≥ 0 neutrals ντ(ex. K0S → π+π−)(\3-prong") (14.55 ± 0.06 ) %64 h−h− h+ντ ( 9.80 ± 0.05 ) %65 h−h− h+ντ (ex.K0) ( 9.46 ± 0.05 ) %66 h−h− h+ντ (ex.K0,ω) ( 9.43 ± 0.05 ) %67 π−π+π− ντ ( 9.31 ± 0.05 ) %68 π−π+π− ντ (ex.K0) ( 9.02 ± 0.05 ) %69 π−π+π− ντ (ex.K0),non-axial ve tor < 2.4 % CL=95%70 π−π+π− ντ (ex.K0,ω) [a ( 8.99 ± 0.05 ) %71 h−h− h+ ≥ 1 neutrals ντ ( 5.29 ± 0.05 ) %72 h−h− h+ ≥ 1π0 ντ (ex. K0) ( 5.09 ± 0.05 ) %73 h−h− h+π0 ντ ( 4.76 ± 0.05 ) %74 h−h− h+π0 ντ (ex.K0) ( 4.57 ± 0.05 ) %75 h−h− h+π0 ντ (ex. K0, ω) ( 2.79 ± 0.07 ) %76 π−π+π−π0 ντ ( 4.62 ± 0.05 ) %77 π−π+π−π0 ντ (ex.K0) ( 4.49 ± 0.05 ) %78 π−π+π−π0 ντ (ex.K0,ω) [a ( 2.74 ± 0.07 ) %79 h−ρπ0 ντ80 h−ρ+ h−ντ81 h−ρ− h+ντ82 h−h− h+ ≥ 2π0ντ (ex.K0) ( 5.17 ± 0.31 )× 10−383 h−h− h+2π0 ντ ( 5.05 ± 0.31 )× 10−384 h−h− h+2π0 ντ (ex.K0) ( 4.95 ± 0.31 )× 10−385 h−h− h+2π0 ντ (ex.K0,ω,η) [a (10 ± 4 )× 10−486 h−h− h+3π0 ντ ( 2.12 ± 0.30 )× 10−487 2π−π+ 3π0ντ (ex.K0) ( 1.94 ± 0.30 )× 10−488 2π−π+ 3π0ντ (ex.K0, η,f1(1285)) ( 1.7 ± 0.4 )× 10−489 2π−π+ 3π0ντ (ex.K0, η,ω, f1(1285)) [a ( 1.4 ± 2.7 )× 10−590 K−h+h− ≥ 0 neutrals ντ ( 6.29 ± 0.14 )× 10−391 K−h+π− ντ (ex.K0) ( 4.37 ± 0.07 )× 10−392 K−h+π−π0 ντ (ex.K0) ( 8.6 ± 1.2 )× 10−493 K−π+π− ≥ 0 neutrals ντ ( 4.77 ± 0.14 )× 10−394 K−π+π− ≥ 0π0ντ (ex.K0) ( 3.73 ± 0.13 )× 10−395 K−π+π−ντ ( 3.45 ± 0.07 )× 10−396 K−π+π−ντ (ex.K0) ( 2.93 ± 0.07 )× 10−397 K−π+π−ντ (ex.K0,ω) [a ( 2.93 ± 0.07 )× 10−398 K−ρ0 ντ →K−π+π−ντ

( 1.4 ± 0.5 )× 10−399 K−π+π−π0 ντ ( 1.31 ± 0.12 )× 10−3100 K−π+π−π0 ντ (ex.K0) ( 7.9 ± 1.2 )× 10−4101 K−π+π−π0 ντ (ex.K0,η) ( 7.6 ± 1.2 )× 10−4102 K−π+π−π0 ντ (ex.K0,ω) ( 3.7 ± 0.9 )× 10−4103 K−π+π−π0 ντ (ex.K0,ω,η)[a ( 3.9 ± 1.4 )× 10−4104 K−π+K− ≥ 0 neut. ντ < 9 × 10−4 CL=95%105 K−K+π− ≥ 0 neut. ντ ( 1.496± 0.033)× 10−3106 K−K+π− ντ [a ( 1.435± 0.027)× 10−3107 K−K+π−π0 ντ [a ( 6.1 ± 1.8 )× 10−5108 K−K+K−ντ ( 2.2 ± 0.8 )× 10−5 S=5.4109 K−K+K−ντ (ex. φ) < 2.5 × 10−6 CL=90%110 K−K+K−π0 ντ < 4.8 × 10−6 CL=90%111 π−K+π− ≥ 0 neut. ντ < 2.5 × 10−3 CL=95%112 e− e− e+νe ντ ( 2.8 ± 1.5 )× 10−5113 µ− e− e+νµ ντ < 3.6 × 10−5 CL=90%

727727727727See key on page 601 Lepton Parti le ListingsτModes with ve harged parti lesModes with ve harged parti lesModes with ve harged parti lesModes with ve harged parti les114 3h−2h+ ≥ 0 neutrals ντ(ex. K0S → π−π+)(\5-prong") ( 9.9 ± 0.4 )× 10−4115 3h−2h+ντ (ex.K0) ( 8.22 ± 0.32 )× 10−4116 3π−2π+ντ (ex.K0, ω) ( 8.21 ± 0.31 )× 10−4117 3π−2π+ντ (ex.K0, ω,f1(1285)) [a ( 7.69 ± 0.30 )× 10−4118 K−2π−2π+ντ (ex.K0) [a ( 6 ±12 )× 10−7119 K+3π−π+ ντ < 5.0 × 10−6 CL=90%120 K+K−2π−π+ ντ < 4.5 × 10−7 CL=90%121 3h−2h+π0 ντ (ex.K0) ( 1.64 ± 0.11 )× 10−4122 3π−2π+π0 ντ (ex.K0) ( 1.62 ± 0.11 )× 10−4123 3π−2π+π0 ντ (ex.K0, η,f1(1285)) ( 1.11 ± 0.10 )× 10−4124 3π−2π+π0 ντ (ex.K0, η, ω,f1(1285)) [a ( 3.8 ± 0.9 )× 10−5125 K−2π−2π+π0 ντ (ex.K0) [a ( 1.1 ± 0.6 )× 10−6126 K+3π−π+π0 ντ < 8 × 10−7 CL=90%127 3h−2h+2π0ντ < 3.4 × 10−6 CL=90%Mis ellaneous other allowed modesMis ellaneous other allowed modesMis ellaneous other allowed modesMis ellaneous other allowed modes128 (5π )− ντ ( 7.8 ± 0.5 )× 10−3129 4h−3h+ ≥ 0 neutrals ντ(\7-prong") < 3.0 × 10−7 CL=90%130 4h−3h+ντ < 4.3 × 10−7 CL=90%131 4h−3h+π0 ντ < 2.5 × 10−7 CL=90%132 X− (S=−1)ντ ( 2.92 ± 0.04 ) %133 K∗(892)− ≥ 0 neutrals ≥0K0Lντ

( 1.42 ± 0.18 ) % S=1.4134 K∗(892)−ντ ( 1.20 ± 0.07 ) % S=1.8135 K∗(892)−ντ → π−K0 ντ ( 7.83 ± 0.26 )× 10−3136 K∗(892)0K− ≥ 0 neutrals ντ ( 3.2 ± 1.4 )× 10−3137 K∗(892)0K−ντ ( 2.1 ± 0.4 )× 10−3138 K∗(892)0π− ≥ 0 neutrals ντ ( 3.8 ± 1.7 )× 10−3139 K∗(892)0π− ντ ( 2.2 ± 0.5 )× 10−3140 (K∗(892)π )− ντ →π−K0π0 ντ

( 1.0 ± 0.4 )× 10−3141 K1(1270)−ντ ( 4.7 ± 1.1 )× 10−3142 K1(1400)−ντ ( 1.7 ± 2.6 )× 10−3 S=1.7143 K∗(1410)−ντ ( 1.5 + 1.4− 1.0 ) × 10−3144 K∗0(1430)−ντ < 5 × 10−4 CL=95%145 K∗2(1430)−ντ < 3 × 10−3 CL=95%146 a0(980)− ≥ 0 neutrals ντ147 ηπ− ντ < 9.9 × 10−5 CL=95%148 ηπ−π0 ντ [a ( 1.39 ± 0.07 )× 10−3149 ηπ−π0π0 ντ [a ( 1.9 ± 0.4 )× 10−4150 ηK−ντ [a ( 1.55 ± 0.08 )× 10−4151 ηK∗(892)−ντ ( 1.38 ± 0.15 )× 10−4152 ηK−π0 ντ [a ( 4.8 ± 1.2 )× 10−5153 ηK−π0 (non-K∗(892))ντ < 3.5 × 10−5 CL=90%154 ηK0π−ντ [a ( 9.4 ± 1.5 )× 10−5155 ηK0π−π0 ντ < 5.0 × 10−5 CL=90%156 ηK−K0 ντ < 9.0 × 10−6 CL=90%157 ηπ+π−π− ≥ 0 neutrals ντ < 3 × 10−3 CL=90%158 ηπ−π+π−ντ (ex.K0) [a ( 2.19 ± 0.13 )× 10−4159 ηπ−π+π−ντ (ex.K0,f1(1285)) ( 9.9 ± 1.6 )× 10−5160 ηa1(1260)− ντ → ηπ− ρ0 ντ < 3.9 × 10−4 CL=90%161 ηηπ− ντ < 7.4 × 10−6 CL=90%162 ηηπ−π0 ντ < 2.0 × 10−4 CL=95%163 ηηK− ντ < 3.0 × 10−6 CL=90%164 η′(958)π− ντ < 4.0 × 10−6 CL=90%165 η′(958)π−π0 ντ < 1.2 × 10−5 CL=90%166 η′(958)K−ντ < 2.4 × 10−6 CL=90%167 φπ− ντ ( 3.4 ± 0.6 )× 10−5168 φK− ντ [a ( 4.4 ± 1.6 )× 10−5169 f1(1285)π−ντ ( 3.9 ± 0.5 )× 10−4 S=1.9170 f1(1285)π−ντ →

ηπ−π+π−ντ

( 1.18 ± 0.07 )× 10−4 S=1.3171 f1(1285)π−ντ → 3π−2π+ντ [a ( 5.2 ± 0.4 )× 10−5172 π(1300)−ντ → (ρπ)− ντ →(3π)− ντ

< 1.0 × 10−4 CL=90%173 π(1300)−ντ →((ππ)S−wave π)− ντ →(3π)− ντ

< 1.9 × 10−4 CL=90%

174 h−ω ≥ 0 neutrals ντ ( 2.40 ± 0.08 ) %175 h−ωντ ( 1.99 ± 0.06 ) %176 π−ωντ [a ( 1.95 ± 0.06 ) %177 K−ωντ [a ( 4.1 ± 0.9 )× 10−4178 h−ωπ0 ντ [a ( 4.1 ± 0.4 )× 10−3179 h−ω2π0 ντ ( 1.4 ± 0.5 )× 10−4180 π−ω2π0ντ [a ( 7.1 ± 1.6 )× 10−5181 h−2ωντ < 5.4 × 10−7 CL=90%182 2h−h+ωντ ( 1.20 ± 0.22 )× 10−4183 2π−π+ωντ (ex.K0) [a ( 8.4 ± 0.6 )× 10−5Lepton Family number (LF ), Lepton number (L),Lepton Family number (LF ), Lepton number (L),Lepton Family number (LF ), Lepton number (L),Lepton Family number (LF ), Lepton number (L),or Baryon number (B) violating modesor Baryon number (B) violating modesor Baryon number (B) violating modesor Baryon number (B) violating modesL means lepton number violation (e.g. τ− → e+π−π−). Following ommon usage, LF means lepton family violation and not lepton numberviolation (e.g. τ− → e−π+π−). B means baryon number violation.184 e−γ LF < 3.3 × 10−8 CL=90%185 µ−γ LF < 4.4 × 10−8 CL=90%186 e−π0 LF < 8.0 × 10−8 CL=90%187 µ−π0 LF < 1.1 × 10−7 CL=90%188 e−K0S LF < 2.6 × 10−8 CL=90%189 µ−K0S LF < 2.3 × 10−8 CL=90%190 e−η LF < 9.2 × 10−8 CL=90%191 µ−η LF < 6.5 × 10−8 CL=90%192 e−ρ0 LF < 1.8 × 10−8 CL=90%193 µ−ρ0 LF < 1.2 × 10−8 CL=90%194 e−ω LF < 4.8 × 10−8 CL=90%195 µ−ω LF < 4.7 × 10−8 CL=90%196 e−K∗(892)0 LF < 3.2 × 10−8 CL=90%197 µ−K∗(892)0 LF < 5.9 × 10−8 CL=90%198 e−K∗(892)0 LF < 3.4 × 10−8 CL=90%199 µ−K∗(892)0 LF < 7.0 × 10−8 CL=90%200 e−η′(958) LF < 1.6 × 10−7 CL=90%201 µ−η′(958) LF < 1.3 × 10−7 CL=90%202 e− f0(980) → e−π+π− LF < 3.2 × 10−8 CL=90%203 µ− f0(980) → µ−π+π− LF < 3.4 × 10−8 CL=90%204 e−φ LF < 3.1 × 10−8 CL=90%205 µ−φ LF < 8.4 × 10−8 CL=90%206 e− e+ e− LF < 2.7 × 10−8 CL=90%207 e−µ+µ− LF < 2.7 × 10−8 CL=90%208 e+µ−µ− LF < 1.7 × 10−8 CL=90%209 µ− e+ e− LF < 1.8 × 10−8 CL=90%210 µ+ e− e− LF < 1.5 × 10−8 CL=90%211 µ−µ+µ− LF < 2.1 × 10−8 CL=90%212 e−π+π− LF < 2.3 × 10−8 CL=90%213 e+π−π− L < 2.0 × 10−8 CL=90%214 µ−π+π− LF < 2.1 × 10−8 CL=90%215 µ+π−π− L < 3.9 × 10−8 CL=90%216 e−π+K− LF < 3.7 × 10−8 CL=90%217 e−π−K+ LF < 3.1 × 10−8 CL=90%218 e+π−K− L < 3.2 × 10−8 CL=90%219 e−K0S K0S LF < 7.1 × 10−8 CL=90%220 e−K+K− LF < 3.4 × 10−8 CL=90%221 e+K−K− L < 3.3 × 10−8 CL=90%222 µ−π+K− LF < 8.6 × 10−8 CL=90%223 µ−π−K+ LF < 4.5 × 10−8 CL=90%224 µ+π−K− L < 4.8 × 10−8 CL=90%225 µ−K0S K0S LF < 8.0 × 10−8 CL=90%226 µ−K+K− LF < 4.4 × 10−8 CL=90%227 µ+K−K− L < 4.7 × 10−8 CL=90%228 e−π0π0 LF < 6.5 × 10−6 CL=90%229 µ−π0π0 LF < 1.4 × 10−5 CL=90%230 e−ηη LF < 3.5 × 10−5 CL=90%231 µ−ηη LF < 6.0 × 10−5 CL=90%232 e−π0 η LF < 2.4 × 10−5 CL=90%233 µ−π0 η LF < 2.2 × 10−5 CL=90%234 pµ−µ− L,B < 4.4 × 10−7 CL=90%235 pµ+µ− L,B < 3.3 × 10−7 CL=90%236 pγ L,B < 3.5 × 10−6 CL=90%237 pπ0 L,B < 1.5 × 10−5 CL=90%238 p2π0 L,B < 3.3 × 10−5 CL=90%239 pη L,B < 8.9 × 10−6 CL=90%240 pπ0 η L,B < 2.7 × 10−5 CL=90%241 π− L,B < 7.2 × 10−8 CL=90%

728728728728Lepton Parti le Listingsτ242 π− L,B < 1.4 × 10−7 CL=90%243 e− light boson LF < 2.7 × 10−3 CL=95%244 µ− light boson LF < 5 × 10−3 CL=95%[a Basis mode for the τ .[b See the Parti le Listings below for the energy limits used in this mea-surement. CONSTRAINED FIT INFORMATIONCONSTRAINED FIT INFORMATIONCONSTRAINED FIT INFORMATIONCONSTRAINED FIT INFORMATIONAn overall t to 85 bran hing ratios uses 169 measurements andone onstraint to determine 46 parameters. The overall t has a

χ2 = 134.9 for 124 degrees of freedom.The following o-diagonal array elements are the orrelation oeÆ ients⟨δxiδxj⟩/(δxi·δxj), in per ent, from the t to the bran hing fra tions, xi ≡i/total.x5 18x9 2 −1x10 3 4 5x14 −18 −19 −17 −5x16 −1 −1 1 −2 −9x20 −11 −11 −14 −4 −46 −1x23 −1 0 −2 −3 −1 −14 −10x27 −6 −5 −10 −1 0 0 −39 1x28 −1 −1 −1 −2 0 −13 −3 −23 −11x30 −4 −4 −11 −1 −9 0 7 −2 −44 2x36 −2 −2 −3 −1 −1 0 −2 0 −1 0x38 0 0 0 0 0 −2 0 −3 0 −3x41 −2 −2 −2 −1 −1 0 −2 0 −1 0x43 −1 −1 −1 −1 0 −3 0 −5 0 −5x45 −5 −5 −5 −2 −3 −1 −5 −2 −1 −2x48 0 0 0 0 0 0 0 0 0 0x49 −5 −5 −5 −2 −3 −1 −5 −2 −1 −2x52 0 0 0 0 0 0 0 −1 0 −1x56 −2 −2 −2 −1 −1 −1 −2 −1 −1 −1x61 −5 −5 −5 −2 −3 −1 −4 −2 −1 −2x70 −7 −9 4 −2 −6 3 −12 −2 −7 −1x78 −4 −4 −5 0 −9 0 1 1 −1 1x85 0 0 −2 0 −2 0 0 0 2 0x89 0 0 0 0 0 0 0 0 0 0x97 −2 −2 −1 −1 −1 −1 −4 −1 −2 −1x103 1 1 0 −1 1 −1 −1 −1 0 −1x106 −2 −2 2 −1 −1 2 −2 −1 −1 −1x107 0 0 0 0 0 0 0 0 0 0x117 −1 0 0 0 0 0 −1 0 −1 0x118 0 0 0 0 0 0 0 0 0 0x124 0 0 0 0 0 0 0 0 0 0x125 0 0 0 0 0 0 0 0 0 0x148 −1 −1 −1 0 −1 0 −2 −1 0 −1x149 −1 −1 −1 0 0 0 −1 0 0 0x150 0 0 0 0 0 0 0 −1 0 −1x152 0 0 0 0 0 0 0 0 0 0x154 0 0 0 0 0 0 0 0 0 0x158 −1 −1 −1 0 0 0 −1 0 0 0x168 0 0 0 0 0 0 0 0 0 0x171 0 0 0 0 0 0 −1 0 0 0x176 −3 −3 −3 −1 −4 −1 −1 0 −1 0x177 0 0 0 0 0 0 0 0 0 0x178 −2 −2 −5 −1 −3 0 −2 −1 2 −1x180 0 0 0 0 0 0 0 0 0 0x183 −1 0 0 0 0 0 −1 0 0 0x3 x5 x9 x10 x14 x16 x20 x23 x27 x28

x36 0x38 0 −22x41 0 −13 4x43 0 2 −21 −20x45 0 −3 0 −6 0x48 0 −1 1 −4 1 0x49 0 −5 0 −4 −1 −10 0x52 0 0 7 0 5 0 −7 0x56 0 −2 0 −2 −1 −4 0 −8 0x61 0 −2 0 −2 0 −4 0 −4 0 −2x70 −5 −2 0 −1 0 −4 1 −4 0 −2x78 3 1 0 1 0 2 0 2 0 1x85 2 0 0 0 0 0 0 0 0 0x89 0 0 0 0 0 0 0 0 −1 0x97 −1 −1 0 −1 0 −2 0 −2 0 −1x103 −1 −1 0 −1 0 −1 0 −1 0 −1x106 −1 −1 0 0 0 −1 0 −1 0 0x107 0 0 0 0 0 0 0 0 0 0x117 −1 0 0 0 0 −1 0 −1 0 0x118 0 0 0 0 0 0 0 0 0 0x124 0 0 0 0 0 0 0 0 0 0x125 0 0 0 0 0 0 0 0 0 0x148 −2 0 0 0 0 −1 1 −1 0 0x149 0 0 0 0 0 −1 0 −1 0 0x150 0 0 0 0 0 0 1 0 0 0x152 0 0 0 0 0 0 0 0 0 0x154 0 0 0 0 0 0 0 −1 0 0x158 −1 0 0 0 0 −1 0 −1 0 0x168 0 0 0 0 0 0 0 0 0 0x171 0 0 0 0 0 0 0 0 0 0x176 1 −1 0 0 0 −1 0 −1 0 0x177 0 0 0 0 0 0 0 0 0 0x178 2 −1 0 0 0 −1 0 −1 0 0x180 0 0 0 0 0 0 0 0 0 0x183 −1 0 0 0 0 0 0 0 0 0x30 x36 x38 x41 x43 x45 x48 x49 x52 x56x70 −4x78 2 −19x85 0 −1 −8x89 0 −1 −1 0x97 −2 19 −6 0 0x103 −1 −4 −14 −1 0 −1x106 −1 15 −4 0 0 0 −1x107 0 −1 −1 0 0 0 −3 0x117 −1 0 0 0 −4 0 0 0 0x118 0 0 0 0 0 0 0 0 0 −1x124 0 0 0 0 0 0 0 0 0 3x125 0 0 0 0 0 0 0 0 0 −1x148 −1 0 0 −5 0 0 0 0 0 0x149 −1 −1 0 0 −11 0 0 0 0 10x150 0 2 0 0 0 0 −1 1 0 0x152 0 0 0 −1 0 0 0 0 0 0x154 0 0 0 0 −2 0 0 0 0 0x158 −1 −1 0 0 −8 0 0 0 0 47x168 0 −1 0 0 0 1 0 1 0 0x171 0 0 0 0 −2 0 0 0 0 35x176 −1 −9 −67 −3 0 −2 10 −2 0 0x177 0 0 12 0 0 −2 −58 0 0 0x178 −1 −2 −11 −64 −1 −1 −1 −1 0 0x180 0 0 0 0 −16 0 0 0 0 8x183 0 0 0 0 −4 0 0 0 0 39x61 x70 x78 x85 x89 x97 x103 x106 x107 x117

729729729729See key on page 601 Lepton Parti le Listingsτx124 0x125 0 −1x148 0 0 0x149 0 2 0 0x150 0 0 0 4 0x152 0 0 0 1 0 1x154 0 0 0 2 −1 1 0x158 −1 3 −1 0 25 0 0 0x168 0 0 0 0 0 0 0 0 0x171 −1 1 0 0 4 0 0 0 20 0x176 0 0 0 0 0 0 0 0 0 0x177 0 0 0 0 0 0 0 0 0 0x178 0 0 0 0 0 0 0 0 0 0x180 0 2 0 0 10 0 0 −1 20 0x183 −1 −2 −1 0 17 0 0 0 39 0x118 x124 x125 x148 x149 x150 x152 x154 x158 x168x176 0x177 0 −14x178 0 −4 0x180 3 0 0 0x183 17 0 0 0 14x171 x176 x177 x178 x180

τ BRANCHING FRACTIONS

Revised April 2016 by S.Banerjee (University of Louisville),K.Hayes (Hillsdale College), A.Lusiani (Scuola Normale Supe-riore and INFN, sezione di Pisa)

In order to make optimal use of the experimental data

to determine the τ branching fractions, their uncertainties,

and their correlations, we perform a global minimum χ2 fit

using the measured values, their uncertainties, their statistical

correlations, their dependencies on external parameters and

common systematics, and the relations that hold between the

branching fractions, including a unitarity constraint on the

sum of all the exclusive τ decay branching fractions. Starting

with this edition, we use a new fit procedure, which has been

elaborated by the Tau Physics Group within the Heavy Flavour

Averaging Group (HFAG) [1].

In the following, we use “branching fraction” to refer to

the partial decay fraction of a particle like the τ into a specific

decay mode, and “branching ratio” to refer to quantities derived

from the branching fractions [2], like for instance a ratio of

two branching fractions, or a ratio of two linear combinations

of branching fractions.

The constrained fit to τ branching fractions.

The τ Listings contains 242 τ decay modes, out of which 61

are Lepton Family number, Lepton number, or Baryon number

violating modes. The fit computes the branching fractions of 112

decay modes. Although no new τ branching fraction and ratio

measurements have been released since the 2015 edition, the fit

in this edition includes more experimental measurements (169,

up from 143 in 2015) and determines in the fit several additional

τ branching fractions and ratios, relying on a larger and

updated set of constraints that relate the branching fractions

and ratios between themselves. The measurements are treated

as follows [1].

Many published measurements depend on external param-

eters such as the τ pair production cross-section in e+e−

annihilations at the Υ(4S) peak. We compute the size and

sign of these dependencies and update the measurements and

their uncertainties to the current values of the external param-

eters. Accordingly, the measurements and their uncertainties

are updated to account for updated values of external pa-

rameters. The dependencies on common systematic effects are

also determined in size and sign, and all the common system-

atic dependencies of different measurements are used together

with the published statistical and systematic uncertainties and

correlations in order to compute a single all-inclusive vari-

ance and covariance matrix of the experimental measurements.

All the measurements, their uncertainties, and their correla-

tions were taken from the respective published papers. Their

values and the constraints used in the fit are reported in

the τ Listings section that follows this review. If only a few

measurements are correlated, the correlation coefficients are

listed in the footnote for each measurement (see for exam-

ple Γ(particle− ≥ 0 neutrals ≥ 0 K0ντ (“1-prong”))/Γtotal). If

a large number of measurements are correlated, then the full

correlation matrix is listed in the footnote to the measurement

that first appears in the τ Listings. Footnotes to the other

measurements refer to the first measurement. For example, the

large correlation matrices for the branching fraction or ratio

measurements contained in Refs. [3,4] are listed in Footnotes to

the Γ(e−νeντ )/Γtotal and Γ(h−ντ )/Γtotal measurements respec-

tively. The constraints between the τ branching fractions and

ratios include coefficients that correspond to physical quantities,

like for instance the branching fractions of the η and ω mesons.

All quantities are taken from the 2015 edition of the Review of

Particle Physics. Their uncertainties are neglected in the fit.

Compared to the 2015 edition, the fit now includes several

additional modes, mainly related to the most recent BaBar

papers on high multiplicity modes [5] and K0SK0

S modes [6] and

the Belle paper on neutral kaon modes [7]:

B(τ → π−π0K0SK0

Sντ )

B(τ → K−K−K+ντ )

B(τ → K−π0ηντ )

B(τ → π−K0ηντ ) ;

Also, the following components of τ -decay modes are now

included [5,8,9]:

B(τ → π−2π0ηντ (η → π+π−π0) (ex. K0))

B(τ → 2π−π+ηντ (η → π+π−π0) (ex. K0))

B(τ → 2π−π+ηντ (η → γγ) (ex. K0))

B(τ → π−2π0ωντ (ex. K0))

B(τ → 2π−π+ωντ (ex. K0))

B(τ → π−f1ντ (f1 → 2π−2π+)) .

B(τ → K−φντ ) .

We obtain the branching fraction of τ → a−1 (→ π−γ)ντ

using the ALEPH estimate for B(a−1 → π−γ) [3], which uses the

measurement of Γ(a−1 → π−γ) [10]. In the fit, we assume that

B(τ− → a−1 ντ ) is equal to B(τ → π−π−π+ντ (ex. K0, ω)) +

B(τ → π−2π0ντ (ex. K0)).

730730730730Lepton Parti le Listingsτ

02468

1012141618202224

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5Pull

Num

ber

of m

easu

rem

ents

Figure 1: Pulls of individual measurementsagainst the respective fitted quantity. No scalefactor is used.

In some cases, constraints describe approximate relations

that nevertheless hold within the present experimental pre-

cision. For instance, the constraint B(τ → K−K−K+ντ ) =

B(τ → K−φντ )×B(φ → K+K−) is justified within the current

experimental evidence.

In the fit, scale factors are applied to the published un-

certainties of measurements only if significant inconsistency

between different measurements remain after accounting for

all relevant uncertainties and correlations. After examining the

data and the fit pulls, it has been decided to apply just one scale

factor of 5.4 on the measurements of B(τ → K−K−K+ντ ). The

scale factor has been computed and applied according to the

standard PDG procedure. Without the scale factor applied, the

χ2 probability of the fit is about 2%. On a per-measurement

basis, the pull distribution in figure 1 indicates that just a few

measurements have more than 3σ pulls. (The uncertainties to

obtain the pulls are computed using the measurements variance

matrix and the variance matrix of the result, accounting for the

fact that the variance matrix of the result is obtained from the

measurement variance with the fit.) The pull probability distri-

bution in figure 2 is reasonably flat. With many measurements

some entries on the tails of the normal distribution must be

expected. There are 169 pulls, one per measurement. They are

partially correlated, and the effective number of independent

pulls is equal to the number of degrees of freedom of the fit,

124. Only the τ → K−K−K+ντ decay mode has a pull that

is inconsistent at the level of more than 3σ even if considered

as the largest pull in a set of 124. This confirms the choice of

adopting just that one scale factor.

After scaling the error the 2016 constrained fit has a χ2 of

134.9 for 124 degrees of freedom, corresponding to a χ2 proba-

bility of 24%. We use 169 measurements and 84 constraints on

the branching fractions and ratios to determine 129 quantities,

consisting of 112 branching fractions and 17 branching ratios.

A total of 85 quantities have at least one measurement in the

fit. The constraints include the unitarity constraint on the sum

of all the exclusive τ decay modes, Ball = 1. If the unitarity

0

2

4

6

8

10

12

14

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Probability

Num

ber

of m

easu

rem

ents

Figure 2: Probability of individual measure-ment pulls against the respective fitted quantity.No scale factor is used.

constraint is released, the fit result for Ball is consistent with

unitarity with 1 − Ball = (0.07 ± 0.10)%.

For the convenience of summarizing the fit results, we list in

the following the values and uncertainties for a set of 46 “basis”

decay modes, from which all remaining branching fractions and

ratios can be obtained using the constraints. Unlike in previous

editions, the basis decay modes are not intended to sum up

to 1. The new unitarity constraint corresponds to a linear

combination of the basis modes weighted by the coefficients

listed in the following. The corresponding correlation matrix is

listed in the τ Listings.

decay mode fit result (%) coefficient

µ−νµντ 17.3936 ± 0.0384 1.0000

e−νeντ 17.8174 ± 0.0399 1.0000

π−ντ 10.8165 ± 0.0512 1.0000

K−ντ 0.6964 ± 0.0096 1.0000

π−π0ντ 25.4940 ± 0.0893 1.0000

K−π0ντ 0.4329 ± 0.0148 1.0000

π−2π0ντ (ex. K0) 9.2595 ± 0.0964 1.0021

K−2π0ντ (ex. K0) 0.0648 ± 0.0218 1.0000

π−3π0ντ (ex. K0) 1.0428 ± 0.0707 1.0000

K−3π0ντ (ex. K0, η) 0.0478 ± 0.0212 1.0000

h−4π0ντ (ex. K0, η) 0.1119 ± 0.0391 1.0000

π−K0ντ 0.8395 ± 0.0140 1.0000

K−K0ντ 0.1479 ± 0.0053 1.0000

π−K0π0ντ 0.3821 ± 0.0129 1.0000

K−π0K0ντ 0.1503 ± 0.0071 1.0000

π−K0π0π0ντ (ex. K0) 0.0263 ± 0.0226 1.0000

π−K0SK0

Sντ 0.0233 ± 0.0007 2.0000

π−K0SK0

Lντ 0.1080 ± 0.0241 1.0000

π−π0K0SK0

Sντ 0.0018 ± 0.0002 2.0000

π−π0K0SK0

Lντ 0.0325 ± 0.0119 1.0000

K0h−h−h+ντ 0.0247 ± 0.0199 1.0000

π−π−π+ντ (ex. K0, ω) 8.9870 ± 0.0514 1.0021

π−π−π+π0ντ (ex. K0, ω) 2.7404 ± 0.0710 1.0000

h−h−h+2π0ντ (ex. K0, ω, η) 0.0980 ± 0.0356 1.0000

731731731731See key on page 601 Lepton Parti le Listingsτ

π−K−K+ντ 0.1435 ± 0.0027 1.0000

π−K−K+π0ντ 0.0061 ± 0.0018 1.0000

π−π0ηντ 0.1389 ± 0.0072 1.0000

K−ηντ 0.0155 ± 0.0008 1.0000

K−π0ηντ 0.0048 ± 0.0012 1.0000

π−K0ηντ 0.0094 ± 0.0015 1.0000

π−π+π−ηντ (ex. K0) 0.0219 ± 0.0013 1.0000

K−ωντ 0.0410 ± 0.0092 1.0000

h−π0ωντ 0.4085 ± 0.0419 1.0000

K−φντ 0.0044 ± 0.0016 0.8310

π−ωντ 1.9494 ± 0.0645 1.0000

K−π−π+ντ (ex. K0, ω) 0.2927 ± 0.0068 1.0000

K−π−π+π0ντ (ex. K0, ω, η) 0.0394 ± 0.0142 1.0000

π−2π0ωντ (ex. K0) 0.0071 ± 0.0016 1.0000

2π−π+3π0ντ (ex. K0, η, ω, f1) 0.0014 ± 0.0027 1.0000

3π−2π+ντ (ex. K0, ω, f1) 0.0769 ± 0.0030 1.0000

K−2π−2π+ντ (ex. K0) 0.0001 ± 0.0001 1.0000

2π−π+ωντ (ex. K0) 0.0084 ± 0.0006 1.0000

3π−2π+π0ντ (ex. K0, η, ω, f1) 0.0038 ± 0.0009 1.0000

K−2π−2π+π0ντ (ex. K0) 0.0001 ± 0.0001 1.0000

π−f1ντ (f1 → 2π−2π+) 0.0052 ± 0.0004 1.0000

π−2π0ηντ 0.0194 ± 0.0038 1.0000

Applying the fit procedure on the PDG 2015 inputs, the

fit results differ from the 2015 fit by at most 20% of their

uncertainty, for fitted quantities that have measurements with

asymmetric errors, and by at most 5% of their uncertainty for

the other quantities. The differences originate from the differ-

ent treatment of asymmetric errors. The present fit procedure

symmetrizes the errors as σ2symm = (σ2

+ +σ2−)/2, while the PDG

2015 fit did model the asymmetric error distributions in the fit.

Comparing the results of the previous edition with the current

fit, there are differences up to 2.3 times the fitted quantity

uncertainty (2.3σ) for quantities that have no measurement in-

cluded in the fit and are derived through the constraints. Those

differences arise mainly from three changes: the unitarity con-

straint has been updated to accomodate several additional decay

modes, the definitions of the respective quantities have been

updated to use the additional decay modes, and the parameters

of all constraints (typically, K, η, ω branching fractions) have

been updated to the values reported in the last published PDG

edition. For quantities that have measurements in the fit, the

fitted values changed at most by 1.1σ, reflecting the inclusion of

several additional measurements, especially on high-multiplicity

decay modes. The uncertainties on the fit results are generally

smaller than in 2015 because only one error scale factor is used

and some additional measurements have been used.

In defining the fit constraints and in selecting the modes

that sum up to one we made some assumptions and choices. We

assume that some channels, like τ− → π−K+π− ≥ 0π0ντ and

τ− → π+K−K− ≥ 0π0ντ , have negligible branching fractions

as expected from the Standard Model, even if the experimental

limits for these branching fractions are not very stringent. The

95% confidence level upper limits are B(τ− → π−K+π− ≥

0π0ντ ) < 0.25% and B(τ− → π+K−K− ≥ 0π0ντ ) < 0.09%,

values not so different from measured branching fractions for

allowed 3-prong modes containing charged kaons. For decays

to final states containing one neutral kaon we assume that

the branching fraction with the K0L are the same as the

corresponding one with a K0S. On decays with two neutral

kaons we assume that the branching fractions with K0LK0

L are

the same as the ones with K0SK0

S.

BaBar and Belle measure on average lower branching

fractions and ratios.

We compare the BaBar and Belle measurements with the

results of a fit where all their measurements have been excluded.

We find that that BaBar and Belle tend to measure lower τ

branching fractions and ratios than the other experiments.

Figure 3 shows histograms of the 27 normalized differences

between the B-factory measurements and the respective non-

B-factory fit results. The normalization is the uncertainty on

the difference. The average normalized difference between the

two sets of measurements is -0.8σ (-0.8σ for the 16 Belle

measurements and -0.9σ for the 11 BaBar measurements).

Belle

0

1

2

3

4

−3 −2 −1 0 1 2 3standard deviations

num

ber

of m

easu

rem

ents

BaBar

0

1

2

3

4

−3 −2 −1 0 1 2 3standard deviations

num

ber

of m

easu

rem

ents

Figure 3: Distribution of the normalized dif-ference between the 27 B-factory measurementsand non-B-factory measurements. The list in-cludes 16 measurements of branching fractionsand ratios published by the Belle collaborationand 11 by the BaBar collaboration that areused in the fit and for which non-B-factorymeasurements exist.

Overconsistency of Leptonic Branching Fraction Mea-

surements.

As observed in the previous editions of this review, measure-

ments of the leptonic branching fractions are more consistent

with each other than expected from the quoted errors on the

individual measurements. The χ2 is 0.34 for Be and 0.08 for

732732732732Lepton Parti le Listingsτ

Bµ. Assuming normal errors, the probability of a smaller χ2 is

1.3% for Be and 0.08% for Bµ.

Technical implementation of the fit.

The fit computes a set of quantities denoted with qi by min-

imizing a χ2 while respecting a series of equality constraints on

the qi. The χ2 is computed using the measurements mi and their

covariance matrix Eij as χ2 = (mi − Aikqk)tE−1

ij (mj − Ajlql)

where the model matrix Aij is used to get the vector of the

predicted measurements m′i from the vector of the fit param-

eters qj as m′i = Aijqj . In this particular implementation the

measurements are grouped by the quantity that they measure,

and all quantities with at least one measurement correspond

to a fit parameter. Therefore, the matrix Aij has one row per

measurement mi and one column per fitted quantity qj , with

unity coefficients for the rows and column that identify a mea-

surement mi of the quantity qj , respectively. The constraints

are equations involving the fit parameters. The fit does not

impose limitations on the functional form of the constraints. In

summary, the fit requires:

min(mi − Aikqk)tE−1

ij (mj − Ajlql), (1a)

subjected to fr(qs) − cr = 0, (1b)

where the left term of Eq. (1b) defines the constraint expressions.

Using the method of Lagrange multipliers, a set of equations

is obtained by taking the derivatives with respect to the fitted

quantities qk and the Lagrange multipliers λr of the sum of the

χ2 and the constraint expressions multiplied by the Lagrange

multipliers λr, one for each constraint:

min[(Aikqk−mi)

tE−1ij (Ajlql−mj) + 2λr(fr(qs) − cr)

](2a)

(∂/∂qk, ∂/∂λr)[expression above] = 0 (2b)

Eq. (2b) defines a set of equations for the vector of the unknowns

(qk, λr), some of which may be non-linear, in case of non-linear

constraints. An iterative minimization procedure approximates

at each step the non-linear constraint expressions by their first

order Taylor expansion around the current values of the fitted

quantities, qs:

fr(qs) − cr = fr(qs) +∂fr(qs)

∂qs

∣∣∣∣qs

(qs − qs) − cr, (3a)

which can be written as

Brsqs − c′r, (3b)

where c′r are the resulting constant known terms, independent

of qs at first order. After linearization, the differentiation by qk

and λr is trivial and leads to a set of linear equations

AtkiE

−1ij Ajlql + Bt

krλr = AtkiE

−1ij mj (4a)

Brsqs = c′r, (4b)

which can be expressed as:

Fijuj = vi (5)

where uj = (qk, λr) and vi is the vector of the known constant

terms running over the index k and then r in the right terms of

Eq. (4a) and Eq. (4b), respectively. Solving the equation set in

Eq. (5) by matrix inversion gives the the fitted quantities and

their variance and covariance matrix, using the measurements

and their variance and covariance matrix. The fit procedure

starts by computing the linear approximation of the non-linear

constraint expressions around the quantities seed values. With

an iterative procedure, the unknowns are updated at each step

by solving the equations and the equations are then linearized

around the updated values, until the variation of the fitted

unknowns is reduced below a numerically small threshold.

References

1. D. Asner et al. (HFAG), arXiv:1010.1589; Y. Amhiset al. (HFAG), arXiv:1412.7515.

2. See the Introduction section of this edition of the Review

of Particle Physics.

3. S. Schael et al. (ALEPH Collab.), Phys. Reports 421, 191(2005).

4. J. Abdallah et al. (DELPHI Collab.), Eur. Phys. J. C46,1 (2006).

5. J.P. Lees et al. (BABAR Collab.), Phys. Rev. D86, 092010(2012), [arXiv:1209.2734].

6. J.P. Lees et al. (BABAR Collab.), Phys. Rev. D86, 092013(2012), [arXiv:1208.0376].

7. S. Ryu et al. (BELLE Collab.), Phys. Rev. D89, 072009(2014).

8. B. Aubert et al. (BABAR Collab.), Phys. Rev. Lett. 100,011801 (2008).

9. K. Inami et al. (BELLE Collab.), Phys. Lett. B643, 5(2006).

10. M. Zielinski et al., Phys. Rev. Lett. 52, 1195 (1984).((τ+) − (τ−)) / ((τ+) + (τ−))((τ+) − (τ−)) / ((τ+) + (τ−))((τ+) − (τ−)) / ((τ+) + (τ−))((τ+) − (τ−)) / ((τ+) + (τ−))τ± → π±K0S ντ (RATE DIFFERENCE) / (RATE SUM)τ± → π±K0S ντ (RATE DIFFERENCE) / (RATE SUM)τ± → π±K0S ντ (RATE DIFFERENCE) / (RATE SUM)τ± → π±K0S ντ (RATE DIFFERENCE) / (RATE SUM)VALUE (%) DOCUMENT ID TECN COMMENT−0.36±0.23±0.11−0.36±0.23±0.11−0.36±0.23±0.11−0.36±0.23±0.11 LEES 12M BABR 476 fb−1 Eee m = 10.6 GeV

τ− BRANCHING RATIOSτ− BRANCHING RATIOSτ− BRANCHING RATIOSτ− BRANCHING RATIOS(parti le− ≥ 0 neutrals ≥ 0K 0ντ (\1-prong"))/total 1/(parti le− ≥ 0 neutrals ≥ 0K 0ντ (\1-prong"))/total 1/(parti le− ≥ 0 neutrals ≥ 0K 0ντ (\1-prong"))/total 1/(parti le− ≥ 0 neutrals ≥ 0K 0ντ (\1-prong"))/total 1/1/ = (3+5+9+10+14+16+20+23+27+28+30+36+38+41+43+45+48+49+50+52+56+57+0.7212148+0.7212150+0.7212152+0.7212154+0.342168+0.0828176+0.0828177+0.0828178)/The harged parti le here an be e, µ, or hadron. In many analyses, the sum of thetopologi al bran hing fra tions (1, 3, and 5 prongs) is onstrained to be unity. Sin ethe 5-prong fra tion is very small, the measured 1-prong and 3-prong fra tions arehighly orrelated and annot be treated as independent quantities in our overall t.We arbitrarily hoose to use the 3-prong fra tion in our t, and leave the 1-prongfra tion out. We do, however, use these 1-prong measurements in our average below.The measurements used only for the average are marked \avg," whereas \f&a" marksa result used for the t and the average.VALUE (%) EVTS DOCUMENT ID TECN COMMENT85.24 ±0.06 OUR FIT85.24 ±0.06 OUR FIT85.24 ±0.06 OUR FIT85.24 ±0.06 OUR FIT85.26 ±0.13 OUR AVERAGE85.26 ±0.13 OUR AVERAGE85.26 ±0.13 OUR AVERAGE85.26 ±0.13 OUR AVERAGE Error in ludes s ale fa tor of 1.6. See the ideogrambelow.• • • We use the following data for averages but not for ts. • • •85.316±0.093±0.049 78k 1 ABREU 01M DLPH 19921995 LEP runs85.274±0.105±0.073 2 ACHARD 01D L3 19921995 LEP runs84.48 ±0.27 ±0.23 ACTON 92H OPAL 19901991 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •85.45 +0.69

−0.73 ±0.65 DECAMP 92C ALEP Repl. by SCHAEL 05C

733733733733See key on page 601 Lepton Parti le Listingsτ1The orrelation oeÆ ients between this measurement and the ABREU 01M measure-ments of B(τ → 3-prong) and B(τ → 5-prong) are −0.98 and −0.08 respe tively.2The orrelation oeÆ ients between this measurement and the ACHARD 01D measure-ments of B(τ → \3-prong") and B(τ → \5-prong") are−0.978 and −0.082 respe tively.

WEIGHTED AVERAGE85.26±0.13 (Error scaled by 1.6)

Values above of weighted average, error,and scale factor are based upon the data inthis ideogram only. They are not neces-sarily the same as our ‘best’ values,obtained from a least-squares constrained fitutilizing measurements of other (related)quantities as additional information.

ACTON 92H OPAL 4.8ACHARD 01D L3 0.0ABREU 01M DLPH 0.3

χ2

5.1(Confidence Level = 0.077)

83.5 84 84.5 85 85.5 86 86.5 87(parti le− ≥ 0 neutrals ≥ 0K0 ντ (\1-prong"))/total (%)(parti le− ≥ 0 neutrals ≥ 0K 0Lντ

)/total 2/(parti le− ≥ 0 neutrals ≥ 0K 0Lντ



)/total 2/2/ = (3+5+9+10+14+16+20+23+27+28+30+0.653436+0.653438+0.653441+0.653443+0.653445+0.094248+0.306949+50+0.094252+0.306956+57+0.7212148+0.7212150+0.7212152+0.4712154+0.1049168+0.0828176+0.0828177+0.0828178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT84.58±0.06 OUR FIT84.58±0.06 OUR FIT84.58±0.06 OUR FIT84.58±0.06 OUR FIT85.1 ±0.4 OUR AVERAGE85.1 ±0.4 OUR AVERAGE85.1 ±0.4 OUR AVERAGE85.1 ±0.4 OUR AVERAGE• • • We use the following data for averages but not for ts. • • •85.6 ±0.6 ±0.3 3300 1 ADEVA 91F L3 Eee m= 88.394.3 GeV84.9 ±0.4 ±0.3 BEHREND 89B CELL Eee m= 1447 GeV84.7 ±0.8 ±0.6 2 AIHARA 87B TPC Eee m= 29 GeV• • • We do not use the following data for averages, ts, limits, et . • • •86.4 ±0.3 ±0.3 ABACHI 89B HRS Eee m= 29 GeV87.1 ±1.0 ±0.7 3 BURCHAT 87 MRK2 Eee m= 29 GeV87.2 ±0.5 ±0.8 SCHMIDKE 86 MRK2 Eee m= 29 GeV84.7 ±1.1 +1.6

−1.3 169 4 ALTHOFF 85 TASS Eee m= 34.5 GeV86.1 ±0.5 ±0.9 BARTEL 85F JADE Eee m= 34.6 GeV87.8 ±1.3 ±3.9 5 BERGER 85 PLUT Eee m= 34.6 GeV86.7 ±0.3 ±0.6 FERNANDEZ 85 MAC Eee m= 29 GeV1Not independent of ADEVA 91F (h− h− h+ ≥ 0 neutrals ≥ 0K0L ντ)/total value.2Not independent of AIHARA 87B (

µ− νµντ)/total, (e− νe ντ

)/total, and(h− ≥ 0 neutrals ≥ 0K0L ντ)/total values.3Not independent of SCHMIDKE 86 value (also not independent of BURCHAT 87 valuefor (h− h− h+ ≥ 0 neutrals ≥ 0K0L ντ

)/total.4Not independent of ALTHOFF 85 (µ− νµντ

)/total, (e− νe ντ)/total, (h− ≥ 0neutrals ≥ 0K0L ντ

)/total, and (h− h− h+ ≥ 0 neutrals ≥ 0K0L ντ)/total values.5Not independent of (1-prong + 0π0) and (1-prong + ≥ 1π0) values.(µ−νµ ντ

)/total 3/(µ−νµ ντ



)/total 3/To minimize the ee t of experiments with large systemati errors, we ex lude exper-iments whi h together would ontribute 5% of the weight in the average.VALUE (%) EVTS DOCUMENT ID TECN COMMENT17.39 ±0.04 OUR FIT17.39 ±0.04 OUR FIT17.39 ±0.04 OUR FIT17.39 ±0.04 OUR FIT17.33 ±0.05 OUR AVERAGE17.33 ±0.05 OUR AVERAGE17.33 ±0.05 OUR AVERAGE17.33 ±0.05 OUR AVERAGE17.319±0.070±0.032 54k 1 SCHAEL 05C ALEP 1991-1995 LEP runs17.34 ±0.09 ±0.06 31.4k ABBIENDI 03 OPAL 1990-1995 LEP runs17.342±0.110±0.067 21.5k 2 ACCIARRI 01F L3 1991-1995 LEP runs17.325±0.095±0.077 27.7k ABREU 99X DLPH 1991-1995 LEP runs• • • We use the following data for averages but not for ts. • • •17.37 ±0.08 ±0.18 3 ANASTASSOV 97 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •17.31 ±0.11 ±0.05 20.7k BUSKULIC 96C ALEP Repl. by SCHAEL 05C17.02 ±0.19 ±0.24 6586 ABREU 95T DLPH Repl. by ABREU 99X17.36 ±0.27 7941 AKERS 95I OPAL Repl. by ABBIENDI 0317.6 ±0.4 ±0.4 2148 ADRIANI 93M L3 Repl. by ACCIARRI 01F17.4 ±0.3 ±0.5 4 ALBRECHT 93G ARG Eee m= 9.410.6 GeV17.35 ±0.41 ±0.37 DECAMP 92C ALEP 1989-1990 LEP runs17.7 ±0.8 ±0.4 568 BEHREND 90 CELL Eee m= 35 GeV17.4 ±1.0 2197 ADEVA 88 MRKJ Eee m= 1416 GeV17.7 ±1.2 ±0.7 AIHARA 87B TPC Eee m= 29 GeV

18.3 ±0.9 ±0.8 BURCHAT 87 MRK2 Eee m= 29 GeV18.6 ±0.8 ±0.7 558 5 BARTEL 86D JADE Eee m= 34.6 GeV12.9 ±1.7 +0.7−0.5 ALTHOFF 85 TASS Eee m= 34.5 GeV18.0 ±0.9 ±0.5 473 5 ASH 85B MAC Eee m= 29 GeV18.0 ±1.0 ±0.6 6 BALTRUSAIT...85 MRK3 Eee m= 3.77 GeV19.4 ±1.6 ±1.7 153 BERGER 85 PLUT Eee m= 34.6 GeV17.6 ±2.6 ±2.1 47 BEHREND 83C CELL Eee m= 34 GeV17.8 ±2.0 ±1.8 BERGER 81B PLUT Eee m= 932 GeV1See footnote to SCHAEL 05C (τ− → e− νe ντ )/total measurement for orrelationswith other measurements.2The orrelation oeÆ ient between this measurement and the ACCIARRI 01F measure-ment of B(τ− → e− νe ντ ) is 0.08.3The orrelation oeÆ ients between this measurement and the ANASTASSOV 97 mea-surements of B(e νe ντ ), B(µνµ ντ )/B(e νe ντ ), B(h− ντ ), and B(h− ντ )/B(e νe ντ )are 0.50, 0.58, 0.50, and 0.08 respe tively.4Not independent of ALBRECHT 92D (µ− νµντ )/(e− νe ντ ) and ALBRECHT 93G(µ− νµ ντ )× (e− νe ντ )/2total values.5Modied using B(e− νe ντ )/B(\1 prong") and B(\1 prong") ,= 0.855.6 Error orrelated with BALTRUSAITIS 85 e ν ν value.(µ−νµ ντ γ)/total 4/(µ−νµ ντ γ)/total 4/(µ−νµ ντ γ)/total 4/(µ−νµ ντ γ)/total 4/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.368±0.010 OUR AVERAGE0.368±0.010 OUR AVERAGE0.368±0.010 OUR AVERAGE0.368±0.010 OUR AVERAGE0.369±0.003±0.010 16k 1 LEES 15G BABR 431 fb−1 Eee m=10.6 GeV0.361±0.016±0.035 2 BERGFELD 00 CLEO Eee m= 10.6 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •0.30 ±0.04 ±0.05 116 3 ALEXANDER 96S OPAL 19911994 LEP runs0.23 ±0.10 10 4 WU 90 MRK2 Eee m= 29 GeV1LEES 15G impose requirements on dete ted γ's orresponding to a τ -rest-frame energy uto E∗γ > 10 MeV.2BERGFELD 00 impose requirements on dete ted γ's orresponding to a τ -rest-frameenergy uto E∗γ > 10 MeV. For E∗γ > 20 MeV, they quote (3.04± 0.14± 0.30)×10−3.3ALEXANDER 96S impose requirements on dete ted γ's orresponding to a τ -rest-frameenergy uto Eγ >20 MeV.4WU 90 reports (µ− νµντ γ)/(µ− νµντ ) = 0.013 ± 0.006, whi h is onverted to(µ− νµ ντ γ)/total using (µ− νµ ντ γ)/total = 17.35%. Requirements on dete tedγ's orrespond to a τ rest frame energy uto Eγ > 37 MeV.(e− νe ντ

)/total 5/(e− νe ντ



)/total 5/To minimize the ee t of experiments with large systemati errors, we ex lude exper-iments whi h together would ontribute 5% of the weight in the average.VALUE (%) EVTS DOCUMENT ID TECN COMMENT17.82 ±0.04 OUR FIT17.82 ±0.04 OUR FIT17.82 ±0.04 OUR FIT17.82 ±0.04 OUR FIT17.82 ±0.05 OUR AVERAGE17.82 ±0.05 OUR AVERAGE17.82 ±0.05 OUR AVERAGE17.82 ±0.05 OUR AVERAGE17.837±0.072±0.036 56k 1 SCHAEL 05C ALEP 1991-1995 LEP runs17.806±0.104±0.076 24.7k 2 ACCIARRI 01F L3 19911995 LEP runs17.81 ±0.09 ±0.06 33.1k ABBIENDI 99H OPAL 19911995 LEP runs17.877±0.109±0.110 23.3k ABREU 99X DLPH 19911995 LEP runs17.76 ±0.06 ±0.17 3 ANASTASSOV 97 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •17.78 ±0.10 ±0.09 25.3k ALEXANDER 96D OPAL Repl. by ABBI-ENDI 99H17.79 ±0.12 ±0.06 20.6k BUSKULIC 96C ALEP Repl. by SCHAEL 05C17.51 ±0.23 ±0.31 5059 ABREU 95T DLPH Repl.. by ABREU 99X17.9 ±0.4 ±0.4 2892 ADRIANI 93M L3 Repl. by ACCIARRI 01F17.5 ±0.3 ±0.5 4 ALBRECHT 93G ARG Eee m= 9.410.6 GeV17.97 ±0.14 ±0.23 3970 AKERIB 92 CLEO Repl. by ANAS-TASSOV 9719.1 ±0.4 ±0.6 2960 5 AMMAR 92 CLEO Eee m= 10.510.9 GeV18.09 ±0.45 ±0.45 DECAMP 92C ALEP Repl. by SCHAEL 05C17.0 ±0.5 ±0.6 1.7k ABACHI 90 HRS Eee m= 29 GeV18.4 ±0.8 ±0.4 644 BEHREND 90 CELL Eee m= 35 GeV16.3 ±0.3 ±3.2 JANSSEN 89 CBAL Eee m= 9.410.6 GeV18.4 ±1.2 ±1.0 AIHARA 87B TPC Eee m= 29 GeV19.1 ±0.8 ±1.1 BURCHAT 87 MRK2 Eee m= 29 GeV16.8 ±0.7 ±0.9 515 5 BARTEL 86D JADE Eee m= 34.6 GeV20.4 ±3.0 +1.4

−0.9 ALTHOFF 85 TASS Eee m= 34.5 GeV17.8 ±0.9 ±0.6 390 5 ASH 85B MAC Eee m= 29 GeV18.2 ±0.7 ±0.5 6 BALTRUSAIT...85 MRK3 Eee m= 3.77 GeV13.0 ±1.9 ±2.9 BERGER 85 PLUT Eee m= 34.6 GeV18.3 ±2.4 ±1.9 60 BEHREND 83C CELL Eee m= 34 GeV16.0 ±1.3 459 7 BACINO 78B DLCO Eee m= 3.17.4 GeV1Correlation matrix for SCHAEL 05C bran hing fra tions, in per ent:(1) (τ− → e− νe ντ )/total(2) (τ− → µ− νµντ )/total(3) (τ− → π− ντ )/total(4) (τ− → π−π0 ντ )/total(5) (τ− → π− 2π0 ντ (ex.K0))/total

734734734734LeptonParti le Listingsτ (6) (τ− → π− 3π0 ντ (ex.K0))/total(7) (τ− → h− 4π0 ντ (ex.K0,η))/total(8) (τ− → π−π+π− ντ (ex.K0,ω))/total(9) (τ− → π−π+π−π0 ντ (ex.K0))/total(10) (τ− → h− h− h+2π0 ντ (ex.K0))/total(11) (τ− → h− h− h+3π0 ντ )/total(12) (τ− → 3h− 2h+ ντ (ex.K0))/total(13) (τ− → 3h− 2h+π0 ντ (ex.K0))/total(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)(2) -20(3) -9 -6(4) -16 -12 2(5) -5 -5 -17 -37(6) 0 -4 -15 2 -27(7) -2 -4 -24 -15 20 -47(8) -14 -9 15 -5 -17 -14 -8(9) -13 -12 -25 -30 4 -2 16 -15(10) 0 -2 -23 -14 4 10 13 -6 -17(11) 1 0 -5 1 4 6 0 -9 -2 -11(12) 0 1 9 4 -8 -4 -6 9 -5 -4 -2(13) 1 -4 -3 -5 3 2 -4 -3 -1 4 1 -242The orrelation oeÆ ient between this measurement and the ACCIARRI 01F measure-ment of B(τ− → µ− νµ ντ ) is 0.08.3The orrelation oeÆ ients between this measurement and the ANASTASSOV 97 mea-surements of B(µνµ ντ ), B(µνµ ντ )/B(e νe ντ ), B(h− ντ ), and B(h− ντ )/B(e νe ντ )are 0.50, −0.42, 0.48, and −0.39 respe tively.4Not independent of ALBRECHT 92D (µ− νµντ )/(e− νe ντ ) and ALBRECHT 93G(µ− νµ ντ )× (e− νe ντ )/2total values.5Modied using B(e− νe ντ )/B(\1 prong") and B(\1 prong") ,= 0.855.6 Error orrelated with BALTRUSAITIS 85 (

µ− νµ ντ)/total.7BACINO 78B value omes from t to events with e± and one other nonele tron hargedprong.(µ−νµ ντ

)/(e− νe ντ

) 3/5(µ−νµ ντ

)/(e− νe ντ

) 3/5(µ−νµ ντ

)/(e− νe ντ

) 3/5(µ−νµ ντ

)/(e− νe ντ

) 3/5Standard Model predi tion in luding mass ee ts is 0.9726.VALUE (units 10−2) EVTS DOCUMENT ID TECN COMMENT97.62±0.28 OUR FIT97.62±0.28 OUR FIT97.62±0.28 OUR FIT97.62±0.28 OUR FIT97.9 ±0.4 OUR AVERAGE97.9 ±0.4 OUR AVERAGE97.9 ±0.4 OUR AVERAGE97.9 ±0.4 OUR AVERAGE97.96±0.16±0.36 731k 1 AUBERT 10F BABR 467 fb−1 Eee m= 10.6 GeV97.77±0.63±0.87 2 ANASTASSOV 97 CLEO Eee m= 10.6 GeV99.7 ±3.5 ±4.0 ALBRECHT 92D ARG Eee m= 9.410.6 GeV1Correlation matrix for AUBERT 10F bran hing fra tions:(1) (τ− → µ− νµντ ) / (τ− → e− νe ντ )(2) (τ− → π− ντ ) / (τ− → e− νe ντ )(3) (τ− → K− ντ ) / (τ− → e− νe ντ )(1) (2)(2) 0.25(3) 0.12 0.332The orrelation oeÆ ients between this measurement and the ANASTASSOV 97 mea-surements of B(µνµ ντ ), B(e νe ντ ), B(h− ντ ), and B(h− ντ )/B(e νe ντ ) are 0.58,−0.42, 0.07, and 0.45 respe tively.(e− νe ντ γ

)/total 6/(e− νe ντ γ)/total 6/(e− νe ντ γ)/total 6/(e− νe ντ γ)/total 6/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.84 ±0.05 OUR AVERAGE1.84 ±0.05 OUR AVERAGE1.84 ±0.05 OUR AVERAGE1.84 ±0.05 OUR AVERAGE1.847±0.015±0.052 18k 1 LEES 15G BABR 431 fb−1 Eee m=10.6 GeV1.75 ±0.06 ±0.17 2 BERGFELD 00 CLEO Eee m= 10.6 GeV1LEES 15G impose requirements on dete ted γ's orresponding to a τ -rest-frame energy uto E∗γ > 10 MeV.2BERGFELD 00 impose requirements on dete ted γ's orresponding to a τ -rest-frameenergy uto E∗γ > 10 MeV.(h− ≥ 0K0L ντ

)/total 7/(h− ≥ 0K0L ντ



)/total 7/7/ = (9+10+1236+1238+50)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT12.03±0.05 OUR FIT12.03±0.05 OUR FIT12.03±0.05 OUR FIT12.03±0.05 OUR FIT12.2 ±0.4 OUR AVERAGE12.2 ±0.4 OUR AVERAGE12.2 ±0.4 OUR AVERAGE12.2 ±0.4 OUR AVERAGE12.47±0.26±0.43 2967 1 ACCIARRI 95 L3 1992 LEP run12.4 ±0.7 ±0.7 283 2 ABREU 92N DLPH 1990 LEP run12.1 ±0.7 ±0.5 309 ALEXANDER 91D OPAL 1990 LEP run• • • We use the following data for averages but not for ts. • • •11.3 ±0.5 ±0.8 798 3 FORD 87 MAC Eee m= 29 GeV• • • We do not use the following data for averages, ts, limits, et . • • •12.44±0.11±0.11 15k 4 BUSKULIC 96 ALEP Repl. by SCHAEL 05C11.7 ±0.6 ±0.8 5 ALBRECHT 92D ARG Eee m= 9.410.6 GeV12.98±0.44±0.33 6 DECAMP 92C ALEP Repl. by SCHAEL 05C12.3 ±0.9 ±0.5 1338 BEHREND 90 CELL Eee m= 35 GeV

11.1 ±1.1 ±1.4 7 BURCHAT 87 MRK2 Eee m= 29 GeV12.3 ±0.6 ±1.1 328 8 BARTEL 86D JADE Eee m= 34.6 GeV13.0 ±2.0 ±4.0 BERGER 85 PLUT Eee m= 34.6 GeV11.2 ±1.7 ±1.2 34 9 BEHREND 83C CELL Eee m= 34 GeV1ACCIARRI 95 with 0.65% added to remove their orre tion for π−K0L ba kgrounds.2ABREU 92N with 0.5% added to remove their orre tion for K∗(892)− ba kgrounds.3 FORD 87 result for B(π− ντ ) with 0.67% added to remove their K− orre tion andadjusted for 1992 B(\1 prong").4BUSKULIC 96 quote 11.78 ± 0.11 ± 0.13 We add 0.66 to undo their orre tion forunseen K0L and modify the systemati error a ordingly.5Not independent of ALBRECHT 92D (µ− νµ ντ )/(e− νe ντ ), (µ− νµ ντ ) ×(e− νe ντ ), and (h− ≥ 0K0L ντ )/(e− νe ντ ) values.6DECAMP 92C quote B(h− ≥ 0K0L ≥ 0 (K0S → π+π−) ντ ) = 13.32 ± 0.44 ± 0.33.We subtra t 0.35 to orre t for their in lusion of the K0S de ays.7BURCHAT 87 with 1.1% added to remove their orre tion for K− and K∗(892)− ba k-grounds.8BARTEL 86D result for B(π− ντ ) with 0.59% added to remove their K− orre tion andadjusted for 1992 B(\1 prong").9BEHREND 83C quote B(π− ντ ) = 9.9± 1.7± 1.3 after subtra ting 1.3± 0.5 to orre tfor B(K− ντ ).(h−ντ

)/total 8/= (9+10)/(h−ντ

)/total 8/= (9+10)/(h−ντ

)/total 8/= (9+10)/(h−ντ

)/total 8/= (9+10)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT11.51 ±0.05 OUR FIT11.51 ±0.05 OUR FIT11.51 ±0.05 OUR FIT11.51 ±0.05 OUR FIT11.63 ±0.12 OUR AVERAGE11.63 ±0.12 OUR AVERAGE11.63 ±0.12 OUR AVERAGE11.63 ±0.12 OUR AVERAGE Error in ludes s ale fa tor of 1.4. See the ideogrambelow.11.571±0.120±0.114 19k 1 ABDALLAH 06A DLPH 19921995 LEP runs11.98 ±0.13 ±0.16 ACKERSTAFF 98M OPAL 19911995 LEP runs11.52 ±0.05 ±0.12 2 ANASTASSOV 97 CLEO Eee m= 10.6 GeV1Correlation matrix for ABDALLAH 06A bran hing fra tions, in per ent:(1) (τ− → h− ντ )/total(2) (τ− → h−π0 ντ )/total(3) (τ− → h− ≥ 1π0 ντ (ex.K0))/total(4) (τ− → h− 2π0 ντ (ex.K0))/total(5) (τ− → h− ≥ 3π0 ντ (ex. K0))/total(6) (τ− → h− h− h+ ντ (ex.K0))/total(7) (τ− → h− h− h+π0 ντ (ex.K0))/total(8) (τ− → h− h− h+ ≥ 1π0 ντ (ex. K0))/total(9) (τ− → h− h− h+ ≥ 2π0 ντ (ex. K0))/total(10) (τ− → 3h− 2h+ ντ (ex.K0))/total(11) (τ− → 3h− 2h+π0 ντ (ex.K0))/total(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)(2) -34(3) -47 56(4) 6 -66 15(5) -6 38 11 -86(6) -7 -8 15 0 -2(7) -2 -1 -5 -3 3 -53(8) -4 -4 -13 -4 -2 -56 75(9) -1 -1 -4 3 -6 26 -78 -16(10) -1 -1 1 0 0 -2 -3 -1 3(11) 0 0 0 0 0 1 0 -5 5 -572The orrelation oeÆ ients between this measurement and the ANASTASSOV 97 mea-surements of B(µνµ ντ ), B(e νe ντ ), B(µνµ ντ )/B(e νe ντ ), and B(h− ντ )/B(e νe ντ )are 0.50, 0.48, 0.07, and 0.63 respe tively.WEIGHTED AVERAGE11.63±0.12 (Error scaled by 1.4)


ANASTASSOV 97 CLEO 0.7ACKERSTAFF 98M OPAL 2.9ABDALLAH 06A DLPH 0.1

χ2


11 11.5 12 12.5 13(h−ντ

)/total (%)

735735735735See key on page 601 LeptonParti le Listingsτ(h−ντ

)/(e− νe ντ

) 8/5 = (9+10)/5(h−ντ

)/(e− νe ντ

) 8/5 = (9+10)/5(h−ντ

)/(e− νe ντ

) 8/5 = (9+10)/5(h−ντ

)/(e− νe ντ

) 8/5 = (9+10)/5VALUE (units 10−2) EVTS DOCUMENT ID TECN COMMENT64.62±0.33 OUR FIT64.62±0.33 OUR FIT64.62±0.33 OUR FIT64.62±0.33 OUR FIT64.0 ±0.7 OUR AVERAGE64.0 ±0.7 OUR AVERAGE64.0 ±0.7 OUR AVERAGE64.0 ±0.7 OUR AVERAGE Error in ludes s ale fa tor of 1.6.• • • We use the following data for averages but not for ts. • • •63.33±0.14±0.61 394k 1 AUBERT 10F BABR 467 fb−1 Eee m=10.6 GeV64.84±0.41±0.60 2 ANASTASSOV 97 CLEO Eee m= 10.6 GeV1Not independent of AUBERT 10F (τ− → π− ντ )/(τ− → e− νe ντ ) and (τ− →K− ντ )/(τ− → e− νe ντ ).2The orrelation oeÆ ients between this measurement and the ANASTASSOV 97 mea-surements of B(µνµντ ), B(e νe ντ ), B(µνµντ )/B(e νe ντ ), and B(h− ντ ) are 0.08,

−0.39, 0.45, and 0.63 respe tively.(π− ντ

)/total 9/(π− ντ



)/total 9/VALUE (%) EVTS DOCUMENT ID TECN COMMENT10.82 ±0.05 OUR FIT10.82 ±0.05 OUR FIT10.82 ±0.05 OUR FIT10.82 ±0.05 OUR FIT10.828±0.070±0.07810.828±0.070±0.07810.828±0.070±0.07810.828±0.070±0.078 38k 1 SCHAEL 05C ALEP 1991-1995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •11.06 ±0.11 ±0.14 2 BUSKULIC 96 ALEP Repl. by SCHAEL 05C11.7 ±0.4 ±1.8 1138 BLOCKER 82D MRK2 Eee m= 3.56.7 GeV1See footnote to SCHAEL 05C (τ− → e− νe ντ )/total measurement for orrelationswith other measurements.2Not independent of BUSKULIC 96 B(h− ντ ) and B(K− ντ ) values.(π− ντ

)/(e− νe ντ

) 9/5(π− ντ

)/(e− νe ντ

) 9/5(π− ντ

)/(e− νe ντ

) 9/5(π− ντ

)/(e− νe ντ

) 9/5VALUE (units 10−2) EVTS DOCUMENT ID TECN COMMENT60.71±0.32 OUR FIT60.71±0.32 OUR FIT60.71±0.32 OUR FIT60.71±0.32 OUR FIT59.45±0.14±0.6159.45±0.14±0.6159.45±0.14±0.6159.45±0.14±0.61 369k 1 AUBERT 10F BABR 467 fb−1 Eee m= 10.6 GeV1See footnote to AUBERT 10F (τ− → µ− νµ ντ )/(τ− → e− νe ντ ) for orrelationswith other measurements.(K−ντ

)/total 10/(K−ντ



)/total 10/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.696±0.010 OUR FIT0.696±0.010 OUR FIT0.696±0.010 OUR FIT0.696±0.010 OUR FIT0.685±0.023 OUR AVERAGE0.685±0.023 OUR AVERAGE0.685±0.023 OUR AVERAGE0.685±0.023 OUR AVERAGE0.658±0.027±0.029 1 ABBIENDI 01J OPAL 19901995 LEP runs0.696±0.025±0.014 2032 BARATE 99K ALEP 19911995 LEP runs0.85 ±0.18 27 ABREU 94K DLPH LEP 1992 Z data0.66 ±0.07 ±0.09 99 BATTLE 94 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.72 ±0.04 ±0.04 728 BUSKULIC 96 ALEP Repl. by BARATE 99K0.59 ±0.18 16 MILLS 84 DLCO Eee m= 29 GeV1.3 ±0.5 15 BLOCKER 82B MRK2 Eee m= 3.96.7 GeV1The orrelation oeÆ ient between this measurement and the ABBIENDI 01J B(τ− →K− ≥ 0π0 ≥ 0K0 ≥ 0γ ντ ) is 0.60.(K−ντ

)/(e−νe ντ

) 10/5(K−ντ

)/(e−νe ντ

) 10/5(K−ντ

)/(e−νe ντ

) 10/5(K−ντ

)/(e−νe ντ

) 10/5VALUE (units 10−2) EVTS DOCUMENT ID TECN COMMENT3.91 ±0.05 OUR FIT3.91 ±0.05 OUR FIT3.91 ±0.05 OUR FIT3.91 ±0.05 OUR FIT3.882±0.032±0.0573.882±0.032±0.0573.882±0.032±0.0573.882±0.032±0.057 25k 1 AUBERT 10F BABR 467 fb−1 Eee m= 10.6 GeV1See footnote to AUBERT 10F (τ− → µ− νµ ντ )/(τ− → e− νe ντ ) for orrelationswith other measurements.(K−ντ

)/(π−ντ

) 10/9(K−ντ

)/(π−ντ

) 10/9(K−ντ

)/(π−ντ

) 10/9(K−ντ

)/(π−ντ

) 10/9VALUE (units 10−2) DOCUMENT ID TECN COMMENT6.44 ±0.09 OUR FIT6.44 ±0.09 OUR FIT6.44 ±0.09 OUR FIT6.44 ±0.09 OUR FIT• • • We use the following data for averages but not for ts. • • •6.531±0.056±0.0936.531±0.056±0.0936.531±0.056±0.0936.531±0.056±0.093 1 AUBERT 10F BABR 467 fb−1 Eee m= 10.6 GeV1Not independent of AUBERT 10F (τ− → π− ντ )/(τ− → e− νe ντ ) and (τ− →K− ντ )/(τ− → e− νe ντ ).(h− ≥ 1 neutralsντ

)/total 11/(h− ≥ 1 neutralsντ



)/total 11/11/ = (14+16+20+23+27+28+30+0.1534436+0.1534438+0.1534441+0.1534443+0.094248+0.094252+0.7212148+0.7212150+0.7212152+0.1107154+0.0828176+0.0828177+0.0828178)/VALUE (%) DOCUMENT ID TECN COMMENT37.00±0.09 OUR FIT37.00±0.09 OUR FIT37.00±0.09 OUR FIT37.00±0.09 OUR FIT• • • We do not use the following data for averages, ts, limits, et . • • •36.14±0.33±0.58 1 AKERS 94E OPAL 19911992 LEP runs38.4 ±1.2 ±1.0 2 BURCHAT 87 MRK2 Eee m= 29 GeV42.7 ±2.0 ±2.9 BERGER 85 PLUT Eee m= 34.6 GeV1Not independent of ACKERSTAFF 98M B(h−π0 ντ ) and B(h− ≥ 2π0 ντ ) values.2BURCHAT 87 quote for B(π± ≥ 1 neutralντ ) = 0.378 ± 0.012 ± 0.010. We add 0.006to a ount for ontribution from (K∗− ντ ) whi h they xed at BR = 0.013.

(h− ≥ 1π0 ντ (ex.K0))/total 12/(h− ≥ 1π0 ντ (ex.K0))/total 12/(h− ≥ 1π0 ντ (ex.K0))/total 12/(h− ≥ 1π0 ντ (ex.K0))/total 12/12/ = (14+16+20+23+27+28+30+0.3268148+0.3268150+0.3268152)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT36.51 ±0.09 OUR FIT36.51 ±0.09 OUR FIT36.51 ±0.09 OUR FIT36.51 ±0.09 OUR FIT• • • We use the following data for averages but not for ts. • • •36.641±0.155±0.12736.641±0.155±0.12736.641±0.155±0.12736.641±0.155±0.127 45k 1 ABDALLAH 06A DLPH 19921995 LEP runs1 See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.(h−π0 ντ

)/total 13/= (14+16)/(h−π0 ντ

)/total 13/= (14+16)/(h−π0 ντ

)/total 13/= (14+16)/(h−π0 ντ

)/total 13/= (14+16)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT25.93 ±0.09 OUR FIT25.93 ±0.09 OUR FIT25.93 ±0.09 OUR FIT25.93 ±0.09 OUR FIT25.73 ±0.16 OUR AVERAGE25.73 ±0.16 OUR AVERAGE25.73 ±0.16 OUR AVERAGE25.73 ±0.16 OUR AVERAGE25.67 ±0.01 ±0.39 5.4M FUJIKAWA 08 BELL 72 fb−1 Eee m=10.6GeV25.740±0.201±0.138 35k 1 ABDALLAH 06A DLPH 19921995 LEP runs25.89 ±0.17 ±0.29 ACKERSTAFF 98M OPAL 19911995 LEP runs25.05 ±0.35 ±0.50 6613 ACCIARRI 95 L3 1992 LEP run25.87 ±0.12 ±0.42 51k 2 ARTUSO 94 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •25.76 ±0.15 ±0.13 31k BUSKULIC 96 ALEP Repl. by SCHAEL 05C25.98 ±0.36 ±0.52 3 AKERS 94E OPAL Repl. by ACKER-STAFF 98M22.9 ±0.8 ±1.3 283 4 ABREU 92N DLPH Eee m= 88.294.2 GeV23.1 ±0.4 ±0.9 1249 5 ALBRECHT 92Q ARG Eee m= 10 GeV25.02 ±0.64 ±0.88 1849 DECAMP 92C ALEP 19891990 LEP runs22.0 ±0.8 ±1.9 779 ANTREASYAN 91 CBAL Eee m= 9.410.6 GeV22.6 ±1.5 ±0.7 1101 BEHREND 90 CELL Eee m= 35 GeV23.1 ±1.9 ±1.6 BEHREND 84 CELL Eee m= 14,22 GeV1See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.2ARTUSO 94 reports the ombined result from three independent methods, one of whi h(23% of the τ− → h−π0 ντ ) is normalized to the in lusive one-prong bran hing fra tion,taken as 0.854 ± 0.004. Renormalization to the present value auses negligible hange.3AKERS 94E quote (26.25 ± 0.36 ± 0.52)× 10−2; we subtra t 0.27% from their numberto orre t for τ− → h−K0L ντ .4ABREU 92N with 0.5% added to remove their orre tion for K∗(892)− ba kgrounds.5ALBRECHT 92Q with 0.5% added to remove their orre tion for τ− → K∗(892)− ντba kground.(π−π0 ντ

)/total 14/(π−π0 ντ



)/total 14/VALUE (%) EVTS DOCUMENT ID TECN COMMENT25.49 ±0.09 OUR FIT25.49 ±0.09 OUR FIT25.49 ±0.09 OUR FIT25.49 ±0.09 OUR FIT25.46 ±0.12 OUR AVERAGE25.46 ±0.12 OUR AVERAGE25.46 ±0.12 OUR AVERAGE25.46 ±0.12 OUR AVERAGE25.471±0.097±0.085 81k 1 SCHAEL 05C ALEP 1991-1995 LEP runs• • • We use the following data for averages but not for ts. • • •25.36 ±0.44 2 ARTUSO 94 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •25.30 ±0.15 ±0.13 3 BUSKULIC 96 ALEP Repl. by SCHAEL 05C21.5 ±0.4 ±1.9 4400 4,5 ALBRECHT 88L ARG Eee m= 10 GeV23.0 ±1.3 ±1.7 582 ADLER 87B MRK3 Eee m= 3.77 GeV25.8 ±1.7 ±2.5 6 BURCHAT 87 MRK2 Eee m= 29 GeV22.3 ±0.6 ±1.4 629 5 YELTON 86 MRK2 Eee m= 29 GeV1See footnote to SCHAEL 05C (τ− → e− νe ντ )/total measurement for orrelationswith other measurements.2Not independent of ARTUSO 94 B(h−π0 ντ ) and BATTLE 94 B(K−π0 ντ ) values.3Not independent of BUSKULIC 96 B(h−π0 ντ ) and B(K−π0 ντ ) values.4The authors divide by ( 3 + 5 + 9 + 10 )/ = 0.467 to obtain this result.5 Experiment had no hadron identi ation. Kaon orre tions were made, but insuÆ ientinformation is given to permit their removal.6BURCHAT 87 value is not independent of YELTON 86 value. Nonresonant de aysin luded.(π−π0 non-ρ(770)ντ

)/total 15/(π−π0 non-ρ(770)ντ



)/total 15/VALUE (%) DOCUMENT ID TECN COMMENT0.3±0.1±0.30.3±0.1±0.30.3±0.1±0.30.3±0.1±0.3 1 BEHREND 84 CELL Eee m= 14,22 GeV1BEHREND 84 assume a at nonresonant mass distribution down to the ρ(770) mass,using events with mass above 1300 to set the level.(K−π0 ντ

)/total 16/(K−π0 ντ



)/total 16/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.433±0.015 OUR FIT0.433±0.015 OUR FIT0.433±0.015 OUR FIT0.433±0.015 OUR FIT0.426±0.016 OUR AVERAGE0.426±0.016 OUR AVERAGE0.426±0.016 OUR AVERAGE0.426±0.016 OUR AVERAGE0.416±0.003±0.018 78k AUBERT 07AP BABR 230 fb−1 Eee m= 10.6 GeV0.471±0.059±0.023 360 ABBIENDI 04J OPAL 1991-1995 LEP runs0.444±0.026±0.024 923 BARATE 99K ALEP 1991-1995 LEP runs0.51 ±0.10 ±0.07 37 BATTLE 94 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.52 ±0.04 ±0.05 395 BUSKULIC 96 ALEP Repl. by BARATE 99K

736736736736LeptonParti le Listingsτ(h− ≥ 2π0 ντ

)/total 17/(h− ≥ 2π0 ντ

)/total 17/(h− ≥ 2π0 ντ

)/total 17/(h− ≥ 2π0 ντ

)/total 17/17/ = (20+23+27+28+30+0.1534436+0.1534438+0.1534441+0.1534443+0.0941948+0.094252+0.3268148+0.3268150+0.3268152)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT10.81±0.09 OUR FIT10.81±0.09 OUR FIT10.81±0.09 OUR FIT10.81±0.09 OUR FIT9.91±0.31±0.279.91±0.31±0.279.91±0.31±0.279.91±0.31±0.27 ACKERSTAFF 98M OPAL 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •9.89±0.34±0.55 1 AKERS 94E OPAL Repl. by ACKER-STAFF 98M14.0 ±1.2 ±0.6 938 2 BEHREND 90 CELL Eee m= 35 GeV12.0 ±1.4 ±2.5 3 BURCHAT 87 MRK2 Eee m= 29 GeV13.9 ±2.0 +1.9

−2.2 4 AIHARA 86E TPC Eee m= 29 GeV1AKERS 94E not independent of AKERS 94E B(h− ≥ 1π0 ντ ) and B(h−π0 ντ ) mea-surements.2No independent of BEHREND 90 (h− 2π0 ντ (exp. K0)) and (h− ≥ 3π0 ντ ).3 Error orrelated with BURCHAT 87 (ρ− νe )/(total) value.4AIHARA 86E (TPC) quote B(2π0π− ντ ) + 1.6B(3π0π− ντ ) + 1.1B(π0 ηπ− ντ ).(h−2π0 ντ

)/total 18/(h−2π0 ντ



)/total 18/18/ = (20+23+0.1534436+0.1534438)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT9.48±0.10 OUR FIT9.48±0.10 OUR FIT9.48±0.10 OUR FIT9.48±0.10 OUR FIT• • • We do not use the following data for averages, ts, limits, et . • • •9.48±0.13±0.10 12k 1 BUSKULIC 96 ALEP Repl. by SCHAEL 05C1BUSKULIC 96 quote 9.29 ± 0.13 ± 0.10. We add 0.19 to undo their orre tion for

τ− → h−K0 ντ .(h−2π0 ντ (ex.K0))/total 19/(h−2π0 ντ (ex.K0))/total 19/(h−2π0 ντ (ex.K0))/total 19/(h−2π0 ντ (ex.K0))/total 19/19/ = (20+23)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT9.32 ±0.10 OUR FIT9.32 ±0.10 OUR FIT9.32 ±0.10 OUR FIT9.32 ±0.10 OUR FIT9.17 ±0.27 OUR AVERAGE9.17 ±0.27 OUR AVERAGE9.17 ±0.27 OUR AVERAGE9.17 ±0.27 OUR AVERAGE9.498±0.320±0.275 9.5k 1 ABDALLAH 06A DLPH 19921995 LEP runs8.88 ±0.37 ±0.42 1060 ACCIARRI 95 L3 1992 LEP run• • • We use the following data for averages but not for ts. • • •8.96 ±0.16 ±0.44 2 PROCARIO 93 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •10.38 ±0.66 ±0.82 809 3 DECAMP 92C ALEP Repl. by SCHAEL 05C5.7 ±0.5 +1.7

−1.0 133 4 ANTREASYAN 91 CBAL Eee m= 9.410.6 GeV10.0 ±1.5 ±1.1 333 5 BEHREND 90 CELL Eee m= 35 GeV8.7 ±0.4 ±1.1 815 6 BAND 87 MAC Eee m= 29 GeV6.2 ±0.6 ±1.2 7 GAN 87 MRK2 Eee m= 29 GeV6.0 ±3.0 ±1.8 BEHREND 84 CELL Eee m= 14,22 GeV1See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.2PROCARIO 93 entry is obtained from B(h− 2π0 ντ )/B(h−π0 ντ ) using ARTUSO 94result for B(h−π0 ντ ).3We subtra t 0.0015 to a ount for τ− → K∗(892)− ντ ontribution.4ANTREASYAN 91 subtra t 0.001 to a ount for the τ− → K∗(892)− ντ ontribution.5BEHREND 90 subtra t 0.002 to a ount for the τ− → K∗(892)− ντ ontribution.6BAND 87 assume B(π− 3π0 ντ ) = 0.01 and B(π−π0 ηντ ) = 0.005.7GAN 87 analysis use photon multipli ity distribution.(h−2π0 ντ (ex.K0))/(h−π0 ντ

) 19/13(h−2π0 ντ (ex.K0))/(h−π0 ντ

) 19/13(h−2π0 ντ (ex.K0))/(h−π0 ντ

) 19/13(h−2π0 ντ (ex.K0))/(h−π0 ντ

) 19/1319/13 = (20+23)/(14+16)VALUE (units 10−2) DOCUMENT ID TECN COMMENT36.0±0.4 OUR FIT36.0±0.4 OUR FIT36.0±0.4 OUR FIT36.0±0.4 OUR FIT34.2±0.6±1.634.2±0.6±1.634.2±0.6±1.634.2±0.6±1.6 1 PROCARIO 93 CLEO Eee m ≈ 10.6 GeV1PROCARIO 93 quote 0.345 ± 0.006 ± 0.016 after orre tion for 2 kaon ba kgroundsassuming B(K∗− ντ )=1.42 ± 0.18% and B(h−K0π0 ντ )=0.48 ± 0.48%. We multiplyby 0.990 ± 0.010 to remove these orre tions to B(h−π0 ντ ).(π− 2π0ντ (ex.K0))/total 20/(π− 2π0ντ (ex.K0))/total 20/(π− 2π0ντ (ex.K0))/total 20/(π− 2π0ντ (ex.K0))/total 20/VALUE (%) EVTS DOCUMENT ID TECN COMMENT9.26 ±0.10 OUR FIT9.26 ±0.10 OUR FIT9.26 ±0.10 OUR FIT9.26 ±0.10 OUR FIT9.239±0.086±0.0909.239±0.086±0.0909.239±0.086±0.0909.239±0.086±0.090 31k 1 SCHAEL 05C ALEP 1991-1995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •9.21 ±0.13 ±0.11 2 BUSKULIC 96 ALEP Repl. by SCHAEL 05C1See footnote to SCHAEL 05C (τ− → e− νe ντ )/total measurement for orrelationswith other measurements.2Not independent of BUSKULIC 96 B(h− 2π0 ντ (ex. K0)) and B(K− 2π0 ντ (ex. K0))values.(π− 2π0ντ (ex.K0), s alar)/(π− 2π0ντ (ex.K0)) 21/20(π− 2π0ντ (ex.K0), s alar)/(π− 2π0ντ (ex.K0)) 21/20(π− 2π0ντ (ex.K0), s alar)/(π− 2π0ντ (ex.K0)) 21/20(π− 2π0ντ (ex.K0), s alar)/(π− 2π0ντ (ex.K0)) 21/20VALUE CL% DOCUMENT ID TECN COMMENT<0.094<0.094<0.094<0.094 95 1 BROWDER 00 CLEO 4.7 fb−1 Eee m= 10.6 GeV1Model-independent limit from stru ture fun tion analysis on ontribution to B(τ− →

π− 2π0 ντ (ex. K0)) from s alars.

(π− 2π0ντ (ex.K0), ve tor)/(π− 2π0 ντ (ex.K0)) 22/20(π− 2π0ντ (ex.K0), ve tor)/(π− 2π0 ντ (ex.K0)) 22/20(π− 2π0ντ (ex.K0), ve tor)/(π− 2π0 ντ (ex.K0)) 22/20(π− 2π0ντ (ex.K0), ve tor)/(π− 2π0 ντ (ex.K0)) 22/20VALUE CL% DOCUMENT ID TECN COMMENT<0.073<0.073<0.073<0.073 95 1 BROWDER 00 CLEO 4.7 fb−1 Eee m= 10.6 GeV1Model-independent limit from stru ture fun tion analysis on ontribution to B(τ− →

π− 2π0 ντ (ex. K0)) from ve tors.(K−2π0 ντ (ex.K0))/total 23/(K−2π0 ντ (ex.K0))/total 23/(K−2π0 ντ (ex.K0))/total 23/(K−2π0 ντ (ex.K0))/total 23/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT6.5± 2.2 OUR FIT6.5± 2.2 OUR FIT6.5± 2.2 OUR FIT6.5± 2.2 OUR FIT5.8± 2.4 OUR AVERAGE5.8± 2.4 OUR AVERAGE5.8± 2.4 OUR AVERAGE5.8± 2.4 OUR AVERAGE5.6± 2.0±1.5 131 BARATE 99K ALEP 19911995 LEP runs9 ±10 ±3 3 1 BATTLE 94 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •8 ± 2 ±2 59 BUSKULIC 96 ALEP Repl. by BARATE 99K1BATTLE 94 quote (14 ± 10 ± 3) × 10−4 or < 30 × 10−4 at 90% CL. We subtra t(5 ± 2)× 10−4 to a ount for τ− → K− (K0 → π0π0)ντ ba kground.(h− ≥ 3π0 ντ

)/total 24/(h− ≥ 3π0 ντ

)/total 24/(h− ≥ 3π0 ντ

)/total 24/(h− ≥ 3π0 ντ

)/total 24/24/ = (27+28+30+0.1534441+0.1534443+0.094248+0.094252+0.3268148+0.3268150+0.3268152+0.0501154)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.34±0.07 OUR FIT1.34±0.07 OUR FIT1.34±0.07 OUR FIT1.34±0.07 OUR FIT• • • We do not use the following data for averages, ts, limits, et . • • •1.53±0.40±0.46 186 DECAMP 92C ALEP Repl. by SCHAEL 05C3.2 ±1.0 ±1.0 BEHREND 90 CELL Eee m= 35 GeV(h− ≥ 3π0 ντ (ex. K0))/total 25/(h− ≥ 3π0 ντ (ex. K0))/total 25/(h− ≥ 3π0 ντ (ex. K0))/total 25/(h− ≥ 3π0 ντ (ex. K0))/total 25/25/ = (27+28+30+0.3268148+0.3268150+0.3268152)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.25 ±0.07 OUR FIT1.25 ±0.07 OUR FIT1.25 ±0.07 OUR FIT1.25 ±0.07 OUR FIT1.403±0.214±0.2241.403±0.214±0.2241.403±0.214±0.2241.403±0.214±0.224 1.1k 1 ABDALLAH 06A DLPH 19921995 LEP runs1 See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.(h−3π0 ντ




)/total 26/26/ = (27+28+0.1534441+0.1534443+0.3268150)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.18±0.07 OUR FIT1.18±0.07 OUR FIT1.18±0.07 OUR FIT1.18±0.07 OUR FIT1.21±0.17 OUR AVERAGE1.21±0.17 OUR AVERAGE1.21±0.17 OUR AVERAGE1.21±0.17 OUR AVERAGE Error in ludes s ale fa tor of 1.2.1.70±0.24±0.38 293 ACCIARRI 95 L3 1992 LEP run• • • We use the following data for averages but not for ts. • • •1.15±0.08±0.13 1 PROCARIO 93 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.24±0.09±0.11 2.3k 2 BUSKULIC 96 ALEP Repl. by SCHAEL 05C0.0 +1.4

−0.1 +1.1−0.1 3 GAN 87 MRK2 Eee m= 29 GeV1PROCARIO 93 entry is obtained from B(h− 3π0 ντ )/B(h−π0 ντ ) using ARTUSO 94result for B(h−π0 ντ ).2BUSKULIC 96 quote B(h− 3π0 ντ (ex. K0)) = 1.17 ± 0.09 ± 0.11. We add 0.07 toremove their orre tion for K0 ba kgrounds.3Highly orrelated with GAN 87 (

ηπ−π0 ντ)/total value. Authors quoteB(π± 3π0 ντ ) + 0.67B(π± ηπ0 ντ ) = 0.047 ± 0.010 ± 0.011.(h−3π0 ντ

)/(h−π0 ντ

) 26/13(h−3π0 ντ

)/(h−π0 ντ

) 26/13(h−3π0 ντ

)/(h−π0 ντ

) 26/13(h−3π0 ντ

)/(h−π0 ντ

) 26/1326/13 = (27+28+0.1534441+0.1534443+0.3268150)/(14+16)VALUE (units 10−2) DOCUMENT ID TECN COMMENT4.54±0.28 OUR FIT4.54±0.28 OUR FIT4.54±0.28 OUR FIT4.54±0.28 OUR FIT4.4 ±0.3 ±0.54.4 ±0.3 ±0.54.4 ±0.3 ±0.54.4 ±0.3 ±0.5 1 PROCARIO 93 CLEO Eee m ≈ 10.6 GeV1PROCARIO 93 quote 0.041 ± 0.003 ± 0.005 after orre tion for 2 kaon ba kgroundsassuming B(K∗− ντ )=1.42 ± 0.18% and B(h−K0π0 ντ )=0.48 ± 0.48%. We add0.003 ± 0.003 and multiply the sum by 0.990 ± 0.010 to remove these orre tions.(π− 3π0ντ (ex.K0))/total 27/(π− 3π0ντ (ex.K0))/total 27/(π− 3π0ντ (ex.K0))/total 27/(π− 3π0ντ (ex.K0))/total 27/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.04 ±0.07 OUR FIT1.04 ±0.07 OUR FIT1.04 ±0.07 OUR FIT1.04 ±0.07 OUR FIT0.977±0.069±0.0580.977±0.069±0.0580.977±0.069±0.0580.977±0.069±0.058 6.1k 1 SCHAEL 05C ALEP 1991-1995 LEP runs1 See footnote to SCHAEL 05C (τ− → e− νe ντ )/total measurement for orrelationswith other measurements.(K−3π0 ντ (ex.K0, η))/total 28/(K−3π0 ντ (ex.K0, η))/total 28/(K−3π0 ντ (ex.K0, η))/total 28/(K−3π0 ντ (ex.K0, η))/total 28/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT4.8± 2.1 OUR FIT4.8± 2.1 OUR FIT4.8± 2.1 OUR FIT4.8± 2.1 OUR FIT3.7± 2.1±1.13.7± 2.1±1.13.7± 2.1±1.13.7± 2.1±1.1 22 BARATE 99K ALEP 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •5 ±13 1 BUSKULIC 94E ALEP Repl. by BARATE 99K1BUSKULIC 94E quote B(K− ≥ 0π0 ≥ 0K0 ντ ) − [B(K− ντ ) + B(K−π0 ντ ) +B(K−K0 ντ ) + B(K−π0π0 ντ ) + B(K−π0K0 ντ ) = (5 ± 13) × 10−4 a ountingfor ommon systemati errors in BUSKULIC 94E and BUSKULIC 94F measurements ofthese modes. We assume B(K− ≥ 2K0 ντ ) and B(K− ≥ 4π0 ντ ) are negligible.

737737737737See key on page 601 LeptonParti le Listingsτ(h−4π0 ντ (ex.K0))/total 29/(h−4π0 ντ (ex.K0))/total 29/(h−4π0 ντ (ex.K0))/total 29/(h−4π0 ντ (ex.K0))/total 29/29/ = (30+0.3268148+0.3268152)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.16±0.04 OUR FIT0.16±0.04 OUR FIT0.16±0.04 OUR FIT0.16±0.04 OUR FIT0.16±0.05±0.050.16±0.05±0.050.16±0.05±0.050.16±0.05±0.05 1 PROCARIO 93 CLEO Eee m ≈ 10.6 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •0.16±0.04±0.09 232 2 BUSKULIC 96 ALEP Repl. by SCHAEL 05C1PROCARIO 93 quotes B(h− 4π0 ντ )/B(h−π0 ντ ) =0.006±0.002±0.002. We multiplyby the ARTUSO 94 result for B(h−π0 ντ ) to obtain B(h− 4π0 ντ ). PROCARIO 93assume B(h− ≥ 5 π0 ντ ) is small and do not orre t for it.2BUSKULIC 96 quote result for τ− → h− ≥ 4π0 ντ . We assume B(h− ≥ 5π0 ντ ) isnegligible.(h−4π0 ντ (ex.K0,η))/total 30/(h−4π0 ντ (ex.K0,η))/total 30/(h−4π0 ντ (ex.K0,η))/total 30/(h−4π0 ντ (ex.K0,η))/total 30/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.11 ±0.04 OUR FIT0.11 ±0.04 OUR FIT0.11 ±0.04 OUR FIT0.11 ±0.04 OUR FIT0.112±0.037±0.0350.112±0.037±0.0350.112±0.037±0.0350.112±0.037±0.035 957 1 SCHAEL 05C ALEP 1991-1995 LEP runs1 See footnote to SCHAEL 05C (τ− → e− νe ντ )/total measurement for orrelationswith other measurements.(a1(1260)ντ → π− γ ντ

)/total 31/ = (0.002120+0.002170)/(a1(1260)ντ → π− γ ντ

)/total 31/ = (0.002120+0.002170)/(a1(1260)ντ → π− γ ντ

)/total 31/ = (0.002120+0.002170)/(a1(1260)ντ → π− γ ντ

)/total 31/ = (0.002120+0.002170)/The un ertainty on (τ− → a1(1260)ντ → π− γ ντ )/total takes into a ountthe non-negligible ontribution from the un ertainty of the oeÆ ient of the re-lationship that denes (τ− → a1(1260)ντ → π− γ ντ ) in terms of (τ− →π− 2π0 ντ (ex.K0)) and (τ− → π−π+π− ντ (ex.K0,ω)).VALUE (units 10−4) DOCUMENT ID3.8±1.5 OUR FIT3.8±1.5 OUR FIT3.8±1.5 OUR FIT3.8±1.5 OUR FIT(K− ≥ 0π0 ≥ 0K0 ≥ 0γ ντ

)/total 32/(K− ≥ 0π0 ≥ 0K0 ≥ 0γ ντ

)/total 32/(K− ≥ 0π0 ≥ 0K0 ≥ 0γ ντ

)/total 32/(K− ≥ 0π0 ≥ 0K0 ≥ 0γ ντ

)/total 32/32/ = (10+16+23+28+38+43+0.7212150+0.1049168)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.552±0.029 OUR FIT1.552±0.029 OUR FIT1.552±0.029 OUR FIT1.552±0.029 OUR FIT1.53 ±0.04 OUR AVERAGE1.53 ±0.04 OUR AVERAGE1.53 ±0.04 OUR AVERAGE1.53 ±0.04 OUR AVERAGE1.528±0.039±0.040 1 ABBIENDI 01J OPAL 19901995 LEP runs1.54 ±0.24 ABREU 94K DLPH LEP 1992 Z data1.70 ±0.12 ±0.19 202 2 BATTLE 94 CLEO Eee m ≈ 10.6 GeV• • • We use the following data for averages but not for ts. • • •1.520±0.040±0.041 4006 3 BARATE 99K ALEP 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •1.70 ±0.05 ±0.06 1610 4 BUSKULIC 96 ALEP Repl. by BARATE 99K1.6 ±0.4 ±0.2 35 AIHARA 87B TPC Eee m= 29 GeV1.71 ±0.29 53 MILLS 84 DLCO Eee m= 29 GeV1The orrelation oeÆ ient between this measurement and the ABBIENDI 01J B(τ− →K− ντ ) is 0.60.2BATTLE 94 quote 1.60 ± 0.12 ± 0.19. We add 0.10 ± 0.02 to orre t for their reje tionof K0S → π+π− de ays.3Not independent of BARATE 99K B(K− ντ ), B(K−π0 ντ ), B(K− 2π0 ντ (ex. K0)),B(K− 3π0 ντ (ex. K0)), B(K−K0 ντ ), and B(K−K0π0 ντ ) values.4Not independent of BUSKULIC 96 B(K− ντ ), B(K−π0 ντ ), B(K− 2π0 ντ ),B(K−K0 ντ ), and B(K−K0π0 ντ ) values.(K− ≥ 1 (π0 orK0 or γ) ντ

)/total 33/(K− ≥ 1 (π0 orK0 or γ) ντ



)/total 33/33/ = (16+23+28+38+43+0.7212150+0.7212152+0.1049168)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.859±0.028 OUR FIT0.859±0.028 OUR FIT0.859±0.028 OUR FIT0.859±0.028 OUR FIT0.86 ±0.05 OUR AVERAGE0.86 ±0.05 OUR AVERAGE0.86 ±0.05 OUR AVERAGE0.86 ±0.05 OUR AVERAGE• • • We use the following data for averages but not for ts. • • •0.869±0.031±0.034 1 ABBIENDI 01J OPAL 19901995 LEP runs0.69 ±0.25 2 ABREU 94K DLPH LEP 1992 Z data• • • We do not use the following data for averages, ts, limits, et . • • •1.2 ±0.5 +0.2

−0.4 9 AIHARA 87B TPC Eee m= 29 GeV1Not independent of ABBIENDI 01J B(τ− → K− ντ ) and B(τ− → K− ≥ 0π0 ≥0K0 ≥ 0γ ντ ) values.2Not independent of ABREU 94K B(K− ντ ) and B(K− ≥ 0 neutralsντ ) measurements.(K0S (parti les)− ντ

)/total 34/(K0S (parti les)− ντ



)/total 34/34/ = (1236+1238+1241+1243+1245+48+49+52+56+0.3606154+0.342168)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.944±0.028 OUR FIT0.944±0.028 OUR FIT0.944±0.028 OUR FIT0.944±0.028 OUR FIT0.918±0.015 OUR AVERAGE0.918±0.015 OUR AVERAGE0.918±0.015 OUR AVERAGE0.918±0.015 OUR AVERAGE0.970±0.058±0.062 929 BARATE 98E ALEP 19911995 LEP runs0.97 ±0.09 ±0.06 141 AKERS 94G OPAL Eee m= 8894 GeV• • • We use the following data for averages but not for ts. • • •0.915±0.001±0.015 398k 1 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV1Not independent of RYU 14 measurements of B(τ− → π−K0 ντ ), B(τ− →K−K0 ντ ), B(τ− → π−K0π0 ντ ), B(τ− → K−K0π0 ντ ), B(τ− →

π−K0S K0S ντ ), and B(τ− → π−K0S K0S π0 ντ ).

(h−K0 ντ

)/total 35/= (36+38)/(h−K0 ντ

)/total 35/= (36+38)/(h−K0 ντ

)/total 35/= (36+38)/(h−K0 ντ

)/total 35/= (36+38)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.987±0.014 OUR FIT0.987±0.014 OUR FIT0.987±0.014 OUR FIT0.987±0.014 OUR FIT0.90 ±0.07 OUR AVERAGE0.90 ±0.07 OUR AVERAGE0.90 ±0.07 OUR AVERAGE0.90 ±0.07 OUR AVERAGE0.855±0.036±0.073 1242 COAN 96 CLEO Eee m ≈ 10.6 GeV• • • We use the following data for averages but not for ts. • • •1.01 ±0.11 ±0.07 555 1 BARATE 98E ALEP 19911995 LEP runs1Not independent of BARATE 98E B(τ− → π−K0 ντ ) and B(τ− → K−K0 ντ ) values.(π−K0 ντ

)/total 36/(π−K0 ντ



)/total 36/VALUE (units 10−3) EVTS DOCUMENT ID TECN COMMENT8.40±0.14 OUR FIT8.40±0.14 OUR FIT8.40±0.14 OUR FIT8.40±0.14 OUR FIT8.39±0.22 OUR AVERAGE8.39±0.22 OUR AVERAGE8.39±0.22 OUR AVERAGE8.39±0.22 OUR AVERAGE Error in ludes s ale fa tor of 1.5. See the ideogram below.8.32±0.02±0.16 158k 1 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV9.33±0.68±0.49 377 ABBIENDI 00C OPAL 19911995 LEP runs9.28±0.45±0.34 937 2 BARATE 99K ALEP 19911995 LEP runs9.5 ±1.5 ±0.6 3 ACCIARRI 95F L3 19911993 LEP runs• • • We use the following data for averages but not for ts. • • •8.55±1.17±0.66 509 4 BARATE 98E ALEP 19911995 LEP runs7.04±0.41±0.72 5 COAN 96 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •8.08±0.04±0.26 53k EPIFANOV 07 BELL Repl. by RYU 147.9 ±1.0 ±0.9 98 6 BUSKULIC 96 ALEP Repl. by BARATE 99K1RYU 14 re onstru t K0's using K0S → π+π− de ays.2BARATE 99K measure K0's by dete ting K0L's in their hadron alorimeter.3ACCIARRI 95F do not identify π−/K− and assume B(K−K0 ντ ) = (0.29 ± 0.12)%.4BARATE 98E re onstru t K0's using K0S → π+π− de ays. Not independent ofBARATE 98E B(K0 parti les− ντ ) value.5Not independent of COAN 96 B(h−K0 ντ ) and B(K−K0 ντ ) measurements.6BUSKULIC 96 measure K0's by dete ting K0L's in their hadron alorimeter.



ACCIARRI 95F L3COAN 96 CLEO 2.7BARATE 98E ALEPBARATE 99K ALEP 2.5ABBIENDI 00C OPAL 1.3RYU 14 BELL 0.2

χ2


4 6 8 10 12 14(π−K0 ντ

)/total (units 10−3)(π−K0 (non-K∗(892)−)ντ

)/total 37/(π−K0 (non-K∗(892)−)ντ

)/total 37/(π−K0 (non-K∗(892)−)ντ

)/total 37/(π−K0 (non-K∗(892)−)ντ

)/total 37/VALUE (units 10−4) CL% DOCUMENT ID TECN COMMENT5.4±2.15.4±2.15.4±2.15.4±2.1 1 EPIFANOV 07 BELL 351 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<17 95 ACCIARRI 95F L3 19911993 LEP runs1EPIFANOV 07 quote B(τ− → K∗(892)− ντ ) B(K∗(892)− → K0S π−) / B(τ− →K0S π− ντ ) = 0.933 ± 0.027. We multiply their B(τ− → K0π− ντ ) by [1−(0.933 ±0.027) to obtain this result.(K−K0ντ

)/total 38/(K−K0ντ



)/total 38/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT14.8 ±0.5 OUR FIT14.8 ±0.5 OUR FIT14.8 ±0.5 OUR FIT14.8 ±0.5 OUR FIT14.9 ±0.5 OUR AVERAGE14.9 ±0.5 OUR AVERAGE14.9 ±0.5 OUR AVERAGE14.9 ±0.5 OUR AVERAGE14.80±0.14±0.54 33k 1 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV16.2 ±2.1 ±1.1 150 2 BARATE 99K ALEP 19911995 LEP runs15.8 ±4.2 ±1.7 46 3 BARATE 98E ALEP 19911995 LEP runs15.1 ±2.1 ±2.2 111 COAN 96 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •26 ±9 ±2 13 4 BUSKULIC 96 ALEP Repl. by BARATE 99K1RYU 14 re onstru t K0's using K0S → π+π− de ays.2BARATE 99K measure K0's by dete ting K0L's in their hadron alorimeter.3BARATE 98E re onstru t K0's using K0S → π+π− de ays.4BUSKULIC 96 measure K0's by dete ting K0L's in their hadron alorimeter.

738738738738LeptonParti le Listingsτ(K−K0 ≥ 0π0 ντ

)/total 39/= (38+43)/(K−K0 ≥ 0π0 ντ

)/total 39/= (38+43)/(K−K0 ≥ 0π0 ντ

)/total 39/= (38+43)/(K−K0 ≥ 0π0 ντ

)/total 39/= (38+43)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.298±0.008 OUR FIT0.298±0.008 OUR FIT0.298±0.008 OUR FIT0.298±0.008 OUR FIT0.330±0.055±0.0390.330±0.055±0.0390.330±0.055±0.0390.330±0.055±0.039 124 ABBIENDI 00C OPAL 19911995 LEP runs(h−K0π0 ντ

)/total 40/= (41+43)/(h−K0π0 ντ

)/total 40/= (41+43)/(h−K0π0 ντ

)/total 40/= (41+43)/(h−K0π0 ντ

)/total 40/= (41+43)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.532±0.013 OUR FIT0.532±0.013 OUR FIT0.532±0.013 OUR FIT0.532±0.013 OUR FIT0.50 ±0.06 OUR AVERAGE0.50 ±0.06 OUR AVERAGE0.50 ±0.06 OUR AVERAGE0.50 ±0.06 OUR AVERAGE Error in ludes s ale fa tor of 1.2.0.562±0.050±0.048 264 COAN 96 CLEO Eee m ≈ 10.6 GeV• • • We use the following data for averages but not for ts. • • •0.446±0.052±0.046 157 1 BARATE 98E ALEP 19911995 LEP runs1Not independent of BARATE 98E B(τ− → π−K0π0 τ) and B(τ− → K−K0π0 ντ )values.(π−K0π0 ντ

)/total 41/(π−K0π0 ντ



)/total 41/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.382±0.013 OUR FIT0.382±0.013 OUR FIT0.382±0.013 OUR FIT0.382±0.013 OUR FIT0.383±0.014 OUR AVERAGE0.383±0.014 OUR AVERAGE0.383±0.014 OUR AVERAGE0.383±0.014 OUR AVERAGE0.386±0.004±0.014 27k 1 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV0.347±0.053±0.037 299 2 BARATE 99K ALEP 19911995 LEP runs0.294±0.073±0.037 142 3 BARATE 98E ALEP 19911995 LEP runs0.41 ±0.12 ±0.03 4 ACCIARRI 95F L3 19911993 LEP runs• • • We use the following data for averages but not for ts. • • •0.417±0.058±0.044 5 COAN 96 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.32 ±0.11 ±0.05 23 6 BUSKULIC 96 ALEP Repl. by BARATE 99K1RYU 14 re onstru t K0's using K0S → π+π− de ays.2BARATE 99K measure K0's by dete ting K0L's in their hadron alorimeter.3BARATE 98E re onstru t K0's using K0S → π+π− de ays.4ACCIARRI 95F do not identify π−/K− and assume B(K−K0π0 ντ ) = (0.05± 0.05)%.5Not independent of COAN 96 B(h−K0π0 ντ ) and B(K−K0π0 ντ ) measurements.6BUSKULIC 96 measure K0's by dete ting K0L's in their hadron alorimeter.(K0ρ− ντ

)/total 42/(K0ρ− ντ



)/total 42/VALUE (%) DOCUMENT ID TECN COMMENT0.22 ±0.05 OUR AVERAGE0.22 ±0.05 OUR AVERAGE0.22 ±0.05 OUR AVERAGE0.22 ±0.05 OUR AVERAGE0.250±0.057±0.044 1 BARATE 99K ALEP 19911995 LEP runs0.188±0.054±0.038 2 BARATE 98E ALEP 19911995 LEP runs1BARATE 99K measure K0's by dete ting K0L's in hadron alorimeter. They determinethe K0 ρ− fra tion in τ− → π−K0π0 ντ de ays to be (0.72 ± 0.12 ± 0.10) andmultiply their B(π−K0π0 ντ ) measurement by this fra tion to obtain the quoted result.2BARATE 98E re onstru t K0's using K0S → π+π− de ays. They determine the K0 ρ−fra tion in τ− → π−K0π0 ντ de ays to be (0.64 ± 0.09 ± 0.10) and multiply theirB(π−K0π0 ντ ) measurement by this fra tion to obtain the quoted result.(K−K0π0 ντ

)/total 43/(K−K0π0 ντ



)/total 43/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT15.0 ±0.7 OUR FIT15.0 ±0.7 OUR FIT15.0 ±0.7 OUR FIT15.0 ±0.7 OUR FIT14.9 ±0.7 OUR AVERAGE14.9 ±0.7 OUR AVERAGE14.9 ±0.7 OUR AVERAGE14.9 ±0.7 OUR AVERAGE14.96±0.20±0.74 8.3k 1 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV14.3 ±2.5 ±1.5 78 2 BARATE 99K ALEP 19911995 LEP runs15.2 ±7.6 ±2.1 15 3 BARATE 98E ALEP 19911995 LEP runs14.5 ±3.6 ±2.0 32 COAN 96 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •10 ±5 ±3 5 4 BUSKULIC 96 ALEP Repl. by BARATE 99K1RYU 14 re onstru t K0's using K0S → π+π− de ays.2BARATE 99K measure K0's by dete ting K0L's in their hadron alorimeter.3BARATE 98E re onstru t K0's using K0S → π+π− de ays.4BUSKULIC 96 measure K0's by dete ting K0L's in their hadron alorimeter.(π−K0 ≥ 1π0 ντ

)/total 44/= (41+45)/(π−K0 ≥ 1π0 ντ

)/total 44/= (41+45)/(π−K0 ≥ 1π0 ντ

)/total 44/= (41+45)/(π−K0 ≥ 1π0 ντ

)/total 44/= (41+45)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.408±0.025 OUR FIT0.408±0.025 OUR FIT0.408±0.025 OUR FIT0.408±0.025 OUR FIT0.324±0.074±0.0660.324±0.074±0.0660.324±0.074±0.0660.324±0.074±0.066 148 ABBIENDI 00C OPAL 19911995 LEP runs(π−K0π0π0 ντ (ex.K0))/total 45/(π−K0π0π0 ντ (ex.K0))/total 45/(π−K0π0π0 ντ (ex.K0))/total 45/(π−K0π0π0 ντ (ex.K0))/total 45/VALUE (units 10−3) CL% EVTS DOCUMENT ID TECN COMMENT0.26±0.23 OUR FIT0.26±0.23 OUR FIT0.26±0.23 OUR FIT0.26±0.23 OUR FIT0.26±0.240.26±0.240.26±0.240.26±0.24 1 BARATE 99R ALEP 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •<0.66 95 17 2 BARATE 99K ALEP 19911995 LEP runs0.58±0.33±0.14 5 3 BARATE 98E ALEP 19911995 LEP runs1BARATE 99R ombine the BARATE 98E and BARATE 99K measurements to obtain thisvalue.2BARATE 99K measure K0's by dete ting K0L's in their hadron alorimeter.3BARATE 98E re onstru t K0's using K0S → π+π− de ays.

(K−K0π0π0 ντ

)/total 46/(K−K0π0π0 ντ



)/total 46/VALUE CL% DOCUMENT ID TECN COMMENT<0.16× 10−3<0.16× 10−3<0.16× 10−3<0.16× 10−3 95 1 BARATE 99R ALEP 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •<0.18× 10−3 95 2 BARATE 99K ALEP 19911995 LEP runs<0.39× 10−3 95 3 BARATE 98E ALEP 19911995 LEP runs1BARATE 99R ombine the BARATE 98E and BARATE 99K bounds to obtain this value.2BARATE 99K measure K0's by dete ting K0L's in hadron alorimeter.3BARATE 98E re onstru t K0's by using K0S → π+π− de ays.(π−K0K0ντ

)/total 47/ = (48+49+50)/(π−K0K0ντ

)/total 47/ = (48+49+50)/(π−K0K0ντ

)/total 47/ = (48+49+50)/(π−K0K0ντ

)/total 47/ = (48+49+50)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.155±0.024 OUR FIT0.155±0.024 OUR FIT0.155±0.024 OUR FIT0.155±0.024 OUR FIT• • • We use the following data for averages but not for ts. • • •0.153±0.030±0.0160.153±0.030±0.0160.153±0.030±0.0160.153±0.030±0.016 74 1 BARATE 98E ALEP 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •0.31 ±0.12 ±0.04 2 ACCIARRI 95F L3 19911993 LEP runs1BARATE 98E obtain this value by adding twi e their B(π−K0S K0S ντ ) value to theirB(π−K0S K0L ντ ) value.2ACCIARRI 95F assume B(π− K0S K0S ν)= B(π− K0S K0L ν) = 1/2B(π− K0S K0L ν).(π−K0S K0S ντ

)/total 48/(π−K0S K0S ντ



)/total 48/Bose-Einstein orrelations might make the mixing fra tion dierent than 1/4.VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT2.33±0.07 OUR FIT2.33±0.07 OUR FIT2.33±0.07 OUR FIT2.33±0.07 OUR FIT2.32±0.06 OUR AVERAGE2.32±0.06 OUR AVERAGE2.32±0.06 OUR AVERAGE2.32±0.06 OUR AVERAGE2.33±0.03±0.09 6.7k RYU 14 BELL 669 fb−1 Eee m=10.6 GeV2.31±0.04±0.08 5.0k LEES 12Y BABR 468 fb−1 Eee m=10.6 GeV2.6 ±1.0 ±0.5 6 BARATE 98E ALEP 19911995 LEP runs2.3 ±0.5 ±0.3 42 COAN 96 CLEO Eee m ≈ 10.6 GeV(π−K0S K0Lντ

)/total 49/(π−K0S K0Lντ



)/total 49/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT10.8±2.4 OUR FIT10.8±2.4 OUR FIT10.8±2.4 OUR FIT10.8±2.4 OUR FIT10.1±2.3±1.310.1±2.3±1.310.1±2.3±1.310.1±2.3±1.3 68 BARATE 98E ALEP 19911995 LEP runs(π−K0LK0L ντ

)/total 50/= 48/(π−K0LK0L ντ



)/total 50/= 48/VALUE (units 10−4) DOCUMENT ID2.33±0.07 OUR FIT2.33±0.07 OUR FIT2.33±0.07 OUR FIT2.33±0.07 OUR FIT(π−K0K0π0 ντ

)/total 51/ = (52+56+57)/(π−K0K0π0 ντ

)/total 51/ = (52+56+57)/(π−K0K0π0 ντ

)/total 51/ = (52+56+57)/(π−K0K0π0 ντ

)/total 51/ = (52+56+57)/VALUE (units 10−4) DOCUMENT ID TECN COMMENT3.6±1.2 OUR FIT3.6±1.2 OUR FIT3.6±1.2 OUR FIT3.6±1.2 OUR FIT• • • We use the following data for averages but not for ts. • • •3.1±2.33.1±2.33.1±2.33.1±2.3 1 BARATE 99R ALEP 19911995 LEP runs1BARATE 99R ombine BARATE 98E (π−K0S K0S π0 ντ )/total and(π−K0S K0Lπ0 ντ )/total measurements to obtain this value.(π−K0S K0S π0 ντ

)/total 52/(π−K0S K0S π0 ντ



)/total 52/VALUE (units 10−5) CL% EVTS DOCUMENT ID TECN COMMENT1.82±0.21 OUR FIT1.82±0.21 OUR FIT1.82±0.21 OUR FIT1.82±0.21 OUR FIT1.80±0.21 OUR AVERAGE1.80±0.21 OUR AVERAGE1.80±0.21 OUR AVERAGE1.80±0.21 OUR AVERAGE2.00±0.22±0.20 303 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV1.60±0.20±0.22 409 LEES 12Y BABR 468 fb−1 Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<20 95 BARATE 98E ALEP 19911995 LEP runs(K∗−K0π0 ντ → π−K0S K0S π0 ντ

)/total 53/(K∗−K0π0 ντ → π−K0S K0S π0 ντ



)/total 53/VALUE (units 10−6) DOCUMENT ID TECN COMMENT10.8±1.4±1.510.8±1.4±1.510.8±1.4±1.510.8±1.4±1.5 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV(f1(1285)π−ντ → π−K0S K0S π0 ντ

)/total 54/(f1(1285)π−ντ → π−K0S K0S π0 ντ



)/total 54/VALUE (units 10−6) DOCUMENT ID TECN COMMENT6.8±1.3±0.76.8±1.3±0.76.8±1.3±0.76.8±1.3±0.7 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV(f1(1420)π−ντ → π−K0S K0S π0 ντ




)/total 55/VALUE (units 10−6) DOCUMENT ID TECN COMMENT2.4±0.5±0.62.4±0.5±0.62.4±0.5±0.62.4±0.5±0.6 RYU 14 BELL 669 fb−1 Eee m=10.6 GeV(π−K0S K0Lπ0 ντ

)/total 56/(π−K0S K0Lπ0 ντ



)/total 56/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT3.2±1.2 OUR FIT3.2±1.2 OUR FIT3.2±1.2 OUR FIT3.2±1.2 OUR FIT3.1±1.1±0.53.1±1.1±0.53.1±1.1±0.53.1±1.1±0.5 11 BARATE 98E ALEP 19911995 LEP runs

739739739739See key on page 601 LeptonParti le Listingsτ(π−K0LK0Lπ0 ντ

)/total 57/= 52/(π−K0LK0Lπ0 ντ



)/total 57/= 52/VALUE (units 10−5) DOCUMENT ID1.82±0.21 OUR FIT1.82±0.21 OUR FIT1.82±0.21 OUR FIT1.82±0.21 OUR FIT(K−K0S K0S ντ

)/total 58/(K−K0S K0S ντ



)/total 58/VALUE CL% DOCUMENT ID TECN COMMENT<6.3× 10−7<6.3× 10−7<6.3× 10−7<6.3× 10−7 90 LEES 12Y BABR 468 fb−1 Eee m=10.6 GeV(K−K0S K0S π0 ντ

)/total 59/(K−K0S K0S π0 ντ



)/total 59/VALUE CL% DOCUMENT ID TECN COMMENT<4.0× 10−7<4.0× 10−7<4.0× 10−7<4.0× 10−7 90 LEES 12Y BABR 468 fb−1 Eee m=10.6 GeV(K0h+ h−h− ≥ 0 neutrals ντ

)/total 60/(K0h+ h−h− ≥ 0 neutrals ντ



)/total 60/VALUE (%) CL% DOCUMENT ID TECN COMMENT<0.17<0.17<0.17<0.17 95 TSCHIRHART 88 HRS Eee m= 29 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<0.27 90 BELTRAMI 85 HRS Eee m= 29 GeV(K0h+ h−h−ντ

)/total 61/(K0h+ h−h−ντ



)/total 61/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT2.5±2.0 OUR FIT2.5±2.0 OUR FIT2.5±2.0 OUR FIT2.5±2.0 OUR FIT2.3±1.9±0.72.3±1.9±0.72.3±1.9±0.72.3±1.9±0.7 6 1 BARATE 98E ALEP 19911995 LEP runs1BARATE 98E re onstru t K0's using K0S → π+π− de ays.(h−h− h+ ≥ 0 neutrals ≥ 0K 0Lντ

)/total 62/(h−h− h+ ≥ 0 neutrals ≥ 0K 0Lντ



)/total 62/62/ = (0.3459836+0.3459838+0.3459841+0.3459843+0.424748+0.692049+0.424752+0.692056+0.653461+70+78+85+86+97+103+106+107+0.2810148+0.2810150+0.2810152+0.2628154+0.7259168+0.9078176+0.9078177+0.9078178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT15.21± 0.06 OUR FIT15.21± 0.06 OUR FIT15.21± 0.06 OUR FIT15.21± 0.06 OUR FIT14.8 ± 0.4 OUR AVERAGE14.8 ± 0.4 OUR AVERAGE14.8 ± 0.4 OUR AVERAGE14.8 ± 0.4 OUR AVERAGE14.4 ± 0.6 ±0.3 ADEVA 91F L3 Eee m= 88.394.3 GeV15.0 ± 0.4 ±0.3 BEHREND 89B CELL Eee m= 1447 GeV15.1 ± 0.8 ±0.6 AIHARA 87B TPC Eee m= 29 GeV• • • We do not use the following data for averages, ts, limits, et . • • •13.5 ± 0.3 ±0.3 ABACHI 89B HRS Eee m= 29 GeV12.8 ± 1.0 ±0.7 1 BURCHAT 87 MRK2 Eee m= 29 GeV12.1 ± 0.5 ±1.2 RUCKSTUHL 86 DLCO Eee m= 29 GeV12.8 ± 0.5 ±0.8 1420 SCHMIDKE 86 MRK2 Eee m= 29 GeV15.3 ± 1.1 +1.3

−1.6 367 ALTHOFF 85 TASS Eee m= 34.5 GeV13.6 ± 0.5 ±0.8 BARTEL 85F JADE Eee m= 34.6 GeV12.2 ± 1.3 ±3.9 2 BERGER 85 PLUT Eee m= 34.6 GeV13.3 ± 0.3 ±0.6 FERNANDEZ 85 MAC Eee m= 29 GeV24 ± 6 35 BRANDELIK 80 TASS Eee m= 30 GeV32 ± 5 692 3 BACINO 78B DLCO Eee m= 3.17.4 GeV35 ±11 3 BRANDELIK 78 DASP Assumes V−A de ay18 ± 6.5 33 3 JAROS 78 LGW Eee m > 6 GeV1BURCHAT 87 value is not independent of SCHMIDKE 86 value.2Not independent of BERGER 85 (µ− νµ ντ

)/total, (e− νe ντ)/total, (h− ≥ 1neutralsντ

)/total, and (h− ≥ 0K0L ντ)/total, and therefore not used in the t.3 Low energy experiments are not in average or t be ause the systemati errors in ba k-ground subtra tion are judged to be large.(h− h−h+ ≥ 0 neutrals ντ (ex. K0S → π+π−)(\3-prong"))/total 63/(h− h−h+ ≥ 0 neutrals ντ (ex. K0S → π+π−)(\3-prong"))/total 63/(h− h−h+ ≥ 0 neutrals ντ (ex. K0S → π+π−)(\3-prong"))/total 63/(h− h−h+ ≥ 0 neutrals ντ (ex. K0S → π+π−)(\3-prong"))/total 63/63/ = (70+78+85+86+97+103+106+107+0.2810148+0.2810150+0.2810152+0.489168+0.9078176+0.9078177+0.9078178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT14.55 ±0.06 OUR FIT14.55 ±0.06 OUR FIT14.55 ±0.06 OUR FIT14.55 ±0.06 OUR FIT14.61 ±0.06 OUR AVERAGE14.61 ±0.06 OUR AVERAGE14.61 ±0.06 OUR AVERAGE14.61 ±0.06 OUR AVERAGE14.556±0.105±0.076 1 ACHARD 01D L3 19921995 LEP runs14.96 ±0.09 ±0.22 10.4k AKERS 95Y OPAL 19911994 LEP runs

• • • We use the following data for averages but not for ts. • • •14.652±0.067±0.086 SCHAEL 05C ALEP 19911995 LEP runs14.569±0.093±0.048 23k 2 ABREU 01M DLPH 19921995 LEP runs14.22 ±0.10 ±0.37 3 BALEST 95C CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •15.26 ±0.26 ±0.22 ACTON 92H OPAL Repl. by AKERS 95Y13.3 ±0.3 ±0.8 4 ALBRECHT 92D ARG Eee m= 9.410.6 GeV14.35 +0.40

−0.45 ±0.24 DECAMP 92C ALEP 19891990 LEP runs1The orrelation oeÆ ients between this measurement and the ACHARD 01D measure-ments of B(τ → \1-prong") and B(τ → \5-prong") are −0.978 and −0.19 respe tively.2The orrelation oeÆ ients between this measurement and the ABREU 01M measure-ments of B(τ → 1-prong) and B(τ → 5-prong) are −0.98 and −0.08 respe tively.3Not independent of BALEST 95C B(h− h− h+ ντ ) and B(h− h− h+π0 ντ ) values, andBORTOLETTO 93 B(h− h− h+2π0 ντ )/B(h− h− h+ ≥ 0 neutrals ντ ) value.4This ALBRECHT 92D value is not independent of their (µ− νµντ )(e− νe ντ )/2totalvalue.

(h−h− h+ντ

)/total 64/(h−h− h+ντ



)/total 64/64/ = (0.3459836+0.3459838+70+97+106+0.489168+0.0153176+0.0153177)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT9.80±0.05 OUR FIT9.80±0.05 OUR FIT9.80±0.05 OUR FIT9.80±0.05 OUR FIT• • • We use the following data for averages but not for ts. • • •7.6 ±0.1 ±0.57.6 ±0.1 ±0.57.6 ±0.1 ±0.57.6 ±0.1 ±0.5 7.5k 1 ALBRECHT 96E ARG Eee m= 9.410.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •9.92±0.10±0.09 11.2k 2 BUSKULIC 96 ALEP Repl. by SCHAEL 05C9.49±0.36±0.63 DECAMP 92C ALEP Repl. by SCHAEL 05C8.7 ±0.7 ±0.3 694 3 BEHREND 90 CELL Eee m= 35 GeV7.0 ±0.3 ±0.7 1566 4 BAND 87 MAC Eee m= 29 GeV6.7 ±0.8 ±0.9 5 BURCHAT 87 MRK2 Eee m= 29 GeV6.4 ±0.4 ±0.9 6 RUCKSTUHL 86 DLCO Eee m= 29 GeV7.8 ±0.5 ±0.8 890 SCHMIDKE 86 MRK2 Eee m= 29 GeV8.4 ±0.4 ±0.7 1255 6 FERNANDEZ 85 MAC Eee m= 29 GeV9.7 ±2.0 ±1.3 BEHREND 84 CELL Eee m= 14,22 GeV1ALBRECHT 96E not independent of ALBRECHT 93C (h− h− h+ ντ (ex. K0) ×(parti le− ≥ 0 neutrals ≥ 0K0L ντ )/2total value.2BUSKULIC 96 quote B(h− h− h+ ντ (ex. K0)) = 9.50 ± 0.10 ± 0.11. We add 0.42 toremove their K0 orre tion and redu e the systemati error a ordingly.3BEHREND 90 subtra t 0.3% to a ount for the τ− → K∗(892)− ντ ontribution tomeasured events.4BAND 87 subtra t for harged kaon modes; not independent of FERNANDEZ 85 value.5BURCHAT 87 value is not independent of SCHMIDKE 86 value.6Value obtained by multiplying paper's R = B(h− h− h+ ντ )/B(3-prong) by B(3-prong)= 0.143 and subtra ting 0.3% for K∗(892) ba kground.(h−h− h+ντ (ex.K0))/total 65/(h−h− h+ντ (ex.K0))/total 65/(h−h− h+ντ (ex.K0))/total 65/(h−h− h+ντ (ex.K0))/total 65/65/ = (70+97+106+0.489168+0.0153176+0.0153177)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT9.46 ±0.05 OUR FIT9.46 ±0.05 OUR FIT9.46 ±0.05 OUR FIT9.46 ±0.05 OUR FIT9.44 ±0.14 OUR AVERAGE9.44 ±0.14 OUR AVERAGE9.44 ±0.14 OUR AVERAGE9.44 ±0.14 OUR AVERAGE Error in ludes s ale fa tor of 1.4. See the ideogram below.9.317±0.090±0.082 12.2k 1 ABDALLAH 06A DLPH 19921995 LEP runs9.51 ±0.07 ±0.20 37.7k BALEST 95C CLEO Eee m ≈ 10.6 GeV• • • We use the following data for averages but not for ts. • • •9.87 ±0.10 ±0.24 2 AKERS 95Y OPAL 19911994 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •9.50 ±0.10 ±0.11 11.2k 3 BUSKULIC 96 ALEP Repl. by SCHAEL 05C1See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.2Not independent of AKERS 95Y B(h− h− h+ ≥ 0 neutralsντ (ex. K0S → π+π−)) andB(h− h− h+ ντ (ex. K0))/B(h− h− h+ ≥ 0 neutralsντ (ex. K0S → π+π−)) values.3Not independent of BUSKULIC 96 B(h− h− h+ ντ ) value.



BALEST 95C CLEO 0.1AKERS 95Y OPAL 2.8ABDALLAH 06A DLPH 1.0

χ2


8.5 9 9.5 10 10.5 11(h−h−h+ ντ (ex.K0))/total (%)(h−h− h+ντ (ex.K0))/(h− h−h+ ≥ 0 neutrals ντ (ex. K0S → π+π−)(\3-prong")) 65/63(h−h− h+ντ (ex.K0))/(h− h−h+ ≥ 0 neutrals ντ (ex. K0S → π+π−)(\3-prong")) 65/63(h−h− h+ντ (ex.K0))/(h− h−h+ ≥ 0 neutrals ντ (ex. K0S → π+π−)(\3-prong")) 65/63(h−h− h+ντ (ex.K0))/(h− h−h+ ≥ 0 neutrals ντ (ex. K0S → π+π−)(\3-prong")) 65/6365/63 = (70+97+106+0.489168+0.0153176+0.0153177)/(0.424752+70+78+85+89+97+103+106+107+0.2810148+0.2292149+0.2810150+0.2810152+0.1131154+0.3268158+0.489168+0.9078176+0.9078177+0.9078178+0.892180)VALUE (units 10−2) DOCUMENT ID TECN COMMENT64.98±0.31 OUR FIT64.98±0.31 OUR FIT64.98±0.31 OUR FIT64.98±0.31 OUR FIT66.0 ±0.4 ±1.466.0 ±0.4 ±1.466.0 ±0.4 ±1.466.0 ±0.4 ±1.4 AKERS 95Y OPAL 19911994 LEP runs

740740740740Lepton Parti le Listingsτ(h−h− h+ντ (ex.K0,ω))/total 66/(h−h− h+ντ (ex.K0,ω))/total 66/(h−h− h+ντ (ex.K0,ω))/total 66/(h−h− h+ντ (ex.K0,ω))/total 66/66/ = (70+97+106+0.489168)/VALUE (%) DOCUMENT ID9.43±0.05 OUR FIT9.43±0.05 OUR FIT9.43±0.05 OUR FIT9.43±0.05 OUR FIT(π−π+π− ντ

)/total 67/ = (0.3459836+70+0.0153176)/(π−π+π− ντ

)/total 67/ = (0.3459836+70+0.0153176)/(π−π+π− ντ

)/total 67/ = (0.3459836+70+0.0153176)/(π−π+π− ντ

)/total 67/ = (0.3459836+70+0.0153176)/VALUE (%) DOCUMENT ID9.31±0.05 OUR FIT9.31±0.05 OUR FIT9.31±0.05 OUR FIT9.31±0.05 OUR FIT(π−π+π− ντ (ex.K0))/total 68/= (70+0.0153176)/(π−π+π− ντ (ex.K0))/total 68/= (70+0.0153176)/(π−π+π− ντ (ex.K0))/total 68/= (70+0.0153176)/(π−π+π− ντ (ex.K0))/total 68/= (70+0.0153176)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT9.02±0.05 OUR FIT9.02±0.05 OUR FIT9.02±0.05 OUR FIT9.02±0.05 OUR FIT8.77±0.13 OUR AVERAGE8.77±0.13 OUR AVERAGE8.77±0.13 OUR AVERAGE8.77±0.13 OUR AVERAGE Error in ludes s ale fa tor of 1.1.8.42±0.00+0.26−0.25 8.9M 1 LEE 10 BELL 666 fb−1 Eee m = 10.6 GeV8.83±0.01±0.13 1.6M 2 AUBERT 08 BABR 342 fb−1 Eee m = 10.6 GeV9.13±0.05±0.46 43k 3 BRIERE 03 CLE3 Eee m= 10.6 GeV1Quoted statisti al error is 0.003%. Correlation matrix for LEE 10 bran hing fra tions:(1) (τ− → π−π+π− ντ (ex.K0))/total(2) (τ− → K−π+π− ντ (ex.K0))/total(3) (τ− → K−K+π− ντ )/total(4) (τ− → K−K+K− ντ )/total(1) (2) (3)(2) 0.175(3) 0.049 0.080(4) -0.053 0.035 -0.0082Correlation matrix for AUBERT 08 bran hing fra tions:(1) (τ− → π−π+π− ντ (ex.K0))/total(2) (τ− → K−π+π− ντ (ex.K0))/total(3) (τ− → K−K+π− ντ )/total(4) (τ− → K−K+K− ντ )/total(1) (2) (3)(2) 0.544(3) 0.390 0.177(4) 0.031 0.093 0.0873 47% orrelated with BRIERE 03 τ− → K−π+π− ντ and 71% orrelated with τ− →K−K+π− ντ be ause of a ommon 5% normalization error.(π−π+π− ντ (ex.K0), non-axial ve tor)/(π−π+π−ντ (ex.K0)) 69/68(π−π+π− ντ (ex.K0), non-axial ve tor)/(π−π+π−ντ (ex.K0)) 69/68(π−π+π− ντ (ex.K0), non-axial ve tor)/(π−π+π−ντ (ex.K0)) 69/68(π−π+π− ντ (ex.K0), non-axial ve tor)/(π−π+π−ντ (ex.K0)) 69/6869/68 = 69/(70+0.0153175)VALUE CL% DOCUMENT ID TECN COMMENT

<0.261<0.261<0.261<0.261 95 1 ACKERSTAFF 97R OPAL 19921994 LEP runs1Model-independent limit from stru ture fun tion analysis on ontribution to B(τ− →π−π+π− ντ (ex. K0)) from non-axial ve tors.(π−π+π− ντ (ex.K0,ω))/total 70/(π−π+π− ντ (ex.K0,ω))/total 70/(π−π+π− ντ (ex.K0,ω))/total 70/(π−π+π− ντ (ex.K0,ω))/total 70/VALUE (%) EVTS DOCUMENT ID TECN COMMENT8.99 ±0.05 OUR FIT8.99 ±0.05 OUR FIT8.99 ±0.05 OUR FIT8.99 ±0.05 OUR FIT9.041±0.060±0.0769.041±0.060±0.0769.041±0.060±0.0769.041±0.060±0.076 29k 1 SCHAEL 05C ALEP 1991-1995 LEP runs1 See footnote to SCHAEL 05C (τ− → e− νe ντ )/total measurement for orrelationswith other measurements.(h−h− h+ ≥ 1 neutrals ντ

)/total 71/(h−h− h+ ≥ 1 neutrals ντ



)/total 71/71/ = (0.3459841+0.3459843+0.424748+0.424752+78+85+86+103+107+0.2810148+0.2810150+0.2810152+0.2926154+0.892176+0.892177+0.9078178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT5.29±0.05 OUR FIT5.29±0.05 OUR FIT5.29±0.05 OUR FIT5.29±0.05 OUR FIT• • • We do not use the following data for averages, ts, limits, et . • • •5.6 ±0.7 ±0.3 352 1 BEHREND 90 CELL Eee m= 35 GeV4.2 ±0.5 ±0.9 203 2 ALBRECHT 87L ARG Eee m= 10 GeV6.1 ±0.8 ±0.9 3 BURCHAT 87 MRK2 Eee m= 29 GeV7.6 ±0.4 ±0.9 4,5 RUCKSTUHL 86 DLCO Eee m= 29 GeV4.7 ±0.5 ±0.8 530 6 SCHMIDKE 86 MRK2 Eee m= 29 GeV5.6 ±0.4 ±0.7 5 FERNANDEZ 85 MAC Eee m= 29 GeV6.2 ±2.3 ±1.7 BEHREND 84 CELL Eee m= 14,22 GeV1BEHREND 90 value is not independent of BEHREND 90 B(3hντ ≥ 1 neutrals) +B(5-prong).2ALBRECHT 87L measure the produ t of bran hing ra-tios B(3π±π0 ντ ) B((e ν orµν orπorK orρ)ντ ) = 0.029 and use the PDG 86 valuesfor the se ond bran hing ratio whi h sum to 0.69 ± 0.03 to get the quoted value.3BURCHAT 87 value is not independent of SCHMIDKE 86 value.4Contributions from kaons and from >1π0 are subtra ted. Not independent of (3-prong+ 0π0) and (3-prong + ≥ 0π0) values.5Value obtained using paper's R = B(h− h− h+ ντ )/B(3-prong) and urrent B(3-prong)= 0.143.6Not independent of SCHMIDKE 86 h− h− h+ ντ and h− h− h+( ≥ 0π0)ντ values.

(h−h− h+ ≥ 1π0 ντ (ex. K0))/total 72/(h−h− h+ ≥ 1π0 ντ (ex. K0))/total 72/(h−h− h+ ≥ 1π0 ντ (ex. K0))/total 72/(h−h− h+ ≥ 1π0 ντ (ex. K0))/total 72/72/ = (78+85+86+103+107+0.2292148+0.2292150+0.2292152+0.892176+0.892177+0.9078178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT5.09 ±0.05 OUR FIT5.09 ±0.05 OUR FIT5.09 ±0.05 OUR FIT5.09 ±0.05 OUR FIT5.10 ±0.12 OUR AVERAGE5.10 ±0.12 OUR AVERAGE5.10 ±0.12 OUR AVERAGE5.10 ±0.12 OUR AVERAGE• • • We use the following data for averages but not for ts. • • •5.106±0.083±0.103 10.1k 1 ABDALLAH 06A DLPH 19921995 LEP runs5.09 ±0.10 ±0.23 2 AKERS 95Y OPAL 19911994 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •4.95 ±0.29 ±0.65 570 DECAMP 92C ALEP Repl. by SCHAEL 05C1See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.2Not independent of AKERS 95Y B(h− h− h+ ≥ 0 neutralsντ (ex. K0S → π+π−))and B(h− h− h+ ≥ 0 neutralsντ (ex. K0))/B(h− h− h+ ≥ 0 neutralsντ (ex. K0S →

π+π−)) values.(h−h− h+π0 ντ

)/total 73/(h−h− h+π0 ντ



)/total 73/73/ = (0.3459841+0.3459843+78+103+107+0.2292150+0.892176+0.892177+0.0153178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT4.76±0.05 OUR FIT4.76±0.05 OUR FIT4.76±0.05 OUR FIT4.76±0.05 OUR FIT• • • We do not use the following data for averages, ts, limits, et . • • •4.45±0.09±0.07 6.1k 1 BUSKULIC 96 ALEP Repl. by SCHAEL 05C1BUSKULIC 96 quote B(h− h− h+π0 ντ (ex. K0)) = 4.30 ± 0.09 ± 0.09. We add 0.15to remove their K0 orre tion and redu e the systemati error a ordingly.(h−h− h+π0 ντ (ex.K0))/total 74/(h−h− h+π0 ντ (ex.K0))/total 74/(h−h− h+π0 ντ (ex.K0))/total 74/(h−h− h+π0 ντ (ex.K0))/total 74/74/ = (78+103+107+0.2292150+0.892176+0.892177+0.0153178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT4.57 ±0.05 OUR FIT4.57 ±0.05 OUR FIT4.57 ±0.05 OUR FIT4.57 ±0.05 OUR FIT4.45 ±0.14 OUR AVERAGE4.45 ±0.14 OUR AVERAGE4.45 ±0.14 OUR AVERAGE4.45 ±0.14 OUR AVERAGE Error in ludes s ale fa tor of 1.2.4.545±0.106±0.103 8.9k 1 ABDALLAH 06A DLPH 19921995 LEP runs4.23 ±0.06 ±0.22 7.2k BALEST 95C CLEO Eee m ≈ 10.6 GeV1See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.(h−h− h+π0 ντ (ex. K0, ω))/total75/= (78+103+107+0.2292150)/(h−h− h+π0 ντ (ex. K0, ω))/total75/= (78+103+107+0.2292150)/(h−h− h+π0 ντ (ex. K0, ω))/total75/= (78+103+107+0.2292150)/(h−h− h+π0 ντ (ex. K0, ω))/total75/= (78+103+107+0.2292150)/VALUE (%) DOCUMENT ID2.79±0.07 OUR FIT2.79±0.07 OUR FIT2.79±0.07 OUR FIT2.79±0.07 OUR FIT(π−π+π−π0 ντ

)/total 76/(π−π+π−π0 ντ



)/total 76/76/ = (0.3459841+78+0.892176+0.0153178)/VALUE (%) DOCUMENT ID4.62±0.05 OUR FIT4.62±0.05 OUR FIT4.62±0.05 OUR FIT4.62±0.05 OUR FIT(π−π+π−π0 ντ (ex.K0))/total 77/(π−π+π−π0 ντ (ex.K0))/total 77/(π−π+π−π0 ντ (ex.K0))/total 77/(π−π+π−π0 ντ (ex.K0))/total 77/77/ = (78+0.892176+0.0153178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT4.49 ±0.05 OUR FIT4.49 ±0.05 OUR FIT4.49 ±0.05 OUR FIT4.49 ±0.05 OUR FIT4.55 ±0.13 OUR AVERAGE4.55 ±0.13 OUR AVERAGE4.55 ±0.13 OUR AVERAGE4.55 ±0.13 OUR AVERAGE Error in ludes s ale fa tor of 1.6.4.598±0.057±0.064 16k 1 SCHAEL 05C ALEP 1991-1995 LEP runs4.19 ±0.10 ±0.21 2 EDWARDS 00A CLEO 4.7 fb−1 Eee m= 10.6 GeV1SCHAEL 05C quote (4.590±0.057±0.064)%. We add 0.008% to remove their orre tionfor τ− → π−π0ωντ → π−π0π+π− ντ de ays. See footnote to SCHAEL 05C(τ− → e− νe ντ )/total measurement for orrelations with other measurements.2 EDWARDS 00A quote (4.19 ± 0.10) × 10−2 with a 5% systemati error.(π−π+π−π0 ντ (ex.K0,ω))/total 78/(π−π+π−π0 ντ (ex.K0,ω))/total 78/(π−π+π−π0 ντ (ex.K0,ω))/total 78/(π−π+π−π0 ντ (ex.K0,ω))/total 78/VALUE (%) DOCUMENT ID2.74±0.07 OUR FIT2.74±0.07 OUR FIT2.74±0.07 OUR FIT2.74±0.07 OUR FIT(h−ρπ0 ντ

)/(h− h−h+π0 ντ

) 79/73(h−ρπ0 ντ


) 79/73(h−ρπ0 ντ


) 79/73(h−ρπ0 ντ


) 79/73VALUE EVTS DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.30±0.04±0.02 393 ALBRECHT 91D ARG Eee m= 9.410.6 GeV(h−ρ+ h−ντ

)/(h−h−h+π0 ντ

) 80/73(h−ρ+ h−ντ


) 80/73(h−ρ+ h−ντ


) 80/73(h−ρ+ h−ντ


) 80/73VALUE EVTS DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.10±0.03±0.04 142 ALBRECHT 91D ARG Eee m= 9.410.6 GeV(h−ρ− h+ντ


) 81/73(h−ρ− h+ντ


) 81/73(h−ρ− h+ντ


) 81/73(h−ρ− h+ντ


) 81/73VALUE EVTS DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.26±0.05±0.01 370 ALBRECHT 91D ARG Eee m= 9.410.6 GeV

741741741741See key on page 601 Lepton Parti le Listingsτ(h−h− h+ ≥ 2π0 ντ (ex. K0))/total 82/(h−h− h+ ≥ 2π0 ντ (ex. K0))/total 82/(h−h− h+ ≥ 2π0 ντ (ex. K0))/total 82/(h−h− h+ ≥ 2π0 ντ (ex. K0))/total 82/82/ = (85+86+0.2292148+0.2292152+0.892178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.517±0.031 OUR FIT0.517±0.031 OUR FIT0.517±0.031 OUR FIT0.517±0.031 OUR FIT0.561±0.068±0.0950.561±0.068±0.0950.561±0.068±0.0950.561±0.068±0.095 1.3k 1 ABDALLAH 06A DLPH 19921995 LEP runs1 See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.(h−h− h+2π0 ντ

)/total 83/(h−h− h+2π0 ντ



)/total 83/83/ = (0.424748+85+0.2292148+0.2292152+0.892178)/VALUE (%) DOCUMENT ID0.505±0.031 OUR FIT0.505±0.031 OUR FIT0.505±0.031 OUR FIT0.505±0.031 OUR FIT(h−h− h+2π0 ντ (ex.K0))/total 84/(h−h− h+2π0 ντ (ex.K0))/total 84/(h−h− h+2π0 ντ (ex.K0))/total 84/(h−h− h+2π0 ντ (ex.K0))/total 84/84/ = (85+0.2292148+0.2292152+0.892178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.495±0.031 OUR FIT0.495±0.031 OUR FIT0.495±0.031 OUR FIT0.495±0.031 OUR FIT0.435±0.030±0.0350.435±0.030±0.0350.435±0.030±0.0350.435±0.030±0.035 2.6k 1 SCHAEL 05C ALEP 1991-1995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •0.50 ±0.07 ±0.07 1.8k BUSKULIC 96 ALEP Repl. by SCHAEL 05C1SCHAEL 05C quote (0.392 ± 0.030 ± 0.035)%. We add 0.043% to remove their or-re tion for τ− → π− ηπ0 ντ → π−π+π− 2π0 ντ and τ− → K∗(892)− ηντ →K−π+π− 2π0 ντ de ays. See footnote to SCHAEL 05C (τ− → e− νe ντ )/totalmeasurement for orrelations with other measurements.(h−h− h+2π0 ντ (ex.K0))/(h− h−h+ ≥ 0 neutrals ≥ 0K 0Lντ

) 84/62(h−h− h+2π0 ντ (ex.K0))/(h− h−h+ ≥ 0 neutrals ≥ 0K 0Lντ



) 84/6284/62 = (85+0.2292148+0.2292152+0.892178)/(0.3459836+0.3459838+0.3459841+0.3459843+0.424748+0.692049+0.849452+0.692056+0.653461+70+78+85+89+97+103+106+107+0.2810148+0.2292149+0.2810150+0.2810152+0.3759154+0.3268158+0.7259168+0.9078176+0.9078177+0.9078178+0.892180)VALUE (units 10−2) EVTS DOCUMENT ID TECN COMMENT3.26±0.20 OUR FIT3.26±0.20 OUR FIT3.26±0.20 OUR FIT3.26±0.20 OUR FIT3.4 ±0.2 ±0.33.4 ±0.2 ±0.33.4 ±0.2 ±0.33.4 ±0.2 ±0.3 668 BORTOLETTO93 CLEO Eee m ≈ 10.6 GeV(h−h− h+2π0 ντ (ex.K0,ω,η))/total 85/(h−h− h+2π0 ντ (ex.K0,ω,η))/total 85/(h−h− h+2π0 ντ (ex.K0,ω,η))/total 85/(h−h− h+2π0 ντ (ex.K0,ω,η))/total 85/VALUE (units 10−4) DOCUMENT ID10±4 OUR FIT10±4 OUR FIT10±4 OUR FIT10±4 OUR FIT(h−h− h+3π0 ντ

)/total 86/= (0.424752+87+0.1131154)/(h−h− h+3π0 ντ

)/total 86/= (0.424752+87+0.1131154)/(h−h− h+3π0 ντ

)/total 86/= (0.424752+87+0.1131154)/(h−h− h+3π0 ντ

)/total 86/= (0.424752+87+0.1131154)/VALUE (units 10−4) CL% EVTS DOCUMENT ID TECN COMMENT2.12±0.30 OUR FIT2.12±0.30 OUR FIT2.12±0.30 OUR FIT2.12±0.30 OUR FIT2.2 ±0.3 ±0.42.2 ±0.3 ±0.42.2 ±0.3 ±0.42.2 ±0.3 ±0.4 139 ANASTASSOV 01 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 4.9 95 SCHAEL 05C ALEP 1991-1995 LEP runs2.85±0.56±0.51 57 ANDERSON 97 CLEO Repl. by ANAS-TASSOV 0111 ±4 ±5 440 1 BUSKULIC 96 ALEP Repl. by SCHAEL 05C1BUSKULIC 96 state their measurement is for B(h− h− h+ ≥ 3π0 ντ ). We assume thatB(h− h− h+ ≥ 4π0 ντ ) is very small.(2π−π+ 3π0ντ (ex.K0))/total 87/(2π−π+ 3π0ντ (ex.K0))/total 87/(2π−π+ 3π0ντ (ex.K0))/total 87/(2π−π+ 3π0ντ (ex.K0))/total 87/87/ = (89+0.2292149+0.3268158+0.892180)/VALUE (units 10−4) DOCUMENT ID TECN COMMENT1.94±0.30 OUR FIT1.94±0.30 OUR FIT1.94±0.30 OUR FIT1.94±0.30 OUR FIT• • • We use the following data for averages but not for ts. • • •2.07±0.18±0.372.07±0.18±0.372.07±0.18±0.372.07±0.18±0.37 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1Not independent of LEES 12X (τ− → ηπ−π+π− ντ (ex.K0))/, (τ− →

ηπ−π0π0 ντ )/, (τ− → π−ω2π0 ντ )/, and (τ− → f1(1285)π− ντ →ηπ−π+π− ντ )/ values.(2π−π+ 3π0ντ (ex.K0, η, f1(1285)) )/total 88/(2π−π+ 3π0ντ (ex.K0, η, f1(1285)) )/total 88/(2π−π+ 3π0ντ (ex.K0, η, f1(1285)) )/total 88/(2π−π+ 3π0ντ (ex.K0, η, f1(1285)) )/total 88/VALUE (units 10−4) DOCUMENT ID TECN COMMENT1.69±0.08±0.431.69±0.08±0.431.69±0.08±0.431.69±0.08±0.43 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV(2π−π+ 3π0ντ (ex.K0, η, ω, f1(1285)) )/total 89/(2π−π+ 3π0ντ (ex.K0, η, ω, f1(1285)) )/total 89/(2π−π+ 3π0ντ (ex.K0, η, ω, f1(1285)) )/total 89/(2π−π+ 3π0ντ (ex.K0, η, ω, f1(1285)) )/total 89/VALUE (units 10−5) DOCUMENT ID TECN COMMENT1.4±2.7 OUR FIT1.4±2.7 OUR FIT1.4±2.7 OUR FIT1.4±2.7 OUR FIT1.0±0.8±3.01.0±0.8±3.01.0±0.8±3.01.0±0.8±3.0 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1LEES 12X meaurement orresponds to the lower limit of < 5.8× 10−5 at 90% CL.(K−h+h− ≥ 0 neutrals ντ

)/total 90/(K−h+h− ≥ 0 neutrals ντ



)/total 90/90/ = (0.3459838+0.3459843+97+103+106+107+0.2810150+0.489168+0.9078177)/VALUE (%) CL% DOCUMENT ID TECN COMMENT0.629±0.014 OUR FIT0.629±0.014 OUR FIT0.629±0.014 OUR FIT0.629±0.014 OUR FIT<0.6<0.6<0.6<0.6 90 AIHARA 84C TPC Eee m= 29 GeV

(K−h+π− ντ (ex.K0))/total 91/= (97+106+0.0153177)/(K−h+π− ντ (ex.K0))/total 91/= (97+106+0.0153177)/(K−h+π− ντ (ex.K0))/total 91/= (97+106+0.0153177)/(K−h+π− ντ (ex.K0))/total 91/= (97+106+0.0153177)/VALUE (%) DOCUMENT ID0.437±0.007 OUR FIT0.437±0.007 OUR FIT0.437±0.007 OUR FIT0.437±0.007 OUR FIT(K−h+π− ντ (ex.K0))/(π−π+π− ντ (ex.K0)) 91/68(K−h+π− ντ (ex.K0))/(π−π+π− ντ (ex.K0)) 91/68(K−h+π− ντ (ex.K0))/(π−π+π− ντ (ex.K0)) 91/68(K−h+π− ντ (ex.K0))/(π−π+π− ντ (ex.K0)) 91/6891/68 = (97+106+0.0153177)/(70+0.0153176)VALUE (%) EVTS DOCUMENT ID TECN COMMENT4.84±0.08 OUR FIT4.84±0.08 OUR FIT4.84±0.08 OUR FIT4.84±0.08 OUR FIT5.44±0.21±0.535.44±0.21±0.535.44±0.21±0.535.44±0.21±0.53 7.9k RICHICHI 99 CLEO Eee m= 10.6 GeV(K−h+π−π0 ντ (ex.K0))/total 92/(K−h+π−π0 ντ (ex.K0))/total 92/(K−h+π−π0 ντ (ex.K0))/total 92/(K−h+π−π0 ντ (ex.K0))/total 92/92/ = (103+107+0.2292150+0.892177)/VALUE (units 10−4) DOCUMENT ID8.6±1.2 OUR FIT8.6±1.2 OUR FIT8.6±1.2 OUR FIT8.6±1.2 OUR FIT(K−h+π−π0 ντ (ex.K0))/(π−π+π−π0 ντ (ex.K0)) 92/77(K−h+π−π0 ντ (ex.K0))/(π−π+π−π0 ντ (ex.K0)) 92/77(K−h+π−π0 ντ (ex.K0))/(π−π+π−π0 ντ (ex.K0)) 92/77(K−h+π−π0 ντ (ex.K0))/(π−π+π−π0 ντ (ex.K0)) 92/7792/77 = (103+107+0.2292150+0.892177)/(78+0.892176+0.0153178)VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.91±0.26 OUR FIT1.91±0.26 OUR FIT1.91±0.26 OUR FIT1.91±0.26 OUR FIT2.61±0.45±0.422.61±0.45±0.422.61±0.45±0.422.61±0.45±0.42 719 RICHICHI 99 CLEO Eee m= 10.6 GeV(K−π+π− ≥ 0 neutrals ντ

)/total 93/(K−π+π− ≥ 0 neutrals ντ



)/total 93/93/ = (0.3459838+0.3459843+97+103+0.2810150+0.9078177)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.477±0.014 OUR FIT0.477±0.014 OUR FIT0.477±0.014 OUR FIT0.477±0.014 OUR FIT0.58 +0.15−0.13 ±0.120.58 +0.15−0.13 ±0.120.58 +0.15−0.13 ±0.120.58 +0.15−0.13 ±0.12 20 1 BAUER 94 TPC Eee m= 29 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •0.22 +0.16−0.13 ±0.05 9 2 MILLS 85 DLCO Eee m= 29 GeV1We multiply 0.58% by 0.20, the relative systemati error quoted by BAUER 94, to obtainthe systemati error.2 Error orrelated with MILLS 85 (K K πν) value. We multiply 0.22% by 0.23, the relativesystemati error quoted by MILLS 85, to obtain the systemati error.(K−π+π− ≥ 0π0 ντ (ex.K0))/total 94/(K−π+π− ≥ 0π0 ντ (ex.K0))/total 94/(K−π+π− ≥ 0π0 ντ (ex.K0))/total 94/(K−π+π− ≥ 0π0 ντ (ex.K0))/total 94/94/ = (97+103+0.2292150+0.9078177)/VALUE (%) DOCUMENT ID TECN COMMENT0.373±0.013 OUR FIT0.373±0.013 OUR FIT0.373±0.013 OUR FIT0.373±0.013 OUR FIT0.30 ±0.05 OUR AVERAGE0.30 ±0.05 OUR AVERAGE0.30 ±0.05 OUR AVERAGE0.30 ±0.05 OUR AVERAGE

• • • We use the following data for averages but not for ts. • • •0.343±0.073±0.031 ABBIENDI 00D OPAL 19901995 LEP runs0.275±0.064 1 BARATE 98 ALEP 19911995 LEP runs1Not independent of BARATE 98 (τ− → K−π+π− ντ )/total and (τ− →K−π+π−π0 ντ )/total values.(K−π+π−ντ

)/total 95/ = (0.3459838+97+0.0153177)/(K−π+π−ντ

)/total 95/ = (0.3459838+97+0.0153177)/(K−π+π−ντ

)/total 95/ = (0.3459838+97+0.0153177)/(K−π+π−ντ

)/total 95/ = (0.3459838+97+0.0153177)/VALUE (%) DOCUMENT ID0.345±0.007 OUR FIT0.345±0.007 OUR FIT0.345±0.007 OUR FIT0.345±0.007 OUR FIT(K−π+π−ντ (ex.K0))/total 96/= (97+0.0153177)/(K−π+π−ντ (ex.K0))/total 96/= (97+0.0153177)/(K−π+π−ντ (ex.K0))/total 96/= (97+0.0153177)/(K−π+π−ντ (ex.K0))/total 96/= (97+0.0153177)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.293±0.007 OUR FIT0.293±0.007 OUR FIT0.293±0.007 OUR FIT0.293±0.007 OUR FIT0.290±0.018 OUR AVERAGE0.290±0.018 OUR AVERAGE0.290±0.018 OUR AVERAGE0.290±0.018 OUR AVERAGE Error in ludes s ale fa tor of 2.4. See the ideogram below.0.330±0.001+0.016−0.017 794k 1 LEE 10 BELL 666 fb−1 Eee m=10.6 GeV0.273±0.002±0.009 70k 2 AUBERT 08 BABR 342 fb−1 Eee m=10.6 GeV0.415±0.053±0.040 269 ABBIENDI 04J OPAL 1991-1995 LEP runs0.384±0.014±0.038 3.5k 3 BRIERE 03 CLE3 Eee m= 10.6 GeV0.214±0.037±0.029 BARATE 98 ALEP 19911995 LEP runs

• • • We use the following data for averages but not for ts. • • •0.346±0.023±0.056 158 4 RICHICHI 99 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.360±0.082±0.048 ABBIENDI 00D OPAL 19901995 LEP runs1 See footnote to LEE 10 (τ− → π−π+π− ντ (ex.K0))/total measurement for orrelations with other measurements. Not independent of LEE 10 (τ− →K−π+π− ντ (ex.K0))/(τ− → π−π+π− ντ (ex.K0)) value.2 See footnote to AUBERT 08 (τ− → π−π+π− ντ (ex.K0))/total measurement for orrelations with other measurements.3 47% orrelated with BRIERE 03 τ− → π−π+π− ντ and 34% orrelated with τ− →K−K+π− ντ be ause of a ommon 5% normalization error.4Not independent of RICHICHI 99(τ− → K− h+π− ντ (ex.K0))/(τ− → π−π+π− ντ (ex.K0)), (τ− →K−K+π− ντ )/(τ− → π−π+π− ντ (ex.K0)) and BALEST 95C (τ− →h− h− h+ ντ (ex.K0))/total values.

742742742742LeptonParti le Listingsτ



BARATE 98 ALEP 2.6RICHICHI 99 CLEOBRIERE 03 CLE3 5.4ABBIENDI 04J OPALAUBERT 08 BABR 3.5LEE 10 BELL 5.4

χ2


0.1 0.2 0.3 0.4 0.5 0.6(K−π+π−ντ (ex.K0))/total (%)(K−π+π−ντ (ex.K0))/(π−π+π− ντ (ex.K0)) 96/68(K−π+π−ντ (ex.K0))/(π−π+π− ντ (ex.K0)) 96/68(K−π+π−ντ (ex.K0))/(π−π+π− ντ (ex.K0)) 96/68(K−π+π−ντ (ex.K0))/(π−π+π− ντ (ex.K0)) 96/6896/68 = (97+0.0153177)/(70+0.0153176)VALUE (units 10−2) EVTS DOCUMENT ID TECN COMMENT3.25±0.07 OUR FIT3.25±0.07 OUR FIT3.25±0.07 OUR FIT3.25±0.07 OUR FIT• • • We use the following data for averages but not for ts. • • •3.92±0.02+0.15

−0.163.92±0.02+0.15−0.163.92±0.02+0.15−0.163.92±0.02+0.15−0.16 794k 1 LEE 10 BELL 666 fb−1 Eee m = 10.6 GeV1Not independent of LEE 10 (τ− → K−π+π− ντ (ex.K0))/total and (τ− →

π−π+π− ντ (ex.K0))/total values.(K−π+π−ντ (ex.K0,ω))/total 97/(K−π+π−ντ (ex.K0,ω))/total 97/(K−π+π−ντ (ex.K0,ω))/total 97/(K−π+π−ντ (ex.K0,ω))/total 97/VALUE (units 10−3) DOCUMENT ID2.93±0.07 OUR FIT2.93±0.07 OUR FIT2.93±0.07 OUR FIT2.93±0.07 OUR FIT(K−ρ0 ντ → K−π+π− ντ

)/(K−π+π− ντ (ex.K0)) 98/96(K−ρ0 ντ → K−π+π− ντ



)/(K−π+π− ντ (ex.K0)) 98/96VALUE DOCUMENT ID TECN COMMENT0.48±0.14±0.100.48±0.14±0.100.48±0.14±0.100.48±0.14±0.10 1 ASNER 00B CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.39±0.14 2 BARATE 99R ALEP 19911995 LEP runs1ASNER 00B assume τ− → K−π+π− ντ (ex. K0) de ays pro eed only through K ρ andK∗π intermediate states. They assume the resonan e stru ture of τ− → K−π+π− ντ(ex. K0) de ays is dominated by K1(1270)− and K1(1400)− resonan es, and assumeB(K1(1270) → K∗(892)π) = (16 ± 5)%, B(K1(1270) → K ρ) = (42 ± 6)%, andB(K1(1400) → K ρ) = 0.2BARATE 99R assume τ− → K−π+π− ντ (ex. K0) de ays pro eed only through K ρand K∗π intermediate states. The quoted error is statisti al only.(K−π+π−π0 ντ

)/total 99/(K−π+π−π0 ντ



)/total 99/99/ = (0.3459843+103+0.2292150+0.892177)/VALUE (units 10−4) DOCUMENT ID13.1±1.2 OUR FIT13.1±1.2 OUR FIT13.1±1.2 OUR FIT13.1±1.2 OUR FIT(K−π+π−π0 ντ (ex.K0))/total 100/(K−π+π−π0 ντ (ex.K0))/total 100/(K−π+π−π0 ντ (ex.K0))/total 100/(K−π+π−π0 ντ (ex.K0))/total 100/100/ = (103+0.2292150+0.892177)/VALUE (units 10−4) CL% DOCUMENT ID TECN COMMENT7.9±1.2 OUR FIT7.9±1.2 OUR FIT7.9±1.2 OUR FIT7.9±1.2 OUR FIT7.3±1.2 OUR AVERAGE7.3±1.2 OUR AVERAGE7.3±1.2 OUR AVERAGE7.3±1.2 OUR AVERAGE7.4±0.8±1.1 1 ARMS 05 CLE3 7.6 fb−1, Eee m= 10.6 GeV6.1±3.9±1.8 BARATE 98 ALEP 19911995 LEP runs• • • We use the following data for averages but not for ts. • • •7.5±2.6±1.8 2 RICHICHI 99 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<17 95 ABBIENDI 00D OPAL 19901995 LEP runs1Not independent of ARMS 05 (τ− → K−π+π−π0 ντ (ex.K0,ω)) / total and(τ− → K−ωντ ) / total values.2Not independent of RICHICHI 99(τ− → K− h+π− ντ (ex.K0))/(τ− → π−π+π− ντ (ex.K0)), (τ− →K−K+π− ντ )/(τ− → π−π+π− ντ (ex.K0)) and BALEST 95C (τ− →h− h− h+ ντ (ex.K0))/total values.(K−π+π−π0 ντ (ex.K0,η))/total 101/= (103+0.892177)/(K−π+π−π0 ντ (ex.K0,η))/total 101/= (103+0.892177)/(K−π+π−π0 ντ (ex.K0,η))/total 101/= (103+0.892177)/(K−π+π−π0 ντ (ex.K0,η))/total 101/= (103+0.892177)/VALUE (units 10−4) DOCUMENT ID7.6±1.2 OUR FIT7.6±1.2 OUR FIT7.6±1.2 OUR FIT7.6±1.2 OUR FIT(K−π+π−π0 ντ (ex.K0,ω))/total 102/(K−π+π−π0 ντ (ex.K0,ω))/total 102/(K−π+π−π0 ντ (ex.K0,ω))/total 102/(K−π+π−π0 ντ (ex.K0,ω))/total 102/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT3.7±0.5±0.83.7±0.5±0.83.7±0.5±0.83.7±0.5±0.8 833 ARMS 05 CLE3 7.6 fb−1, Eee m= 10.6 GeV

(K−π+π−π0 ντ (ex.K0,ω,η))/total 103/(K−π+π−π0 ντ (ex.K0,ω,η))/total 103/(K−π+π−π0 ντ (ex.K0,ω,η))/total 103/(K−π+π−π0 ντ (ex.K0,ω,η))/total 103/VALUE (units 10−4) DOCUMENT ID3.9±1.4 OUR FIT3.9±1.4 OUR FIT3.9±1.4 OUR FIT3.9±1.4 OUR FIT(K−π+K− ≥ 0 neut. ντ

)/total 104/(K−π+K− ≥ 0 neut. ντ



)/total 104/VALUE (%) CL% DOCUMENT ID TECN COMMENT<0.09<0.09<0.09<0.09 95 BAUER 94 TPC Eee m= 29 GeV(K−K+π− ≥ 0 neut. ντ

)/total 105/= (106+107)/(K−K+π− ≥ 0 neut. ντ

)/total 105/= (106+107)/(K−K+π− ≥ 0 neut. ντ

)/total 105/= (106+107)/(K−K+π− ≥ 0 neut. ντ

)/total 105/= (106+107)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.1496±0.0033 OUR FIT0.1496±0.0033 OUR FIT0.1496±0.0033 OUR FIT0.1496±0.0033 OUR FIT0.203 ±0.031 OUR AVERAGE0.203 ±0.031 OUR AVERAGE0.203 ±0.031 OUR AVERAGE0.203 ±0.031 OUR AVERAGE0.159 ±0.053 ±0.020 ABBIENDI 00D OPAL 19901995 LEP runs0.15 +0.09−0.07 ±0.03 4 1 BAUER 94 TPC Eee m= 29 GeV

• • • We use the following data for averages but not for ts. • • •0.238 ±0.042 2 BARATE 98 ALEP 19911995 LEP runs1We multiply 0.15% by 0.20, the relative systemati error quoted by BAUER 94, to obtainthe systemati error.2Not independent of BARATE 98 (τ− → K−K+π− ντ )/total and (τ− →K−K+π−π0 ντ )/total values.(K−K+π− ντ

)/total 106/(K−K+π− ντ



)/total 106/VALUE (units 10−3) EVTS DOCUMENT ID TECN COMMENT1.435±0.027 OUR FIT1.435±0.027 OUR FIT1.435±0.027 OUR FIT1.435±0.027 OUR FIT1.43 ±0.07 OUR AVERAGE1.43 ±0.07 OUR AVERAGE1.43 ±0.07 OUR AVERAGE1.43 ±0.07 OUR AVERAGE Error in ludes s ale fa tor of 2.4. See the ideogram below.1.55 ±0.01 +0.06−0.05 108k 1 LEE 10 BELL 666 fb−1 Eee m=10.6 GeV1.346±0.010±0.036 18k 2 AUBERT 08 BABR 342 fb−1 Eee m= 10.6 GeV1.55 ±0.06 ±0.09 932 3 BRIERE 03 CLE3 Eee m= 10.6 GeV1.63 ±0.21 ±0.17 BARATE 98 ALEP 19911995 LEP runs

• • • We use the following data for averages but not for ts. • • •0.87 ±0.56 ±0.40 ABBIENDI 00D OPAL 19901995 LEP runs1.45 ±0.13 ±0.28 2.3k 4 RICHICHI 99 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •2.2 +1.7

−1.1 ±0.5 9 5 MILLS 85 DLCO Eee m= 29 GeV1See footnote to LEE 10 (τ− → π−π+π− ντ (ex.K0))/total measurement for orrelations with other measurements. Not independent of LEE 10 (τ− →K−K+π− ντ )/(τ− → π−π+π− ντ (ex.K0)) value.2 See footnote to AUBERT 08 (τ− → π−π+π− ντ (ex.K0))/total measurement for orrelations with other measurements.3 71% orrelated with BRIERE 03 τ− → π−π+π− ντ and 34% orrelated with τ →K−π+π− ντ be ause of a ommon 5% normalization error.4Not independent of RICHICHI 99 (τ− → K−K+π− ντ )/ (τ− →π−π+π− ντ (ex.K0)) and BALEST 95C (τ− → h− h− h+ ντ (ex.K0))/total val-ues.5 Error orrelated with MILLS 85 (K πππ0 ν) value. We multiply 0.22% by 0.23, therelative systemati error quoted by MILLS 85, to obtain the systemati error.



BARATE 98 ALEPRICHICHI 99 CLEOABBIENDI 00D OPALBRIERE 03 CLE3 1.3AUBERT 08 BABR 4.9LEE 10 BELL 5.7

χ2


1 1.2 1.4 1.6 1.8 2 2.2(K−K+π−ντ

)/total (units 10−3)(K−K+π− ντ

)/(π−π+π−ντ (ex.K0)) 106/68(K−K+π− ντ

)/(π−π+π−ντ (ex.K0)) 106/68(K−K+π− ντ

)/(π−π+π−ντ (ex.K0)) 106/68(K−K+π− ντ

)/(π−π+π−ντ (ex.K0)) 106/68106/68 = 106/(70+0.0153176)VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.592±0.030 OUR FIT1.592±0.030 OUR FIT1.592±0.030 OUR FIT1.592±0.030 OUR FIT1.83 ±0.05 OUR AVERAGE1.83 ±0.05 OUR AVERAGE1.83 ±0.05 OUR AVERAGE1.83 ±0.05 OUR AVERAGE1.60 ±0.15 ±0.30 2.3k RICHICHI 99 CLEO Eee m= 10.6 GeV• • • We use the following data for averages but not for ts. • • •1.84 ±0.01 ±0.05 108k 1 LEE 10 BELL 666 fb−1 Eee m= 10.6 GeV1Not independent of LEE 10 (τ− → K−K+π− ντ )/total and (τ− →

π−π+π− ντ (ex.K0))/total values.

743743743743See key on page 601 LeptonParti le Listingsτ(K−K+π−π0 ντ

)/total 107/(K−K+π−π0 ντ



)/total 107/VALUE (units 10−4) CL% EVTS DOCUMENT ID TECN COMMENT0.61±0.18 OUR FIT0.61±0.18 OUR FIT0.61±0.18 OUR FIT0.61±0.18 OUR FIT0.60±0.18 OUR AVERAGE0.60±0.18 OUR AVERAGE0.60±0.18 OUR AVERAGE0.60±0.18 OUR AVERAGE0.55±0.14±0.12 48 ARMS 05 CLE3 7.6 fb−1,Eee m=10.6 GeV7.5 ±2.9 ±1.5 BARATE 98 ALEP 19911995 LEP runs• • • We use the following data for averages but not for ts. • • •3.3 ±1.8 ±0.7 158 1 RICHICHI 99 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<27 95 ABBIENDI 00D OPAL 19901995 LEP runs1Not independent of RICHICHI 99(τ− → K−K+π− ντ )/(τ− → π−π+π− ντ (ex.K0)) and BALEST 95C (τ− →h− h− h+ ντ (ex.K0))/total values.(K−K+π−π0 ντ

)/(π−π+π−π0 ντ (ex.K0)) 107/77(K−K+π−π0 ντ



)/(π−π+π−π0 ντ (ex.K0)) 107/77107/77 = 107/(78+0.892176+0.0153178)VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.14±0.04 OUR FIT0.14±0.04 OUR FIT0.14±0.04 OUR FIT0.14±0.04 OUR FIT0.79±0.44±0.160.79±0.44±0.160.79±0.44±0.160.79±0.44±0.16 158 1 RICHICHI 99 CLEO Eee m= 10.6 GeV1RICHICHI 99 also quote a 95%CL upper limit of 0.0157 for this measurement.(K−K+K−ντ

)/total 108/= 0.489168/(K−K+K−ντ

)/total 108/= 0.489168/(K−K+K−ντ

)/total 108/= 0.489168/(K−K+K−ντ

)/total 108/= 0.489168/VALUE (units 10−5) CL% EVTS DOCUMENT ID TECN COMMENT2.2 ±0.8 OUR FIT2.2 ±0.8 OUR FIT2.2 ±0.8 OUR FIT2.2 ±0.8 OUR FIT Error in ludes s ale fa tor of 5.4.2.1 ±0.8 OUR AVERAGE2.1 ±0.8 OUR AVERAGE2.1 ±0.8 OUR AVERAGE2.1 ±0.8 OUR AVERAGE Error in ludes s ale fa tor of 5.4.3.29±0.17+0.19−0.20 3.2k 1 LEE 10 BELL 666 fb−1 Eee m = 10.6 GeV1.58±0.13±0.12 275 2 AUBERT 08 BABR 342 fb−1 Eee m= 10.6 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •< 3.7 90 BRIERE 03 CLE3 Eee m= 10.6 GeV< 19 90 BARATE 98 ALEP 19911995 LEP runs1 See footnote to LEE 10 (τ− → π−π+π− ντ (ex.K0))/total measurement for orrelations with other measurements. Not independent of LEE 10 (τ− →K−K+K− ντ )/(τ− → π−π+π− ντ (ex.K0)) value.2 See footnote to AUBERT 08 (τ− → π−π+π− ντ (ex.K0))/total measurement for orrelations with other measurements.(K−K+K−ντ

)/(π−π+π− ντ (ex.K0)) 108/68(K−K+K−ντ

)/(π−π+π− ντ (ex.K0)) 108/68(K−K+K−ντ

)/(π−π+π− ντ (ex.K0)) 108/68(K−K+K−ντ

)/(π−π+π− ντ (ex.K0)) 108/68VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •3.90±0.02+0.22

−0.23 3.2k 1 LEE 10 BELL 666 fb−1 Eee m = 10.6 GeV1Not independent of LEE 10 (τ− → K−K+K− ντ )/total and (τ− →π−π+π− ντ (ex.K0))/total values.(K−K+K−ντ (ex. φ))/total 109/(K−K+K−ντ (ex. φ))/total 109/(K−K+K−ντ (ex. φ))/total 109/(K−K+K−ντ (ex. φ))/total 109/VALUE CL% DOCUMENT ID TECN COMMENT

<2.5× 10−6<2.5× 10−6<2.5× 10−6<2.5× 10−6 90 AUBERT 08 BABR 342 fb−1 Eee m = 10.6 GeV(K−K+K−π0 ντ

)/total 110/(K−K+K−π0 ντ



)/total 110/VALUE CL% DOCUMENT ID TECN COMMENT<4.8× 10−6<4.8× 10−6<4.8× 10−6<4.8× 10−6 90 ARMS 05 CLE3 7.6 fb−1, Eee m= 10.6 GeV(π−K+π− ≥ 0 neut. ντ

)/total 111/(π−K+π− ≥ 0 neut. ντ



)/total 111/VALUE (%) CL% DOCUMENT ID TECN COMMENT<0.25<0.25<0.25<0.25 95 BAUER 94 TPC Eee m= 29 GeV(e− e− e+νe ντ

)/total 112/(e− e− e+νe ντ



)/total 112/VALUE (units 10−5) EVTS DOCUMENT ID TECN COMMENT2.8±1.4±0.42.8±1.4±0.42.8±1.4±0.42.8±1.4±0.4 5 ALAM 96 CLEO Eee m= 10.6 GeV(µ− e− e+νµ ντ

)/total 113/(µ− e− e+νµ ντ



)/total 113/VALUE (units 10−5) CL% DOCUMENT ID TECN COMMENT<3.6<3.6<3.6<3.6 90 ALAM 96 CLEO Eee m= 10.6 GeV

(3h−2h+ ≥ 0 neutrals ντ (ex. K0S → π−π+)(\5-prong"))/total 114/(3h−2h+ ≥ 0 neutrals ντ (ex. K0S → π−π+)(\5-prong"))/total 114/(3h−2h+ ≥ 0 neutrals ντ (ex. K0S → π−π+)(\5-prong"))/total 114/(3h−2h+ ≥ 0 neutrals ντ (ex. K0S → π−π+)(\5-prong"))/total 114/114/ = (115+121)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.099±0.004 OUR FIT0.099±0.004 OUR FIT0.099±0.004 OUR FIT0.099±0.004 OUR FIT0.107±0.007 OUR AVERAGE0.107±0.007 OUR AVERAGE0.107±0.007 OUR AVERAGE0.107±0.007 OUR AVERAGE Error in ludes s ale fa tor of 1.1.0.170±0.022±0.026 1 ACHARD 01D L3 19921995 LEP runs0.097±0.005±0.011 419 GIBAUT 94B CLEO Eee m= 10.6 GeV0.102±0.029 13 BYLSMA 87 HRS Eee m= 29 GeV• • • We use the following data for averages but not for ts. • • •0.093±0.009±0.012 SCHAEL 05C ALEP 1991-1995 LEP runs0.115±0.013±0.006 112 2 ABREU 01M DLPH 19921995 LEP runs0.119±0.013±0.008 119 3 ACKERSTAFF 99E OPAL 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •0.26 ±0.06 ±0.05 ACTON 92H OPAL Eee m= 88.294.2 GeV0.10 +0.05

−0.04 ±0.03 DECAMP 92C ALEP 19891990 LEP runs0.16 ±0.13 ±0.04 BEHREND 89B CELL Eee m= 1447 GeV0.3 ±0.1 ±0.2 BARTEL 85F JADE Eee m= 34.6 GeV0.13 ±0.04 10 BELTRAMI 85 HRS Repl. by BYLSMA 870.16 ±0.08 ±0.04 4 BURCHAT 85 MRK2 Eee m= 29 GeV1.0 ±0.4 10 BEHREND 82 CELL Repl. by BEHREND 89B1The orrelation oeÆ ients between this measurement and the ACHARD 01D measure-ments of B(τ → \1-prong") and B(τ → \3-prong") are −0.082 and −0.19 respe tively.2The orrelation oeÆ ients between this measurement and the ABREU 01M measure-ments of B(τ → 1-prong) and B(τ → 3-prong) are −0.08 and −0.08 respe tively.3Not independent of ACKERSTAFF 99E B(τ− → 3h− 2h+ ντ (ex. K0)) and B(τ− →3h− 2h+π0 ντ (ex. K0)) measurements.(3h−2h+ντ (ex.K0))/total 115/= (116+118+0.0153183)/(3h−2h+ντ (ex.K0))/total 115/= (116+118+0.0153183)/(3h−2h+ντ (ex.K0))/total 115/= (116+118+0.0153183)/(3h−2h+ντ (ex.K0))/total 115/= (116+118+0.0153183)/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT8.22±0.32 OUR FIT8.22±0.32 OUR FIT8.22±0.32 OUR FIT8.22±0.32 OUR FIT8.32±0.35 OUR AVERAGE8.32±0.35 OUR AVERAGE8.32±0.35 OUR AVERAGE8.32±0.35 OUR AVERAGE9.7 ±1.5 ±0.5 96 1 ABDALLAH 06A DLPH 19921995 LEP runs7.2 ±0.9 ±1.2 165 2 SCHAEL 05C ALEP 1991-1995 LEP runs9.1 ±1.4 ±0.6 97 ACKERSTAFF 99E OPAL 19911995 LEP runs7.7 ±0.5 ±0.9 295 GIBAUT 94B CLEO Eee m= 10.6 GeV6.4 ±2.3 ±1.0 12 ALBRECHT 88B ARG Eee m= 10 GeV5.1 ±2.0 7 BYLSMA 87 HRS Eee m= 29 GeV• • • We use the following data for averages but not for ts. • • •8.56±0.05±0.42 34k AUBERT,B 05W BABR 232 fb−1, Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •8.0 ±1.1 ±1.3 58 BUSKULIC 96 ALEP Repl. by SCHAEL 05C6.7 ±3.0 5 3 BELTRAMI 85 HRS Repl. by BYLSMA 871See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.2 See footnote to SCHAEL 05C (τ− → e− νe ντ )/total measurement for orrelationswith other measurements.3The error quoted is statisti al only.(3π−2π+ντ (ex.K0, ω))/total 116/= (117+171)/(3π−2π+ντ (ex.K0, ω))/total 116/= (117+171)/(3π−2π+ντ (ex.K0, ω))/total 116/= (117+171)/(3π−2π+ντ (ex.K0, ω))/total 116/= (117+171)/VALUE (units 10−4) DOCUMENT ID TECN COMMENT8.21±0.31 OUR FIT8.21±0.31 OUR FIT8.21±0.31 OUR FIT8.21±0.31 OUR FIT• • • We use the following data for averages but not for ts. • • •8.33±0.04±0.438.33±0.04±0.438.33±0.04±0.438.33±0.04±0.43 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1Not independent of LEES 12X (τ− → f1(1285)π− ντ → 3π− 2π+ ντ )/ and (τ− →3π− 2π+ ντ (ex.K0, ω, f1(1285)))/ values.(3π−2π+ντ (ex.K0, ω, f1(1285)))/total 117/(3π−2π+ντ (ex.K0, ω, f1(1285)))/total 117/(3π−2π+ντ (ex.K0, ω, f1(1285)))/total 117/(3π−2π+ντ (ex.K0, ω, f1(1285)))/total 117/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT7.69±0.30 OUR FIT7.69±0.30 OUR FIT7.69±0.30 OUR FIT7.69±0.30 OUR FIT7.68±0.04±0.407.68±0.04±0.407.68±0.04±0.407.68±0.04±0.40 69k LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV(K−2π−2π+ντ (ex.K0))/total 118/(K−2π−2π+ντ (ex.K0))/total 118/(K−2π−2π+ντ (ex.K0))/total 118/(K−2π−2π+ντ (ex.K0))/total 118/VALUE (units 10−6) DOCUMENT ID TECN COMMENT0.6±1.2 OUR FIT0.6±1.2 OUR FIT0.6±1.2 OUR FIT0.6±1.2 OUR FIT0.6±0.5±1.10.6±0.5±1.10.6±0.5±1.10.6±0.5±1.1 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1LEES 12X meaurement orresponds to the lower limit of < 2.4× 10−6 at 90% CL.(K+3π−π+ ντ

)/total 119/(K+3π−π+ ντ



)/total 119/VALUE CL% DOCUMENT ID TECN COMMENT<5.0× 10−6<5.0× 10−6<5.0× 10−6<5.0× 10−6 90 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV(K+K−2π−π+ ντ

)/total 120/(K+K−2π−π+ ντ



)/total 120/VALUE CL% DOCUMENT ID TECN COMMENT<4.5× 10−7<4.5× 10−7<4.5× 10−7<4.5× 10−7 90 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV

744744744744Lepton Parti le Listingsτ(3h−2h+π0 ντ (ex.K0))/total 121/= (122+125)/(3h−2h+π0 ντ (ex.K0))/total 121/= (122+125)/(3h−2h+π0 ντ (ex.K0))/total 121/= (122+125)/(3h−2h+π0 ντ (ex.K0))/total 121/= (122+125)/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT1.64±0.11 OUR FIT1.64±0.11 OUR FIT1.64±0.11 OUR FIT1.64±0.11 OUR FIT1.74±0.27 OUR AVERAGE1.74±0.27 OUR AVERAGE1.74±0.27 OUR AVERAGE1.74±0.27 OUR AVERAGE1.6 ±1.2 ±0.6 13 1 ABDALLAH 06A DLPH 19921995 LEP runs2.1 ±0.7 ±0.9 95 2 SCHAEL 05C ALEP 1991-1995 LEP runs1.7 ±0.2 ±0.2 231 ANASTASSOV 01 CLEO Eee m= 10.6 GeV2.7 ±1.8 ±0.9 23 ACKERSTAFF 99E OPAL 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •1.8 ±0.7 ±1.2 18 BUSKULIC 96 ALEP Repl. by SCHAEL 05C1.9 ±0.4 ±0.4 31 GIBAUT 94B CLEO Repl. by ANASTASSOV 015.1 ±2.2 6 BYLSMA 87 HRS Eee m= 29 GeV6.7 ±3.0 5 3 BELTRAMI 85 HRS Repl. by BYLSMA 871See footnote to ABDALLAH 06A (τ− → h− ντ )/total measurement for orrelationswith other measurements.2 SCHAEL 05C quote (1.4 ± 0.7 ± 0.9) × 10−4. We add 0.7 × 10−4 to remove their orre tion for τ− → ηπ−π+π− ντ → 3π− 2π+π0 ντ and τ− → K∗(892)− ηντ →3π− 2π+π0 ντ de ays. See footnote to SCHAEL 05C (τ− → e− νe ντ )/total mea-surement for orrelations with other measurements.3The error quoted is statisti al only.(3π−2π+π0 ντ (ex.K0))/total 122/(3π−2π+π0 ντ (ex.K0))/total 122/(3π−2π+π0 ντ (ex.K0))/total 122/(3π−2π+π0 ντ (ex.K0))/total 122/122/ = (124+0.2292158+0.892183)/VALUE (units 10−4) DOCUMENT ID TECN COMMENT1.62±0.11 OUR FIT1.62±0.11 OUR FIT1.62±0.11 OUR FIT1.62±0.11 OUR FIT• • • We use the following data for averages but not for ts. • • •1.65±0.05±0.091.65±0.05±0.091.65±0.05±0.091.65±0.05±0.09 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1Not independent of LEES 12X measurements of (τ− → 2π−π+ωντ (ex.K0))/,(τ− → ηπ−π+π− ντ (ex.K0))/, and (τ− → 3π− 2π+π0 ντ (ex.K0, η, ω,f1(1285)))/.(3π−2π+π0 ντ (ex.K0, η, f1(1285)))/total 123/(3π−2π+π0 ντ (ex.K0, η, f1(1285)))/total 123/(3π−2π+π0 ντ (ex.K0, η, f1(1285)))/total 123/(3π−2π+π0 ντ (ex.K0, η, f1(1285)))/total 123/VALUE (units 10−4) DOCUMENT ID TECN COMMENT1.11±0.04±0.091.11±0.04±0.091.11±0.04±0.091.11±0.04±0.09 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1Not independent of LEES 12X (τ− → 2π−π+ωντ (ex.K0))/ and (τ− →3π− 2π+π0 ντ (ex.K0, η, ω, f1(1285)))/ values.(3π−2π+π0 ντ (ex.K0, η, ω, f1(1285)))/total 124/(3π−2π+π0 ντ (ex.K0, η, ω, f1(1285)))/total 124/(3π−2π+π0 ντ (ex.K0, η, ω, f1(1285)))/total 124/(3π−2π+π0 ντ (ex.K0, η, ω, f1(1285)))/total 124/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT0.38±0.09 OUR FIT0.38±0.09 OUR FIT0.38±0.09 OUR FIT0.38±0.09 OUR FIT0.36±0.03±0.090.36±0.03±0.090.36±0.03±0.090.36±0.03±0.09 7.3k LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV(K−2π−2π+π0 ντ (ex.K0))/total 125/(K−2π−2π+π0 ντ (ex.K0))/total 125/(K−2π−2π+π0 ντ (ex.K0))/total 125/(K−2π−2π+π0 ντ (ex.K0))/total 125/VALUE (units 10−6) DOCUMENT ID TECN COMMENT1.1±0.6 OUR FIT1.1±0.6 OUR FIT1.1±0.6 OUR FIT1.1±0.6 OUR FIT1.1±0.4±0.41.1±0.4±0.41.1±0.4±0.41.1±0.4±0.4 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1LEES 12X meaurement orresponds to the lower limit of < 1.9× 10−6 at 90% CL.(K+3π−π+π0 ντ

)/total 126/(K+3π−π+π0 ντ



)/total 126/VALUE CL% DOCUMENT ID TECN COMMENT<8× 10−7<8× 10−7<8× 10−7<8× 10−7 90 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV(3h−2h+2π0ντ

)/total 127/(3h−2h+2π0ντ



)/total 127/VALUE CL% DOCUMENT ID TECN COMMENT<3.4× 10−6<3.4× 10−6<3.4× 10−6<3.4× 10−6 90 AUBERT,B 06 BABR 232 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.1× 10−4 90 GIBAUT 94B CLEO Eee m= 10.6 GeV((5π )− ντ

)/total 128/((5π )− ντ

)/total 128/((5π )− ντ

)/total 128/((5π )− ντ

)/total 128/128/ = (30+1245+48+1261+85+115+0.5559148+0.892178)/VALUE (%) DOCUMENT ID TECN COMMENT0.78±0.05 OUR FIT0.78±0.05 OUR FIT0.78±0.05 OUR FIT0.78±0.05 OUR FIT• • • We use the following data for averages but not for ts. • • •0.61±0.06±0.080.61±0.06±0.080.61±0.06±0.080.61±0.06±0.08 1 GIBAUT 94B CLEO Eee m= 10.6 GeV1Not independent of GIBAUT 94B B(3h− 2h+ ντ ), PROCARIO 93 B(h− 4π0 ντ ), andBORTOLETTO 93 B(2h− h+2π0 ντ )/B(\3prong") measurements. Result is orre tedfor η ontributions.(4h−3h+ ≥ 0 neutrals ντ (\7-prong"))/total 129/(4h−3h+ ≥ 0 neutrals ντ (\7-prong"))/total 129/(4h−3h+ ≥ 0 neutrals ντ (\7-prong"))/total 129/(4h−3h+ ≥ 0 neutrals ντ (\7-prong"))/total 129/VALUE CL% DOCUMENT ID TECN COMMENT<3.0× 10−7<3.0× 10−7<3.0× 10−7<3.0× 10−7 90 AUBERT,B 05F BABR 232 fb−1, Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.8× 10−5 95 ACKERSTAFF 97J OPAL 19901995 LEP runs<2.4× 10−6 90 EDWARDS 97B CLEO Eee m= 10.6 GeV<2.9× 10−4 90 BYLSMA 87 HRS Eee m= 29 GeV(4h−3h+ντ

)/total 130/(4h−3h+ντ



)/total 130/VALUE CL% DOCUMENT ID TECN COMMENT<4.3× 10−7<4.3× 10−7<4.3× 10−7<4.3× 10−7 90 AUBERT,B 05F BABR 232 fb−1, Eee m= 10.6GeV

(4h−3h+π0 ντ

)/total 131/(4h−3h+π0 ντ



)/total 131/VALUE CL% DOCUMENT ID TECN COMMENT<2.5× 10−7<2.5× 10−7<2.5× 10−7<2.5× 10−7 90 AUBERT,B 05F BABR 232 fb−1, Eee m= 10.6 GeV(X− (S=−1)ντ

)/total 132/(X− (S=−1)ντ

)/total 132/(X− (S=−1)ντ

)/total 132/(X− (S=−1)ντ

)/total 132/132/ = (10+16+23+28+36+41+45+61+97+103+118+125+150+152+154+0.8312168+177)/VALUE (%) DOCUMENT ID TECN COMMENT2.92±0.04 OUR FIT2.92±0.04 OUR FIT2.92±0.04 OUR FIT2.92±0.04 OUR FIT• • • We use the following data for averages but not for ts. • • •2.87±0.122.87±0.122.87±0.122.87±0.12 1 BARATE 99R ALEP 19911995 LEP runs1BARATE 99R perform a ombined analysis of all ALEPH LEP 1 data on τ bran hingfra tion measurements for de ay modes having total strangeness equal to −1.(K∗(892)− ≥ 0 neutrals ≥ 0K 0Lντ

)/total 133/(K∗(892)− ≥ 0 neutrals ≥ 0K 0Lντ



)/total 133/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.42±0.18 OUR AVERAGE1.42±0.18 OUR AVERAGE1.42±0.18 OUR AVERAGE1.42±0.18 OUR AVERAGE Error in ludes s ale fa tor of 1.4. See the ideogram below.1.19±0.15+0.13−0.18 104 ALBRECHT 95H ARG Eee m= 9.410.6 GeV1.94±0.27±0.15 74 1 AKERS 94G OPAL Eee m= 8894 GeV1.43±0.11±0.13 475 2 GOLDBERG 90 CLEO Eee m= 9.410.9 GeV1AKERS 94G reje t events in whi h a K0S a ompanies the K∗(892)−. We do not orre tfor them.2GOLDBERG 90 estimates that 10% of observed K∗(892) are a ompanied by a π0.


GOLDBERG 90 CLEO 0.0AKERS 94G OPAL 2.8ALBRECHT 95H ARG 1.3

χ2


0.5 1 1.5 2 2.5 3 3.5(K∗(892)− ≥ 0 neutrals ≥ 0K0L ντ

)/total (%)(K∗(892)− ντ

)/total 134/(K∗(892)− ντ

)/total 134/(K∗(892)− ντ

)/total 134/(K∗(892)− ντ

)/total 134/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.20 ±0.07 OUR AVERAGE1.20 ±0.07 OUR AVERAGE1.20 ±0.07 OUR AVERAGE1.20 ±0.07 OUR AVERAGE Error in ludes s ale fa tor of 1.8. See the ideogram below.1.131±0.006±0.051 49k 1 EPIFANOV 07 BELL 351 fb−1 Eee m=10.6 GeV1.326±0.063 BARATE 99R ALEP 19911995 LEP runs1.11 ±0.12 2 COAN 96 CLEO Eee m ≈ 10.6 GeV1.42 ±0.22 ±0.09 3 ACCIARRI 95F L3 19911993 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •1.39 ±0.09 ±0.10 4 BUSKULIC 96 ALEP Repl. by BARATE 99R1.45 ±0.13 ±0.11 273 5 BUSKULIC 94F ALEP Repl. by BUSKULIC 961.23 ±0.21 +0.11

−0.21 54 6 ALBRECHT 88L ARG Eee m= 10 GeV1.9 ±0.3 ±0.4 44 7 TSCHIRHART 88 HRS Eee m= 29 GeV1.5 ±0.4 ±0.4 15 8 AIHARA 87C TPC Eee m= 29 GeV1.3 ±0.3 ±0.3 31 YELTON 86 MRK2 Eee m= 29 GeV1.7 ±0.7 11 DORFAN 81 MRK2 Eee m= 4.26.7 GeV1EPIFANOV 07 quote B(τ− → K∗(892)− ντ ) B(K∗(892)− → K0S π−) = (3.77 ±0.02(stat) ±0.12(syst) ±0.12(mod)) × 10−3. We add the systemati and model un- ertainties in quadrature and divide by B(K∗(892)− → K0S π−) = 0.3333.2Not independent of COAN 96 B(π−K0 ντ ) and BATTLE 94 B(K−π0 ντ ) measure-ments. K π nal states are onsistent with and assumed to originate from K∗(892)−produ tion.3This result is obtained from their B(π−K0 ντ ) assuming all those de ays originate inK∗(892)− de ays.4Not independent of BUSKULIC 96 B(π−K0 ντ ) and B(K−π0 ντ ) measurements.5BUSKULIC 94F obtain this result from BUSKULIC 94F B(K0π− ντ ) and BUSKULIC 94EB(K−π0 ντ ) assuming all of those de ays originate in K∗(892)− de ays.6The authors divide by 2/ = 0.865 to obtain this result.7Not independent of TSCHIRHART 88 (τ− → h−K0 ≥ 0 neutrals ≥ 0K0L ντ ) / .8De ay π− identied in this experiment, is assumed in the others.

745745745745See key on page 601 LeptonParti le Listingsτ


ACCIARRI 95F L3COAN 96 CLEO 0.6BARATE 99R ALEP 3.7EPIFANOV 07 BELL 2.0

χ2


0.8 1 1.2 1.4 1.6 1.8 2 2.2(K∗(892)− ντ

)/total (%)(K∗(892)− ντ

)/(π−π0 ντ

) 134/14(K∗(892)− ντ

)/(π−π0 ντ

) 134/14(K∗(892)− ντ

)/(π−π0 ντ

) 134/14(K∗(892)− ντ

)/(π−π0 ντ

) 134/14VALUE DOCUMENT ID TECN COMMENT0.075±0.0270.075±0.0270.075±0.0270.075±0.027 1 ABREU 94K DLPH LEP 1992 Z data1ABREU 94K quote B(τ− → K∗(892)− ντ )B(K∗(892)− → K−π0)/B(τ− → ρ− ντ )= 0.025 ± 0.009. We divide by B(K∗(892)− → K−π0) = 0.333 to obtain this result.(K∗(892)− ντ → π−K0ντ

)/(π−K0 ντ

) 135/36(K∗(892)− ντ → π−K0ντ

)/(π−K0 ντ

) 135/36(K∗(892)− ντ → π−K0ντ

)/(π−K0 ντ

) 135/36(K∗(892)− ντ → π−K0ντ

)/(π−K0 ντ

) 135/36VALUE EVTS DOCUMENT ID TECN COMMENT0.933±0.0270.933±0.0270.933±0.0270.933±0.027 49k EPIFANOV 07 BELL 351 fb−1 Eee m= 10.6 GeV(K∗(892)0K− ≥ 0 neutrals ντ

)/total 136/(K∗(892)0K− ≥ 0 neutrals ντ



)/total 136/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.32±0.08±0.120.32±0.08±0.120.32±0.08±0.120.32±0.08±0.12 119 GOLDBERG 90 CLEO Eee m= 9.410.9 GeV(K∗(892)0K−ντ

)/total 137/(K∗(892)0K−ντ

)/total 137/(K∗(892)0K−ντ

)/total 137/(K∗(892)0K−ντ

)/total 137/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.21 ±0.04 OUR AVERAGE0.21 ±0.04 OUR AVERAGE0.21 ±0.04 OUR AVERAGE0.21 ±0.04 OUR AVERAGE0.213±0.048 1 BARATE 98 ALEP 19911995 LEP runs0.20 ±0.05 ±0.04 47 ALBRECHT 95H ARG Eee m= 9.410.6 GeV1BARATE 98 measure the K− (ρ0 → π+π−) fra tion in τ− → K−π+π− ντ de- ays to be (35 ± 11)% and derive this result from their measurement of (τ− →K−π+π− ντ )/total assuming the intermediate states are all K− ρ and K−K∗(892)0.(K∗(892)0π− ≥ 0 neutrals ντ

)/total 138/(K∗(892)0π− ≥ 0 neutrals ντ



)/total 138/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.38±0.11±0.130.38±0.11±0.130.38±0.11±0.130.38±0.11±0.13 105 GOLDBERG 90 CLEO Eee m= 9.410.9 GeV(K∗(892)0π− ντ

)/total 139/(K∗(892)0π− ντ

)/total 139/(K∗(892)0π− ντ

)/total 139/(K∗(892)0π− ντ

)/total 139/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.22 ±0.05 OUR AVERAGE0.22 ±0.05 OUR AVERAGE0.22 ±0.05 OUR AVERAGE0.22 ±0.05 OUR AVERAGE0.209±0.058 1 BARATE 98 ALEP 19911995 LEP runs0.25 ±0.10 ±0.05 27 ALBRECHT 95H ARG Eee m= 9.410.6 GeV1BARATE 98 measure the K−K∗(892)0 fra tion in τ− → K−K+π− ντ de- ays to be (87 ± 13)% and derive this result from their measurement of (τ− →K−K+π− ντ )/total.((K∗(892)π )− ντ → π−K0π0 ντ

)/total 140/((K∗(892)π )− ντ → π−K0π0 ντ

)/total 140/((K∗(892)π )− ντ → π−K0π0 ντ

)/total 140/((K∗(892)π )− ντ → π−K0π0 ντ

)/total 140/VALUE (%) DOCUMENT ID TECN COMMENT0.10 ±0.04 OUR AVERAGE0.10 ±0.04 OUR AVERAGE0.10 ±0.04 OUR AVERAGE0.10 ±0.04 OUR AVERAGE0.097±0.044±0.036 1 BARATE 99K ALEP 19911995 LEP runs0.106±0.037±0.032 2 BARATE 98E ALEP 19911995 LEP runs1BARATE 99K measure K0's by dete ting K0L's in their hadron alorimeter. They de-termine the K0 ρ− fra tion in τ− → π−K0π0 ντ de ays to be (0.72 ± 0.12 ± 0.10)and multiply their B(π−K0π0 ντ ) measurement by one minus this fra tion to obtainthe quoted result.2BARATE 98E re onstru t K0's using K0S → π+π− de ays. They determine the K0 ρ−fra tion in τ− → π−K0π0 ντ de ays to be (0.64 ± 0.09 ± 0.10) and multiply theirB(π−K0π0 ντ ) measurement by one minus this fra tion to obtain the quoted result.(K1(1270)−ντ

)/total 141/(K1(1270)−ντ

)/total 141/(K1(1270)−ντ

)/total 141/(K1(1270)−ντ

)/total 141/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.47±0.11 OUR AVERAGE0.47±0.11 OUR AVERAGE0.47±0.11 OUR AVERAGE0.47±0.11 OUR AVERAGE0.48±0.11 BARATE 99R ALEP 19911995 LEP runs0.41+0.41−0.35±0.10 5 1 BAUER 94 TPC Eee m= 29 GeV1We multiply 0.41% by 0.25, the relative systemati error quoted by BAUER 94, to obtainthe systemati error.

(K1(1400)−ντ

)/total 142/(K1(1400)−ντ

)/total 142/(K1(1400)−ντ

)/total 142/(K1(1400)−ντ

)/total 142/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.17±0.26 OUR AVERAGE0.17±0.26 OUR AVERAGE0.17±0.26 OUR AVERAGE0.17±0.26 OUR AVERAGE Error in ludes s ale fa tor of 1.7.0.05±0.17 BARATE 99R ALEP 19911995 LEP runs0.76+0.40−0.33±0.20 11 1 BAUER 94 TPC Eee m= 29 GeV1We multiply 0.76% by 0.25, the relative systemati error quoted by BAUER 94, to obtainthe systemati error.

[(K1(1270)−ντ

)+(K1(1400)−ντ

)]/total (141+142)/[(K1(1270)−ντ

)+(K1(1400)−ντ

)]/total (141+142)/[(K1(1270)−ντ

)+(K1(1400)−ντ

)]/total (141+142)/[(K1(1270)−ντ

)+(K1(1400)−ντ

)]/total (141+142)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.17+0.41−0.37±0.291.17+0.41−0.37±0.291.17+0.41−0.37±0.291.17+0.41−0.37±0.29 16 1 BAUER 94 TPC Eee m= 29 GeV1We multiply 1.17% by 0.25, the relative systemati error quoted by BAUER 94, to obtainthe systemati error. Not independent of BAUER 94 B(K1(1270)− ντ ) and BAUER 94B(K1(1400)− ντ ) measurements.(K1(1270)−ντ

)/[(K1(1270)− ντ

)+(K1(1400)− ντ

)] 141/(141+142)(K1(1270)−ντ

)/[(K1(1270)− ντ

)+(K1(1400)− ντ

)] 141/(141+142)(K1(1270)−ντ

)/[(K1(1270)− ντ

)+(K1(1400)− ντ

)] 141/(141+142)(K1(1270)−ντ

)/[(K1(1270)− ντ

)+(K1(1400)− ντ

)] 141/(141+142)VALUE DOCUMENT ID TECN COMMENT0.69±0.15 OUR AVERAGE0.69±0.15 OUR AVERAGE0.69±0.15 OUR AVERAGE0.69±0.15 OUR AVERAGE0.71±0.16±0.11 1 ABBIENDI 00D OPAL 19901995 LEP runs0.66±0.19±0.13 2 ASNER 00B CLEO Eee m= 10.6 GeV1ABBIENDI 00D assume the resonan e stru ture of τ− → K−π+π− ντ de ays isdominated by the K1(1270)− and K1(1400)− resonan es.2ASNER 00B assume the resonan e stru ture of τ− → K−π+π− ντ (ex. K0) de aysis dominated by K1(1270)− and K1(1400)− resonan es.(K∗(1410)−ντ

)/total 143/(K∗(1410)−ντ

)/total 143/(K∗(1410)−ντ

)/total 143/(K∗(1410)−ντ

)/total 143/VALUE (units 10−3) DOCUMENT ID TECN COMMENT1.5+1.4−1.01.5+1.4−1.01.5+1.4−1.01.5+1.4−1.0 BARATE 99R ALEP 19911995 LEP runs(K∗0(1430)−ντ

)/total 144/(K∗0(1430)−ντ

)/total 144/(K∗0(1430)−ντ

)/total 144/(K∗0(1430)−ντ

)/total 144/VALUE (units 10−3) CL% DOCUMENT ID TECN COMMENT<0.5<0.5<0.5<0.5 95 BARATE 99R ALEP 19911995 LEP runs(K∗2(1430)−ντ

)/total 145/(K∗2(1430)−ντ

)/total 145/(K∗2(1430)−ντ

)/total 145/(K∗2(1430)−ντ

)/total 145/VALUE (%) CL% EVTS DOCUMENT ID TECN COMMENT<0.3<0.3<0.3<0.3 95 TSCHIRHART 88 HRS Eee m= 29 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<0.33 95 1 ACCIARRI 95F L3 19911993 LEP runs<0.9 95 0 DORFAN 81 MRK2 Eee m= 4.26.7 GeV1ACCIARRI 95F quote B(τ− → K∗(1430)− → π−K0 ντ ) < 0.11%. We divide byB(K∗(1430)− → π−K0) = 0.33 to obtain the limit shown.(a0(980)− ≥ 0 neutrals ντ

)/total ×B(a0(980)→ K0K−) 146/× B(a0(980)− ≥ 0 neutrals ντ



)/total ×B(a0(980)→ K0K−) 146/× BVALUE (units 10−4) CL% DOCUMENT ID TECN COMMENT<2.8<2.8<2.8<2.8 90 GOLDBERG 90 CLEO Eee m= 9.410.9 GeV(ηπ− ντ

)/total 147/(ηπ− ντ



)/total 147/VALUE (units 10−4) CL% EVTS DOCUMENT ID TECN COMMENT< 0.99< 0.99< 0.99< 0.99 95 1 DEL-AMO-SA...11E BABR 470 fb−1 Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 6.2 95 BUSKULIC 97C ALEP 19911994 LEP runs< 1.4 95 0 BARTELT 96 CLEO Eee m ≈ 10.6 GeV< 3.4 95 ARTUSO 92 CLEO Eee m ≈ 10.6 GeV< 90 95 ALBRECHT 88M ARG Eee m ≈ 10 GeV<140 90 BEHREND 88 CELL Eee m= 1446.8 GeV<180 95 BARINGER 87 CLEO Eee m= 10.5 GeV<250 90 0 COFFMAN 87 MRK3 Eee m= 3.77 GeV510 ±100±120 65 DERRICK 87 HRS Eee m= 29 GeV<100 95 GAN 87B MRK2 Eee m= 29 GeV1DEL-AMO-SANCHEZ 11E also quote B(τ− → ηπ− ντ ) = (3.4 ± 3.4 ± 2.1)× 10−5.(ηπ−π0 ντ

)/total 148/(ηπ−π0 ντ



)/total 148/VALUE (units 10−3) CL% EVTS DOCUMENT ID TECN COMMENT1.39± 0.07 OUR FIT1.39± 0.07 OUR FIT1.39± 0.07 OUR FIT1.39± 0.07 OUR FIT1.38± 0.09 OUR AVERAGE1.38± 0.09 OUR AVERAGE1.38± 0.09 OUR AVERAGE1.38± 0.09 OUR AVERAGE Error in ludes s ale fa tor of 1.2.1.35± 0.03± 0.07 6.0k INAMI 09 BELL 490 fb−1 Eee m= 10.6GeV1.8 ± 0.4 ± 0.2 BUSKULIC 97C ALEP 19911994 LEP runs1.7 ± 0.2 ± 0.2 125 ARTUSO 92 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 11.0 95 ALBRECHT 88M ARG Eee m ≈ 10 GeV< 21.0 95 BARINGER 87 CLEO Eee m= 10.5 GeV42.0 + 7.0

−12.0 ±16.0 1 GAN 87 MRK2 Eee m= 29 GeV1Highly orrelated with GAN 87 (π− 3π0 ντ )/(total) value.

746746746746LeptonParti le Listingsτ(ηπ−π0π0 ντ

)/total 149/(ηπ−π0π0 ντ



)/total 149/VALUE (units 10−4) CL% EVTS DOCUMENT ID TECN COMMENT1.9 ±0.4 OUR FIT1.9 ±0.4 OUR FIT1.9 ±0.4 OUR FIT1.9 ±0.4 OUR FIT1.81±0.31 OUR AVERAGE1.81±0.31 OUR AVERAGE1.81±0.31 OUR AVERAGE1.81±0.31 OUR AVERAGE2.01±0.34±0.22 381 LEES 12X BABR 468 fb−1 Eee m =10.6 GeV• • • We use the following data for averages but not for ts. • • •1.5 ±0.5 30 1 ANASTASSOV 01 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.4 ±0.6 ±0.3 15 2 BERGFELD 97 CLEO Repl. by ANAS-TASSOV 01< 4.3 95 ARTUSO 92 CLEO Eee m ≈ 10.6 GeV<120 95 ALBRECHT 88M ARG Eee m ≈ 10 GeV1Weighted average of BERGFELD 97 and ANASTASSOV 01 value of (1.5 ± 0.6± 0.3)×10−4 obtained using η's re onstru ted from η → π+π−π0 de ays.2BERGFELD 97 re onstru t η's using η → γ γ de ays.(ηK−ντ

)/total 150/(ηK−ντ



)/total 150/VALUE (units 10−4) CL% EVTS DOCUMENT ID TECN COMMENT1.55±0.08 OUR FIT1.55±0.08 OUR FIT1.55±0.08 OUR FIT1.55±0.08 OUR FIT1.54±0.08 OUR AVERAGE1.54±0.08 OUR AVERAGE1.54±0.08 OUR AVERAGE1.54±0.08 OUR AVERAGE1.42±0.11±0.07 690 DEL-AMO-SA...11E BABR 470 fb−1 Eee m= 10.6 GeV1.58±0.05±0.09 1.6k INAMI 09 BELL 490 fb−1 Eee m= 10.6 GeV2.9 +1.3−1.2 ±0.7 BUSKULIC 97C ALEP 19911994 LEP runs2.6 ±0.5 ±0.5 85 BARTELT 96 CLEO Eee m ≈ 10.6 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •< 4.7 95 ARTUSO 92 CLEO Eee m ≈ 10.6 GeV(ηK∗(892)−ντ

)/total 151/(ηK∗(892)−ντ

)/total 151/(ηK∗(892)−ντ

)/total 151/(ηK∗(892)−ντ

)/total 151/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT1.38±0.15 OUR AVERAGE1.38±0.15 OUR AVERAGE1.38±0.15 OUR AVERAGE1.38±0.15 OUR AVERAGE1.34±0.12±0.09 245 1 INAMI 09 BELL 490 fb−1 Eee m= 10.6GeV2.90±0.80±0.42 25 BISHAI 99 CLEO Eee m= 10.6 GeV1Not independent of INAMI 09 B(τ− → ηK−π0 ντ ) and B(τ− → ηK0π− ντ ) values.(ηK−π0 ντ

)/total 152/(ηK−π0 ντ



)/total 152/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT0.48±0.12 OUR FIT0.48±0.12 OUR FIT0.48±0.12 OUR FIT0.48±0.12 OUR FIT0.48±0.12 OUR AVERAGE0.48±0.12 OUR AVERAGE0.48±0.12 OUR AVERAGE0.48±0.12 OUR AVERAGE0.46±0.11±0.04 270 INAMI 09 BELL 490 fb−1 Eee m= 10.6 GeV1.77±0.56±0.71 36 BISHAI 99 CLEO Eee m= 10.6 GeV(ηK−π0 (non-K∗(892))ντ

)/total 153/(ηK−π0 (non-K∗(892))ντ



)/total 153/VALUE CL% DOCUMENT ID TECN COMMENT<3.5× 10−5<3.5× 10−5<3.5× 10−5<3.5× 10−5 90 INAMI 09 BELL 490 fb−1 Eee m= 10.6 GeV(ηK0π− ντ

)/total 154/(ηK0π− ντ



)/total 154/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT0.94±0.15 OUR FIT0.94±0.15 OUR FIT0.94±0.15 OUR FIT0.94±0.15 OUR FIT0.93±0.15 OUR AVERAGE0.93±0.15 OUR AVERAGE0.93±0.15 OUR AVERAGE0.93±0.15 OUR AVERAGE0.88±0.14±0.06 161 1 INAMI 09 BELL 490 fb−1 Eee m= 10.6GeV2.20±0.70±0.22 15 2 BISHAI 99 CLEO Eee m= 10.6 GeV1We multiply the INAMI 09 measurement B(τ− → ηK0S π− ντ ) = (0.44 ± 0.07 ±0.03) × 10−4 by 2 to obtain the listed value.2We multiply the BISHAI 99 measurement B(τ− → ηK0S π− ντ ) = (1.10 ± 0.35 ±0.11) × 10−4 by 2 to obtain the listed value.(ηK0π−π0 ντ

)/total 155/(ηK0π−π0 ντ



)/total 155/VALUE CL% DOCUMENT ID TECN COMMENT<5.0× 10−5<5.0× 10−5<5.0× 10−5<5.0× 10−5 90 1 INAMI 09 BELL 490 fb−1 Eee m= 10.6 GeV1We multiply the INAMI 09 measurement B(τ− → ηK0S π−π0 ντ ) < 2.5 × 10−5 by2 to obtain the listed value.(ηK−K0 ντ

)/total 156/(ηK−K0 ντ



)/total 156/VALUE CL% DOCUMENT ID TECN COMMENT<9.0× 10−6<9.0× 10−6<9.0× 10−6<9.0× 10−6 90 1 INAMI 09 BELL 490 fb−1 Eee m= 10.6 GeV1We multiply the INAMI 09 measurement B(τ− → ηK−K0S ντ ) < 4.5 × 10−6 by 2to obtain the listed value.(ηπ+π−π− ≥ 0 neutrals ντ

)/total 157/(ηπ+π−π− ≥ 0 neutrals ντ



)/total 157/VALUE (%) CL% DOCUMENT ID TECN COMMENT<0.3<0.3<0.3<0.3 90 ABACHI 87B HRS Eee m= 29 GeV

(ηπ−π+π−ντ (ex.K0))/total 158/(ηπ−π+π−ντ (ex.K0))/total 158/(ηπ−π+π−ντ (ex.K0))/total 158/(ηπ−π+π−ντ (ex.K0))/total 158/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT2.19±0.13 OUR FIT2.19±0.13 OUR FIT2.19±0.13 OUR FIT2.19±0.13 OUR FIT2.23±0.12 OUR AVERAGE2.23±0.12 OUR AVERAGE2.23±0.12 OUR AVERAGE2.23±0.12 OUR AVERAGE2.10±0.09±0.13 2.9k 1 LEES 12X BABR η → γ γ2.37±0.12±0.18 1.4k 1 LEES 12X BABR η → π+π−π02.54±0.27±0.25 315 1 LEES 12X BABR η → 3π0• • • We use the following data for averages but not for ts. • • •2.3 ±0.5 170 2 ANASTASSOV 01 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.60±0.05±0.11 1.8 k AUBERT 08AE BABR Repl. by LEES 12X3.4 +0.6

−0.5 ±0.6 89 3 BERGFELD 97 CLEO Repl. by ANASTASSOV 011LEES 12X uses 468 fb−1 of data taken at Eee m = 10.6 GeV. It gives the average of thethree measurements listed here as (2.25 ± 0.07 ± 0.12) × 10−4.2Weighted average of BERGFELD 97 and ANASTASSOV 01 measurements using η'sre onstru ted from η → π+π−π0 and η → 3π0 de ays.3BERGFELD 97 re onstru t η's using η → γ γ and η → 3π0 de ays.(ηπ−π+π−ντ (ex.K0,f1(1285)))/total 159/(ηπ−π+π−ντ (ex.K0,f1(1285)))/total 159/(ηπ−π+π−ντ (ex.K0,f1(1285)))/total 159/(ηπ−π+π−ντ (ex.K0,f1(1285)))/total 159/VALUE (units 10−4) DOCUMENT ID TECN COMMENT0.99±0.09±0.130.99±0.09±0.130.99±0.09±0.130.99±0.09±0.13 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1LEES 12X obtain this result by subtra ting their B(τ− → f1(1285)π− ντ →ηπ−π+π− ντ ) measurement from their B(τ− → ηπ−π+π− ντ (ex.K0)) measure-ment.(ηa1(1260)− ντ → ηπ− ρ0 ντ

)/total 160/(ηa1(1260)− ντ → ηπ− ρ0 ντ

)/total 160/(ηa1(1260)− ντ → ηπ− ρ0 ντ

)/total 160/(ηa1(1260)− ντ → ηπ− ρ0 ντ

)/total 160/VALUE CL% DOCUMENT ID TECN COMMENT<3.9× 10−4<3.9× 10−4<3.9× 10−4<3.9× 10−4 90 BERGFELD 97 CLEO Eee m= 10.6 GeV(ηηπ− ντ

)/total 161/(ηηπ− ντ



)/total 161/VALUE CL% DOCUMENT ID TECN COMMENT<7.4× 10−6<7.4× 10−6<7.4× 10−6<7.4× 10−6 90 INAMI 09 BELL 490 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.1× 10−4 95 ARTUSO 92 CLEO Eee m ≈ 10.6 GeV<8.3× 10−3 95 ALBRECHT 88M ARG Eee m ≈ 10 GeV(ηηπ−π0 ντ

)/total 162/(ηηπ−π0 ντ



)/total 162/VALUE (units 10−4) CL% DOCUMENT ID TECN COMMENT< 2.0< 2.0< 2.0< 2.0 95 ARTUSO 92 CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<90 95 ALBRECHT 88M ARG Eee m ≈ 10 GeV(ηηK− ντ

)/total 163/(ηηK− ντ



)/total 163/VALUE CL% DOCUMENT ID TECN COMMENT<3.0× 10−6<3.0× 10−6<3.0× 10−6<3.0× 10−6 90 INAMI 09 BELL 490 fb−1 Eee m= 10.6 GeV(η′(958)π− ντ

)/total 164/(η′(958)π− ντ

)/total 164/(η′(958)π− ντ

)/total 164/(η′(958)π− ντ

)/total 164/VALUE CL% DOCUMENT ID TECN COMMENT<4.0× 10−6<4.0× 10−6<4.0× 10−6<4.0× 10−6 90 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<7.2× 10−6 90 AUBERT 08AE BABR 384 fb−1, Eee m= 10.6 GeV<7.4× 10−5 90 BERGFELD 97 CLEO Eee m= 10.6 GeV(η′(958)π−π0 ντ

)/total 165/(η′(958)π−π0 ντ

)/total 165/(η′(958)π−π0 ντ

)/total 165/(η′(958)π−π0 ντ

)/total 165/VALUE CL% DOCUMENT ID TECN COMMENT<1.2× 10−5<1.2× 10−5<1.2× 10−5<1.2× 10−5 90 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<8.0× 10−5 90 BERGFELD 97 CLEO Eee m= 10.6 GeV(η′(958)K−ντ

)/total 166/(η′(958)K−ντ

)/total 166/(η′(958)K−ντ

)/total 166/(η′(958)K−ντ

)/total 166/VALUE CL% DOCUMENT ID TECN COMMENT<2.4× 10−6<2.4× 10−6<2.4× 10−6<2.4× 10−6 90 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV(φπ− ντ

)/total 167/(φπ− ντ



)/total 167/VALUE (units 10−5) CL% EVTS DOCUMENT ID TECN COMMENT3.42±0.55±0.253.42±0.55±0.253.42±0.55±0.253.42±0.55±0.25 344 AUBERT 08 BABR 342 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 20 90 1 AVERY 97 CLEO Eee m= 10.6 GeV< 35 90 ALBRECHT 95H ARG Eee m= 9.410.6 GeV1AVERY 97 limit varies from (1.22.0)× 10−4 depending on de ay model assumptions.

747747747747See key on page 601 LeptonParti le Listingsτ(φK− ντ

)/total 168/(φK− ντ



)/total 168/VALUE (units 10−5) CL% EVTS DOCUMENT ID TECN COMMENT4.4 ±1.6 OUR FIT4.4 ±1.6 OUR FIT4.4 ±1.6 OUR FIT4.4 ±1.6 OUR FIT3.70±0.33 OUR AVERAGE3.70±0.33 OUR AVERAGE3.70±0.33 OUR AVERAGE3.70±0.33 OUR AVERAGE Error in ludes s ale fa tor of 1.3.• • • We use the following data for averages but not for ts. • • •3.39±0.20±0.28 274 AUBERT 08 BABR 342 fb−1 Eee m = 10.6 GeV4.05±0.25±0.26 551 INAMI 06 BELL 401 fb−1 Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<6.7 90 1 AVERY 97 CLEO Eee m= 10.6 GeV1AVERY 97 limit varies from (5.46.7)× 10−5 depending on de ay model assumptions.(f1(1285)π−ντ

)/total 169/(f1(1285)π−ντ

)/total 169/(f1(1285)π−ντ

)/total 169/(f1(1285)π−ντ

)/total 169/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT3.9 ±0.5 OUR AVERAGE3.9 ±0.5 OUR AVERAGE3.9 ±0.5 OUR AVERAGE3.9 ±0.5 OUR AVERAGE Error in ludes s ale fa tor of 1.9.4.73±0.28±0.45 3.7k 1 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV3.60±0.18±0.23 2.5k 2 LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •3.19±0.18±1.00 1.3 k 3 AUBERT 08AE BABR Repl. by LEES 12X3.9 ±0.7 ±0.5 1.4 k 4 AUBERT,B 05W BABR Repl. by LEES 12X5.8 +1.4

−1.3 ±1.8 54 5 BERGFELD 97 CLEO Eee m= 10.6 GeV1LEES 12X obtain this value by dividing their B(τ− → f1(1285)π− ντ → 3π− 2π+ ντ )measurement by the PDG 12 value of B(f1(1285) → 2π+2π−) = 0.111+0.007−0.006.2 LEES 12X obtain this value by dividing their B(τ− → f1(1285)π− ντ →

ηπ−π+π− ντ ) measurement by 2/3 of the PDG 12 value of B(f1(1285) → ηππ)= 0.524+0.019−0.021.3AUBERT 08AE obtain this value by dividing their B(τ− → f1(1285)π− ντ →

ηπ−π+π− ντ ) measurement by the PDG 06 value of B(f1(1285) → ηπ−π+) =0.35 ± 0.11. The quote (3.19 ± 0.18 ± 0.16 ± 0.99)× 10−4 where the nal error is dueto the un ertainty on B(f1(1285) → ηπ−π+). We ombine the two systemati errorsin quadrature.4AUBERT,B 05W use the f1(1285) → 2π+2π− de ay mode and the PDG 04 value ofB(f1(1285) → 2π+2π−) = 0.110+0.007−0.006.5BERGFELD 97 use the f1(1285) → ηπ+π− de ay mode.(f1(1285)π−ντ → ηπ−π+π− ντ

)/total 170/(f1(1285)π−ντ → ηπ−π+π− ντ



)/total 170/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT1.18±0.07 OUR AVERAGE1.18±0.07 OUR AVERAGE1.18±0.07 OUR AVERAGE1.18±0.07 OUR AVERAGE Error in ludes s ale fa tor of 1.3.1.26±0.06±0.06 2.5k LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV1.11±0.06±0.05 1.3 k AUBERT 08AE BABR 384 fb−1, Eee m= 10.6 GeV(f1(1285)π−ντ → ηπ−π+π− ντ

)/(ηπ−π+π− ντ (ex.K0)) 170/158(f1(1285)π−ντ → ηπ−π+π− ντ



)/(ηπ−π+π− ντ (ex.K0)) 170/158VALUE DOCUMENT ID TECN COMMENT0.69±0.01±0.050.69±0.01±0.050.69±0.01±0.050.69±0.01±0.05 1 AUBERT 08AE BABR 384 fb−1, Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.55±0.14 BERGFELD 97 CLEO Eee m= 10.6 GeV1Not independent of AUBERT 08AE B(τ− → f1(1285)π− ντ → ηπ−π+π− ντ ) andB(τ− → ηπ−π+π− ντ (ex.K0)) values.(f1(1285)π−ντ → 3π− 2π+ντ

)/total 171/(f1(1285)π−ντ → 3π− 2π+ντ

)/total 171/(f1(1285)π−ντ → 3π− 2π+ντ

)/total 171/(f1(1285)π−ντ → 3π− 2π+ντ

)/total 171/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT0.52 ±0.04 OUR FIT0.52 ±0.04 OUR FIT0.52 ±0.04 OUR FIT0.52 ±0.04 OUR FIT0.520±0.031±0.0370.520±0.031±0.0370.520±0.031±0.0370.520±0.031±0.037 3.7k LEES 12X BABR 468 fb−1 Eee m=10.6 GeV(π(1300)−ντ → (ρπ)− ντ → (3π)−ντ

)/total 172/(π(1300)−ντ → (ρπ)− ντ → (3π)−ντ



)/total 172/VALUE CL% DOCUMENT ID TECN COMMENT<1.0× 10−4<1.0× 10−4<1.0× 10−4<1.0× 10−4 90 ASNER 00 CLEO Eee m= 10.6 GeV(π(1300)−ντ → ((ππ)S−wave π)− ντ → (3π)−ντ

)/total 173/(π(1300)−ντ → ((ππ)S−wave π)− ντ → (3π)−ντ



)/total 173/VALUE CL% DOCUMENT ID TECN COMMENT<1.9× 10−4<1.9× 10−4<1.9× 10−4<1.9× 10−4 90 ASNER 00 CLEO Eee m= 10.6 GeV(h−ω ≥ 0 neutrals ντ

)/total 174/(h−ω ≥ 0 neutrals ντ



)/total 174/174/ = (176+177+178)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT2.40±0.08 OUR FIT2.40±0.08 OUR FIT2.40±0.08 OUR FIT2.40±0.08 OUR FIT• • • We use the following data for averages but not for ts. • • •1.65±0.3 ±0.21.65±0.3 ±0.21.65±0.3 ±0.21.65±0.3 ±0.2 1513 ALBRECHT 88M ARG Eee m ≈ 10 GeV(h−ωντ

)/total 175/= (176+177)/(h−ωντ

)/total 175/= (176+177)/(h−ωντ

)/total 175/= (176+177)/(h−ωντ

)/total 175/= (176+177)/VALUE (%) EVTS DOCUMENT ID TECN COMMENT1.99±0.06 OUR FIT1.99±0.06 OUR FIT1.99±0.06 OUR FIT1.99±0.06 OUR FIT1.92±0.07 OUR AVERAGE1.92±0.07 OUR AVERAGE1.92±0.07 OUR AVERAGE1.92±0.07 OUR AVERAGE1.91±0.07±0.06 5803 BUSKULIC 97C ALEP 19911994 LEP runs1.60±0.27±0.41 139 BARINGER 87 CLEO Eee m= 10.5 GeV• • • We use the following data for averages but not for ts. • • •1.95±0.07±0.11 2223 1 BALEST 95C CLEO Eee m ≈ 10.6 GeV1Not independent of BALEST 95C B(τ− → h−ωντ )/B(τ− → h− h− h+π0 ντ ) value.

[(π−ωντ

)+(K−ωντ

)]/(h−h− h+π0 ντ (ex.K0)) (176+177)/74[(π−ωντ

)+(K−ωντ

)]/(h−h− h+π0 ντ (ex.K0)) (176+177)/74[(π−ωντ

)+(K−ωντ

)]/(h−h− h+π0 ντ (ex.K0)) (176+177)/74[(π−ωντ

)+(K−ωντ

)]/(h−h− h+π0 ντ (ex.K0)) (176+177)/74(176+177)/74 = (176+177)/(78+103+107+0.2292150+0.892176+0.892177+0.0153178)VALUE (units 10−2) EVTS DOCUMENT ID TECN COMMENT43.5±1.4 OUR FIT43.5±1.4 OUR FIT43.5±1.4 OUR FIT43.5±1.4 OUR FIT45.3±1.9 OUR AVERAGE45.3±1.9 OUR AVERAGE45.3±1.9 OUR AVERAGE45.3±1.9 OUR AVERAGE43.1±3.3 2350 1 BUSKULIC 96 ALEP LEP 19911993 data46.4±1.6±1.7 2223 2 BALEST 95C CLEO Eee m ≈ 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •37 ±5 ±2 458 3 ALBRECHT 91D ARG Eee m= 9.410.6 GeV1BUSKULIC 96 quote the fra tion of τ → h− h− h+π0 ντ (ex. K0) de ays whi horiginate in a h−ω nal state = 0.383 ± 0.029. We divide this by the ω(782) →

π+π−π0 bran hing fra tion (0.888).2BALEST 95C quote the fra tion of τ− → h− h− h+π0 ντ (ex. K0) de ays whi horiginate in a h−ω nal state equals 0.412 ± 0.014 ± 0.015. We divide this by theω(782) → π+π−π0 bran hing fra tion (0.888).3ALBRECHT 91D quote the fra tion of τ− → h− h− h+π0 ντ de ays whi h originate ina π−ω nal state equals 0.33± 0.04± 0.02. We divide this by the ω(782) → π+π−π0bran hing fra tion (0.888).(π−ωντ

)/total 176/(π−ωντ



)/total 176/VALUE (%) DOCUMENT ID1.95±0.06 OUR FIT1.95±0.06 OUR FIT1.95±0.06 OUR FIT1.95±0.06 OUR FIT(K−ωντ

)/total 177/(K−ωντ



)/total 177//medskipVALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT4.1±0.9 OUR FIT4.1±0.9 OUR FIT4.1±0.9 OUR FIT4.1±0.9 OUR FIT4.1±0.6±0.74.1±0.6±0.74.1±0.6±0.74.1±0.6±0.7 500 ARMS 05 CLE3 7.6 fb−1, Eee m= 10.6 GeV(h−ωπ0 ντ

)/total 178/(h−ωπ0 ντ



)/total 178/VALUE (%) EVTS DOCUMENT ID TECN COMMENT0.41±0.04 OUR FIT0.41±0.04 OUR FIT0.41±0.04 OUR FIT0.41±0.04 OUR FIT0.43±0.06±0.050.43±0.06±0.050.43±0.06±0.050.43±0.06±0.05 7283 BUSKULIC 97C ALEP 19911994 LEP runs(h−ωπ0 ντ

)/(h−h− h+ ≥ 0 neutrals ≥ 0K 0Lντ

) 178/62(h−ωπ0 ντ


) 178/62(h−ωπ0 ντ


) 178/62(h−ωπ0 ντ


) 178/62178/62 = 178/(0.3459836+0.3459838+0.3459841+0.3459843+0.424748+0.692049+0.849452+0.692056+0.653461+70+78+85+89+97+103+106+107+0.2810148+0.2292149+0.2810150+0.2810152+0.3759154+0.3268158+0.7259168+0.9078176+0.9078177+0.9078178+0.892180)VALUE EVTS DOCUMENT ID TECN COMMENT(2.69 ±0.28 )× 10−2 OUR FIT(2.69 ±0.28 )× 10−2 OUR FIT(2.69 ±0.28 )× 10−2 OUR FIT(2.69 ±0.28 )× 10−2 OUR FIT• • • We use the following data for averages but not for ts. • • •0.028±0.003±0.0030.028±0.003±0.0030.028±0.003±0.0030.028±0.003±0.003 430 1 BORTOLETTO 93 CLEO Eee m ≈ 10.6 GeV1Not independent of BORTOLETTO 93 (τ− → h−ωπ0 ντ )/(τ− →h− h− h+2π0 ντ (ex.K0)) value.(h−ωπ0 ντ

)/(h−h− h+2π0 ντ (ex.K0)) 178/84(h−ωπ0 ντ

)/(h−h− h+2π0 ντ (ex.K0)) 178/84(h−ωπ0 ντ

)/(h−h− h+2π0 ντ (ex.K0)) 178/84(h−ωπ0 ντ

)/(h−h− h+2π0 ντ (ex.K0)) 178/84178/84 = 178/(85+0.2292148+0.2292152+0.892178)VALUE (units 10−2) DOCUMENT ID TECN COMMENT82±8 OUR FIT82±8 OUR FIT82±8 OUR FIT82±8 OUR FIT81±6±681±6±681±6±681±6±6 BORTOLETTO93 CLEO Eee m ≈ 10.6 GeV(h−ω2π0 ντ

)/total 179/(h−ω2π0 ντ



)/total 179/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT1.4 ±0.4 ±0.31.4 ±0.4 ±0.31.4 ±0.4 ±0.31.4 ±0.4 ±0.3 53 ANASTASSOV 01 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.89+0.74

−0.67±0.40 19 ANDERSON 97 CLEO Repl. by ANASTASSOV 01(π−ω2π0ντ

)/total 180/(π−ω2π0ντ



)/total 180/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT0.71±0.16 OUR FIT0.71±0.16 OUR FIT0.71±0.16 OUR FIT0.71±0.16 OUR FIT0.73±0.12±0.120.73±0.12±0.120.73±0.12±0.120.73±0.12±0.12 1.1k LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV(h−2ωντ

)/total 181/(h−2ωντ



)/total 181/VALUE CL% DOCUMENT ID TECN COMMENT<5.4× 10−7<5.4× 10−7<5.4× 10−7<5.4× 10−7 90 AUBERT,B 06 BABR 232 fb−1 Eee m = 10.6 GeV(2h−h+ωντ

)/total 182/(2h−h+ωντ



)/total 182/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT1.2±0.2±0.11.2±0.2±0.11.2±0.2±0.11.2±0.2±0.1 110 ANASTASSOV 01 CLEO Eee m= 10.6 GeV

748748748748LeptonParti le Listingsτ(2π−π+ωντ (ex.K0))/total 183/(2π−π+ωντ (ex.K0))/total 183/(2π−π+ωντ (ex.K0))/total 183/(2π−π+ωντ (ex.K0))/total 183/VALUE (units 10−4) EVTS DOCUMENT ID TECN COMMENT0.84±0.06 OUR FIT0.84±0.06 OUR FIT0.84±0.06 OUR FIT0.84±0.06 OUR FIT0.84±0.04±0.060.84±0.04±0.060.84±0.04±0.060.84±0.04±0.06 2.4k LEES 12X BABR 468 fb−1 Eee m = 10.6 GeV(e− γ

)/total 184/(e− γ)/total 184/(e− γ)/total 184/(e− γ)/total 184/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<3.3× 10−8<3.3× 10−8<3.3× 10−8<3.3× 10−8 90 AUBERT 10B BABR 516 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.2× 10−7 90 HAYASAKA 08 BELL 535 fb−1, Eee m= 10.6 GeV<1.1× 10−7 90 AUBERT 06C BABR 232 fb−1, Eee m= 10.6 GeV<3.9× 10−7 90 HAYASAKA 05 BELL 86.7 fb−1, Eee m=10.6 GeV<2.7× 10−6 90 EDWARDS 97 CLEO<1.1× 10−4 90 ABREU 95U DLPH 19901993 LEP runs<1.2× 10−4 90 ALBRECHT 92K ARG Eee m= 10 GeV<2.0× 10−4 90 KEH 88 CBAL Eee m= 10 GeV<6.4× 10−4 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV(µ−γ

)/total 185/(µ−γ)/total 185/(µ−γ)/total 185/(µ−γ)/total 185/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

< 4.4 × 10−8< 4.4 × 10−8< 4.4 × 10−8< 4.4 × 10−8 90 AUBERT 10B BABR 516 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 4.5 × 10−8 90 HAYASAKA 08 BELL 535 fb−1, Eee m = 10.6 GeV< 6.8 × 10−8 90 AUBERT,B 05A BABR 232 fb−1, Eee m= 10.6 GeV< 3.1 × 10−7 90 ABE 04B BELL 86.3 fb−1, Eee m = 10.6 GeV< 1.1 × 10−6 90 AHMED 00 CLEO Eee m= 10.6 GeV< 3.0 × 10−6 90 EDWARDS 97 CLEO< 6.2 × 10−5 90 ABREU 95U DLPH 19901993 LEP runs< 0.42× 10−5 90 BEAN 93 CLEO Eee m= 10.6 GeV< 3.4 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<55 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV(e−π0)/total 186/(e−π0)/total 186/(e−π0)/total 186/(e−π0)/total 186/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 8.0× 10−8< 8.0× 10−8< 8.0× 10−8< 8.0× 10−8 90 MIYAZAKI 07 BELL 401 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 1.3× 10−7 90 AUBERT 07I BABR 339 fb−1, Eee m=10.6 GeV< 1.9× 10−7 90 ENARI 05 BELL 154 fb−1, Eee m= 10.6 GeV< 3.7× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV< 17 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV< 14 × 10−5 90 KEH 88 CBAL Eee m= 10 GeV<210 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV(µ−π0)/total 187/(µ−π0)/total 187/(µ−π0)/total 187/(µ−π0)/total 187/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 1.1× 10−7< 1.1× 10−7< 1.1× 10−7< 1.1× 10−7 90 AUBERT 07I BABR 339 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 1.2× 10−7 90 MIYAZAKI 07 BELL 401 fb−1, Eee m=10.6 GeV< 4.1× 10−7 90 ENARI 05 BELL 154 fb−1, Eee m= 10.6 GeV< 4.0× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV< 4.4× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<82 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV(e−K0S)/total 188/(e−K0S)/total 188/(e−K0S)/total 188/(e−K0S)/total 188/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<2.6× 10−8<2.6× 10−8<2.6× 10−8<2.6× 10−8 90 MIYAZAKI 10A BELL 671 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<3.3× 10−8 90 AUBERT 09D BABR 469 fb−1 Eee m = 10.6 GeV<5.6× 10−8 90 MIYAZAKI 06A BELL 281 fb−1 Eee m = 10.6 GeV<9.1× 10−7 90 CHEN 02C CLEO Eee m= 10.6 GeV<1.3× 10−3 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV(µ−K0S)/total 189/(µ−K0S)/total 189/(µ−K0S)/total 189/(µ−K0S)/total 189/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<2.3× 10−8<2.3× 10−8<2.3× 10−8<2.3× 10−8 90 MIYAZAKI 10A BELL 671 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<4.0× 10−8 90 AUBERT 09D BABR 469 fb−1 Eee m = 10.6 GeV<4.9× 10−8 90 MIYAZAKI 06A BELL 281 fb−1 Eee m = 10.6 GeV<9.5× 10−7 90 CHEN 02C CLEO Eee m= 10.6 GeV<1.0× 10−3 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV

(e− η)/total 190/(e− η)/total 190/(e− η)/total 190/(e− η)/total 190/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

< 9.2× 10−8< 9.2× 10−8< 9.2× 10−8< 9.2× 10−8 90 MIYAZAKI 07 BELL 401 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 1.6× 10−7 90 AUBERT 07I BABR 339 fb−1, Eee m=10.6 GeV< 2.4× 10−7 90 ENARI 05 BELL 154 fb−1, Eee m= 10.6 GeV< 8.2× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV< 6.3× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<24 × 10−5 90 KEH 88 CBAL Eee m= 10 GeV(µ−η

)/total 191/(µ−η)/total 191/(µ−η)/total 191/(µ−η)/total 191/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<6.5× 10−8<6.5× 10−8<6.5× 10−8<6.5× 10−8 90 MIYAZAKI 07 BELL 401 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.5× 10−7 90 AUBERT 07I BABR 339 fb−1, Eee m=10.6 GeV<1.5× 10−7 90 ENARI 05 BELL 154 fb−1, Eee m= 10.6 GeV<3.4× 10−7 90 ENARI 04 BELL 84.3 fb−1, Eee m=10.6 GeV<9.6× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV<7.3× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV(e− ρ0)/total 192/(e− ρ0)/total 192/(e− ρ0)/total 192/(e− ρ0)/total 192/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 1.8× 10−8< 1.8× 10−8< 1.8× 10−8< 1.8× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 4.6× 10−8 90 AUBERT 09W BABR 451 fb−1 Eee m = 10.6 GeV< 6.3× 10−8 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV< 6.5× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV< 2.0× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV< 4.2× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98< 1.9× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<37 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV1BARTELT 94 assume phase spa e de ays.(µ−ρ0)/total 193/(µ−ρ0)/total 193/(µ−ρ0)/total 193/(µ−ρ0)/total 193/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 1.2× 10−8< 1.2× 10−8< 1.2× 10−8< 1.2× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 2.6× 10−8 90 AUBERT 09W BABR 451 fb−1 Eee m = 10.6 GeV< 6.8× 10−8 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV< 2.0× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV< 6.3× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV< 5.7× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98< 2.9× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<44 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV1BARTELT 94 assume phase spa e de ays.(e−ω

)/total 194/(e−ω)/total 194/(e−ω)/total 194/(e−ω)/total 194/VALUE CL% DOCUMENT ID TECN COMMENT

<4.8× 10−8<4.8× 10−8<4.8× 10−8<4.8× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.1× 10−7 90 AUBERT 08K BABR 384 fb−1 Eee m = 10.6 GeV<1.8× 10−7 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV(µ−ω

)/total 195/(µ−ω)/total 195/(µ−ω)/total 195/(µ−ω)/total 195/VALUE CL% DOCUMENT ID TECN COMMENT

<4.7× 10−8<4.7× 10−8<4.7× 10−8<4.7× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.0× 10−7 90 AUBERT 08K BABR 384 fb−1 Eee m = 10.6 GeV<8.9× 10−8 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV(e−K∗(892)0)/total 196/(e−K∗(892)0)/total 196/(e−K∗(892)0)/total 196/(e−K∗(892)0)/total 196/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<3.2× 10−8<3.2× 10−8<3.2× 10−8<3.2× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<5.9× 10−8 90 AUBERT 09W BABR 451 fb−1 Eee m = 10.6 GeV<7.8× 10−8 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV<3.0× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<5.1× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<6.3× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<3.8× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV1BARTELT 94 assume phase spa e de ays.

749749749749See key on page 601 LeptonParti le Listingsτ(µ−K∗(892)0)/total 197/(µ−K∗(892)0)/total 197/(µ−K∗(892)0)/total 197/(µ−K∗(892)0)/total 197/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<5.9× 10−8<5.9× 10−8<5.9× 10−8<5.9× 10−8 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<7.2× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV<1.7× 10−7 90 AUBERT 09W BABR 451 fb−1 Eee m = 10.6 GeV<3.9× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<7.5× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<9.4× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<4.5× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV1BARTELT 94 assume phase spa e de ays.(e−K∗(892)0)/total 198/(e−K∗(892)0)/total 198/(e−K∗(892)0)/total 198/(e−K∗(892)0)/total 198/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<3.4× 10−8<3.4× 10−8<3.4× 10−8<3.4× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<4.6× 10−8 90 AUBERT 09W BABR 451 fb−1 Eee m = 10.6 GeV<7.7× 10−8 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV<4.0× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<7.4× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<1.1× 10−5 90 1 BARTELT 94 CLEO Repl. by BLISS 981BARTELT 94 assume phase spa e de ays.(µ−K∗(892)0)/total 199/(µ−K∗(892)0)/total 199/(µ−K∗(892)0)/total 199/(µ−K∗(892)0)/total 199/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<7.0× 10−8<7.0× 10−8<7.0× 10−8<7.0× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<7.3× 10−8 90 AUBERT 09W BABR 451 fb−1 Eee m = 10.6 GeV<1.0× 10−7 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV<4.0× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<7.5× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<8.7× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 981BARTELT 94 assume phase spa e de ays.(e− η′(958))/total 200/(e− η′(958))/total 200/(e− η′(958))/total 200/(e− η′(958))/total 200/VALUE CL% DOCUMENT ID TECN COMMENT< 1.6× 10−7< 1.6× 10−7< 1.6× 10−7< 1.6× 10−7 90 MIYAZAKI 07 BELL 401 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 2.4× 10−7 90 AUBERT 07I BABR 339 fb−1, Eee m=10.6 GeV<10. × 10−7 90 ENARI 05 BELL 154 fb−1, Eee m= 10.6 GeV(µ−η′(958))/total 201/(µ−η′(958))/total 201/(µ−η′(958))/total 201/(µ−η′(958))/total 201/VALUE CL% DOCUMENT ID TECN COMMENT<1.3× 10−7<1.3× 10−7<1.3× 10−7<1.3× 10−7 90 MIYAZAKI 07 BELL 401 fb−1, Eee m=10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.4× 10−7 90 AUBERT 07I BABR 339 fb−1, Eee m=10.6 GeV<4.7× 10−7 90 ENARI 05 BELL 154 fb−1, Eee m= 10.6 GeV(e− f0(980)→ e−π+π−)/total 202/(e− f0(980)→ e−π+π−)/total 202/(e− f0(980)→ e−π+π−)/total 202/(e− f0(980)→ e−π+π−)/total 202/VALUE CL% DOCUMENT ID TECN COMMENT<3.2× 10−8<3.2× 10−8<3.2× 10−8<3.2× 10−8 90 MIYAZAKI 09 BELL 671 fb−1 Eee m= 10.6 GeV(µ− f0(980)→ µ−π+π−)/total 203/(µ− f0(980)→ µ−π+π−)/total 203/(µ− f0(980)→ µ−π+π−)/total 203/(µ− f0(980)→ µ−π+π−)/total 203/VALUE CL% DOCUMENT ID TECN COMMENT<3.4× 10−8<3.4× 10−8<3.4× 10−8<3.4× 10−8 90 MIYAZAKI 09 BELL 671 fb−1 Eee m= 10.6 GeV(e−φ

)/total 204/(e−φ)/total 204/(e−φ)/total 204/(e−φ)/total 204/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<3.1× 10−8<3.1× 10−8<3.1× 10−8<3.1× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV<3.1× 10−8<3.1× 10−8<3.1× 10−8<3.1× 10−8 90 AUBERT 09W BABR 451 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<7.3× 10−8 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV<7.3× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<6.9× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV(µ−φ

)/total 205/(µ−φ)/total 205/(µ−φ)/total 205/(µ−φ)/total 205/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<8.4× 10−8<8.4× 10−8<8.4× 10−8<8.4× 10−8 90 MIYAZAKI 11 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.9× 10−7 90 AUBERT 09W BABR 451 fb−1 Eee m = 10.6 GeV<1.3× 10−7 90 NISHIO 08 BELL 543 fb−1 Eee m = 10.6 GeV<7.7× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<7.0× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV

(e− e+ e−)/total 206/(e− e+ e−)/total 206/(e− e+ e−)/total 206/(e− e+ e−)/total 206/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 2.7 × 10−8< 2.7 × 10−8< 2.7 × 10−8< 2.7 × 10−8 90 HAYASAKA 10 BELL 782 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 2.9 × 10−8 90 LEES 10A BABR 468 fb−1 Eee m= 10.6 GeV< 3.6 × 10−8 90 MIYAZAKI 08 BELL 535 fb−1 Eee m= 10.6 GeV< 4.3 × 10−8 90 AUBERT 07BK BABR 376 fb−1 Eee m= 10.6 GeV< 2.0 × 10−7 90 AUBERT 04J BABR 91.5 fb−1 Eee m= 10.6 GeV< 3.5 × 10−7 90 YUSA 04 BELL 87.1 fb−1 Eee m= 10.6 GeV< 2.9 × 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV< 0.33× 10−5 90 1 BARTELT 94 CLEO Repl. by BLISS 98< 1.3 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV< 2.7 × 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.9<40 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV1BARTELT 94 assume phase spa e de ays.(e−µ+µ−)/total 207/(e−µ+µ−)/total 207/(e−µ+µ−)/total 207/(e−µ+µ−)/total 207/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 2.7 × 10−8< 2.7 × 10−8< 2.7 × 10−8< 2.7 × 10−8 90 HAYASAKA 10 BELL 782 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 3.2 × 10−8 90 LEES 10A BABR 468 fb−1 Eee m= 10.6 GeV< 4.1 × 10−8 90 MIYAZAKI 08 BELL 535 fb−1 Eee m= 10.6 GeV< 3.7 × 10−8 90 AUBERT 07BK BABR 376 fb−1 Eee m= 10.6 GeV< 3.3 × 10−7 90 AUBERT 04J BABR 91.5 fb−1 Eee m= 10.6 GeV< 2.0 × 10−7 90 YUSA 04 BELL 87.1 fb−1 Eee m= 10.6 GeV< 1.8 × 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV< 0.36× 10−5 90 1 BARTELT 94 CLEO Repl. by BLISS 98< 1.9 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV< 2.7 × 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.9<33 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV1BARTELT 94 assume phase spa e de ays.(e+µ−µ−)/total 208/(e+µ−µ−)/total 208/(e+µ−µ−)/total 208/(e+µ−µ−)/total 208/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<1.7 × 10−8<1.7 × 10−8<1.7 × 10−8<1.7 × 10−8 90 HAYASAKA 10 BELL 782 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<2.6 × 10−8 90 LEES 10A BABR 468 fb−1 Eee m= 10.6 GeV<2.3 × 10−8 90 MIYAZAKI 08 BELL 535 fb−1 Eee m= 10.6 GeV<5.6 × 10−8 90 AUBERT 07BK BABR 376 fb−1 Eee m= 10.6 GeV<1.3 × 10−7 90 AUBERT 04J BABR 91.5 fb−1 Eee m= 10.6 GeV<2.0 × 10−7 90 YUSA 04 BELL 87.1 fb−1 Eee m= 10.6 GeV<1.5 × 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<0.35× 10−5 90 1 BARTELT 94 CLEO Repl. by BLISS 98<1.8 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<1.6 × 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(µ− e+ e−)/total 209/(µ− e+ e−)/total 209/(µ− e+ e−)/total 209/(µ− e+ e−)/total 209/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 1.8 × 10−8< 1.8 × 10−8< 1.8 × 10−8< 1.8 × 10−8 90 HAYASAKA 10 BELL 782 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 2.2 × 10−8 90 LEES 10A BABR 468 fb−1 Eee m= 10.6 GeV< 2.7 × 10−8 90 MIYAZAKI 08 BELL 535 fb−1 Eee m= 10.6 GeV< 8.0 × 10−8 90 AUBERT 07BK BABR 376 fb−1 Eee m= 10.6 GeV< 2.7 × 10−7 90 AUBERT 04J BABR 91.5 fb−1 Eee m= 10.6 GeV< 1.9 × 10−7 90 YUSA 04 BELL 87.1 fb−1 Eee m= 10.6 GeV< 1.7 × 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV< 0.34× 10−5 90 1 BARTELT 94 CLEO Repl. by BLISS 98< 1.4 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV< 2.7 × 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.9<44 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV1BARTELT 94 assume phase spa e de ays.

750750750750LeptonParti le Listingsτ(µ+ e− e−)/total 210/(µ+ e− e−)/total 210/(µ+ e− e−)/total 210/(µ+ e− e−)/total 210/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<1.5 × 10−8<1.5 × 10−8<1.5 × 10−8<1.5 × 10−8 90 HAYASAKA 10 BELL 782 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.8 × 10−8 90 LEES 10A BABR 468 fb−1 Eee m= 10.6 GeV<2.0 × 10−8 90 MIYAZAKI 08 BELL 535 fb−1 Eee m= 10.6 GeV<5.8 × 10−8 90 AUBERT 07BK BABR 376 fb−1 Eee m= 10.6 GeV<1.1 × 10−7 90 AUBERT 04J BABR 91.5 fb−1 Eee m= 10.6 GeV<2.0 × 10−7 90 YUSA 04 BELL 87.1 fb−1 Eee m= 10.6 GeV<1.5 × 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<0.34× 10−5 90 1 BARTELT 94 CLEO Repl. by BLISS 98<1.4 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<1.6 × 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(µ−µ+µ−)/total 211/(µ−µ+µ−)/total 211/(µ−µ+µ−)/total 211/(µ−µ+µ−)/total 211/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 2.1 × 10−8< 2.1 × 10−8< 2.1 × 10−8< 2.1 × 10−8 90 HAYASAKA 10 BELL 782 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 4.6 × 10−8 90 AAIJ 15AI LHCB 3.0 fb−1 √

s = 7, 8 TeV< 8.0 × 10−8 90 1 AAIJ 13AH LHCB 1.0 fb−1, √s = 7 TeV< 3.3 × 10−8 90 LEES 10A BABR 468 fb−1 Eee m= 10.6 GeV< 3.2 × 10−8 90 MIYAZAKI 08 BELL 535 fb−1 Eee m= 10.6 GeV< 5.3 × 10−8 90 AUBERT 07BK BABR 376 fb−1 Eee m= 10.6 GeV< 1.9 × 10−7 90 AUBERT 04J BABR 91.5 fb−1 Eee m= 10.6 GeV< 2.0 × 10−7 90 YUSA 04 BELL 87.1 fb−1 Eee m= 10.6 GeV< 1.9 × 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV< 0.43× 10−5 90 2 BARTELT 94 CLEO Repl. by BLISS 98< 1.9 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV< 1.7 × 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.9<49 × 10−5 90 HAYES 82 MRK2 Eee m= 3.86.8 GeV1Repl. by AAIJ 15AI.2BARTELT 94 assume phase spa e de ays.(e−π+π−)/total 212/(e−π+π−)/total 212/(e−π+π−)/total 212/(e−π+π−)/total 212/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<2.3× 10−8<2.3× 10−8<2.3× 10−8<2.3× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<4.4× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<7.3× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<1.2× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<2.2× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<4.4× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<2.7× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<6.0× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(e+π−π−)/total 213/(e+π−π−)/total 213/(e+π−π−)/total 213/(e+π−π−)/total 213/Test of lepton number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<2.0× 10−8<2.0× 10−8<2.0× 10−8<2.0× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<8.8× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<2.0× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<2.7× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<1.9× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<4.4× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<1.8× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<1.7× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(µ−π+π−)/total 214/(µ−π+π−)/total 214/(µ−π+π−)/total 214/(µ−π+π−)/total 214/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<2.1× 10−8<2.1× 10−8<2.1× 10−8<2.1× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<3.3× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<4.8× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<2.9× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<8.2× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<7.4× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<3.6× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<3.9× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.

(µ+π−π−)/total 215/(µ+π−π−)/total 215/(µ+π−π−)/total 215/(µ+π−π−)/total 215/Test of lepton number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<3.9× 10−8<3.9× 10−8<3.9× 10−8<3.9× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<3.7× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<3.4× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<7 × 10−8 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<3.4× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<6.9× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<6.3× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<3.9× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(e−π+K−)/total 216/(e−π+K−)/total 216/(e−π+K−)/total 216/(e−π+K−)/total 216/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<3.7× 10−8<3.7× 10−8<3.7× 10−8<3.7× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<5.8× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<7.2× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<3.2× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<6.4× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<7.7× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<2.9× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<5.8× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(e−π−K+)/total 217/(e−π−K+)/total 217/(e−π−K+)/total 217/(e−π−K+)/total 217/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<3.1× 10−8<3.1× 10−8<3.1× 10−8<3.1× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<5.2× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<1.6× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<1.7× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<3.8× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<4.6× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<5.8× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(e+π−K−)/total 218/(e+π−K−)/total 218/(e+π−K−)/total 218/(e+π−K−)/total 218/Test of lepton number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<3.2× 10−8<3.2× 10−8<3.2× 10−8<3.2× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<6.7× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<1.9× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<1.8× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<2.1× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<4.5× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<2.0× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<4.9× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(e−K0S K0S)/total 219/(e−K0S K0S)/total 219/(e−K0S K0S)/total 219/(e−K0S K0S)/total 219/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<7.1× 10−8<7.1× 10−8<7.1× 10−8<7.1× 10−8 90 MIYAZAKI 10A BELL 671 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<2.2× 10−6 90 CHEN 02C CLEO Eee m= 10.6 GeV(e−K+K−)/total 220/(e−K+K−)/total 220/(e−K+K−)/total 220/(e−K+K−)/total 220/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<3.4× 10−8<3.4× 10−8<3.4× 10−8<3.4× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<5.4× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<3.0× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<1.4× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<6.0× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV(e+K−K−)/total 221/(e+K−K−)/total 221/(e+K−K−)/total 221/(e+K−K−)/total 221/Test of lepton number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<3.3× 10−8<3.3× 10−8<3.3× 10−8<3.3× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<6.0× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<3.1× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<1.5× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<3.8× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV

751751751751See key on page 601 Lepton Parti le Listingsτ(µ−π+K−)/total 222/(µ−π+K−)/total 222/(µ−π+K−)/total 222/(µ−π+K−)/total 222/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

< 8.6× 10−8< 8.6× 10−8< 8.6× 10−8< 8.6× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 1.6× 10−7 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13< 2.7× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV< 2.6× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV< 7.5× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV< 8.7× 10−6 90 1 BARTELT 94 CLEO Repl. by BLISS 98<11 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV< 7.7× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(µ−π−K+)/total 223/(µ−π−K+)/total 223/(µ−π−K+)/total 223/(µ−π−K+)/total 223/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<4.5× 10−8<4.5× 10−8<4.5× 10−8<4.5× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<1.0× 10−7 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<7.3× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<3.2× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<7.4× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<1.5× 10−5 90 1 BARTELT 94 CLEO Repl. by BLISS 98<7.7× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(µ+π−K−)/total 224/(µ+π−K−)/total 224/(µ+π−K−)/total 224/(µ+π−K−)/total 224/Test of lepton number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<4.8× 10−8<4.8× 10−8<4.8× 10−8<4.8× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<9.4× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<2.9× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<2.2× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<7.0× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV<2.0× 10−5 90 1 BARTELT 94 CLEO Repl. by BLISS 98<5.8× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV<4.0× 10−5 90 BOWCOCK 90 CLEO Eee m= 10.410.91BARTELT 94 assume phase spa e de ays.(µ−K0S K0S)/total 225/(µ−K0S K0S)/total 225/(µ−K0S K0S)/total 225/(µ−K0S K0S)/total 225/VALUE CL% DOCUMENT ID TECN COMMENT<8.0× 10−8<8.0× 10−8<8.0× 10−8<8.0× 10−8 90 MIYAZAKI 10A BELL 671 fb−1 Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<3.4× 10−6 90 CHEN 02C CLEO Eee m= 10.6 GeV(µ−K+K−)/total 226/(µ−K+K−)/total 226/(µ−K+K−)/total 226/(µ−K+K−)/total 226/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT< 4.4× 10−8< 4.4× 10−8< 4.4× 10−8< 4.4× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •< 6.8× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13< 8.0× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV< 2.5× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<15 × 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV(µ+K−K−)/total 227/(µ+K−K−)/total 227/(µ+K−K−)/total 227/(µ+K−K−)/total 227/Test of lepton number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<4.7× 10−8<4.7× 10−8<4.7× 10−8<4.7× 10−8 90 MIYAZAKI 13 BELL 854 fb−1 Eee m = 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<9.6× 10−8 90 MIYAZAKI 10 BELL Repl. by MIYAZAKI 13<4.4× 10−7 90 YUSA 06 BELL 158 fb−1 Eee m = 10.6 GeV<4.8× 10−7 90 AUBERT,BE 05D BABR 221 fb−1, Eee m= 10.6 GeV<6.0× 10−6 90 BLISS 98 CLEO Eee m= 10.6 GeV(e−π0π0)/total 228/(e−π0π0)/total 228/(e−π0π0)/total 228/(e−π0π0)/total 228/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<6.5× 10−6<6.5× 10−6<6.5× 10−6<6.5× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV(µ−π0π0)/total 229/(µ−π0π0)/total 229/(µ−π0π0)/total 229/(µ−π0π0)/total 229/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<14× 10−6<14× 10−6<14× 10−6<14× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV(e− ηη

)/total 230/(e− ηη)/total 230/(e− ηη)/total 230/(e− ηη)/total 230/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<35× 10−6<35× 10−6<35× 10−6<35× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV

(µ−ηη)/total 231/(µ−ηη)/total 231/(µ−ηη)/total 231/(µ−ηη)/total 231/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<60× 10−6<60× 10−6<60× 10−6<60× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV(e−π0 η)/total 232/(e−π0 η)/total 232/(e−π0 η)/total 232/(e−π0 η)/total 232/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<24× 10−6<24× 10−6<24× 10−6<24× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV(µ−π0 η)/total 233/(µ−π0 η)/total 233/(µ−π0 η)/total 233/(µ−π0 η)/total 233/Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<22× 10−6<22× 10−6<22× 10−6<22× 10−6 90 BONVICINI 97 CLEO Eee m= 10.6 GeV(pµ−µ−)/total 234/(pµ−µ−)/total 234/(pµ−µ−)/total 234/(pµ−µ−)/total 234/VALUE CL% DOCUMENT ID TECN COMMENT<4.4× 10−7<4.4× 10−7<4.4× 10−7<4.4× 10−7 90 AAIJ 13AH LHCB 1.0 fb−1, √s = 7 TeV(pµ+µ−)/total 235/(pµ+µ−)/total 235/(pµ+µ−)/total 235/(pµ+µ−)/total 235/VALUE CL% DOCUMENT ID TECN COMMENT<3.3× 10−7<3.3× 10−7<3.3× 10−7<3.3× 10−7 90 AAIJ 13AH LHCB 1.0 fb−1, √s = 7 TeV(pγ

)/total 236/(pγ)/total 236/(pγ)/total 236/(pγ)/total 236/Test of lepton number and baryon number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

< 3.5× 10−6< 3.5× 10−6< 3.5× 10−6< 3.5× 10−6 90 GODANG 99 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<29 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV(pπ0)/total 237/(pπ0)/total 237/(pπ0)/total 237/(pπ0)/total 237/Test of lepton number and baryon number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<15× 10−6<15× 10−6<15× 10−6<15× 10−6 90 GODANG 99 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<66× 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV(p2π0)/total 238/(p2π0)/total 238/(p2π0)/total 238/(p2π0)/total 238/Test of lepton number and baryon number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<33× 10−6<33× 10−6<33× 10−6<33× 10−6 90 GODANG 99 CLEO Eee m= 10.6 GeV(pη

)/total 239/(pη)/total 239/(pη)/total 239/(pη)/total 239/Test of lepton number and baryon number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

< 8.9× 10−6< 8.9× 10−6< 8.9× 10−6< 8.9× 10−6 90 GODANG 99 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<130 × 10−5 90 ALBRECHT 92K ARG Eee m= 10 GeV(pπ0 η

)/total 240/(pπ0 η)/total 240/(pπ0 η)/total 240/(pπ0 η)/total 240/Test of lepton number and baryon number onservation.VALUE CL% DOCUMENT ID TECN COMMENT

<27× 10−6<27× 10−6<27× 10−6<27× 10−6 90 GODANG 99 CLEO Eee m= 10.6 GeV(π−)/total 241/(π−)/total 241/(π−)/total 241/(π−)/total 241/Test of lepton number and baryon number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<0.72× 10−7<0.72× 10−7<0.72× 10−7<0.72× 10−7 90 MIYAZAKI 06 BELL 154 fb−1, Eee m= 10.6 GeV(π−)/total 242/(π−)/total 242/(π−)/total 242/(π−)/total 242/Test of lepton number and baryon number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<1.4× 10−7<1.4× 10−7<1.4× 10−7<1.4× 10−7 90 MIYAZAKI 06 BELL 154 fb−1, Eee m= 10.6 GeV

752752752752Lepton Parti le Listingsτ(e− light boson)/(e−νe ντ

) 243/5(e− light boson)/(e−νe ντ



) 243/5Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<0.015<0.015<0.015<0.015 95 1 ALBRECHT 95G ARG Eee m= 9.410.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<0.018 95 2 ALBRECHT 90E ARG Eee m= 9.410.6 GeV<0.040 95 3 BALTRUSAIT...85 MRK3 Eee m= 3.77 GeV1ALBRECHT 95G limit holds for bosons with mass < 0.4 GeV. The limit rises to 0.036for a mass of 1.0 GeV, then falls to 0.006 at the upper mass limit of 1.6 GeV.2ALBRECHT 90E limit applies for spinless boson with mass < 100 MeV, and rises to0.050 for mass = 500 MeV.3BALTRUSAITIS 85 limit applies for spinless boson with mass < 100 MeV.(µ− light boson)/(e−νe ντ

) 244/5(µ− light boson)/(e−νe ντ



) 244/5Test of lepton family number onservation.VALUE CL% DOCUMENT ID TECN COMMENT<0.026<0.026<0.026<0.026 95 1 ALBRECHT 95G ARG Eee m= 9.410.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •<0.033 95 2 ALBRECHT 90E ARG Eee m= 9.410.6 GeV<0.125 95 3 BALTRUSAIT...85 MRK3 Eee m= 3.77 GeV1ALBRECHT 95G limit holds for bosons with mass < 1.3 GeV. The limit rises to 0.034for a mass of 1.4 GeV, then falls to 0.003 at the upper mass limit of 1.6 GeV.2ALBRECHT 90E limit applies for spinless boson with mass < 100 MeV, and rises to0.071 for mass = 500 MeV.3BALTRUSAITIS 85 limit applies for spinless boson with mass < 100 MeV.

τ -DECAY PARAMETERSτ -DECAY PARAMETERSτ -DECAY PARAMETERSτ -DECAY PARAMETERSτ -LEPTON DECAY PARAMETERS

Updated August 2011 by A. Stahl (RWTH Aachen).

The purpose of the measurements of the decay parameters

(also known as Michel parameters) of the τ is to determine

the structure (spin and chirality) of the current mediating its

decays.

Leptonic Decays: The Michel parameters are extracted from

the energy spectrum of the charged daughter lepton ℓ = e, µ in

the decays τ → ℓνℓντ . Ignoring radiative corrections, neglect-

ing terms of order (mℓ/mτ )2 and (mτ/√

s)2, and setting the

neutrino masses to zero, the spectrum in the laboratory frame

reads

dΓ

dx=

G2τℓ m5

τ

192 π3×

f0 (x) + ρf1 (x) + η

mℓ

mτf2 (x) − Pτ [ξg1 (x) + ξδg2 (x)]

, (1)

with

f0 (x) = 2 − 6 x2 + 4 x3

f1 (x) = −4

9+ 4 x2 − 32

9x3 g1 (x) = −2

3+ 4 x − 6 x2 +

8

3x3

f2 (x) = 12 (1 − x)2 g2 (x) =4

9− 16

3x + 12 x2 − 64

9x3 .

The quantity x is the fractional energy of the daughter lepton

ℓ, i.e., x = Eℓ/Eℓ,max ≈ Eℓ/(√

s/2) and Pτ is the polarization

of the tau leptons. The integrated decay width is given by

Γ =G2

τℓ m5τ

192 π3

(1 + 4 η

mℓ

mτ

). (2)

The situation is similar to muon decays µ → eνeνµ. The gener-

alized matrix element with the couplings gγεµ and their relations

to the Michel parameters ρ, η, ξ, and δ have been described in

the “Note on Muon Decay Parameters.” The Standard Model

expectations are 3/4, 0, 1, and 3/4, respectively. For more

details, see Ref. 1.

Hadronic Decays: In the case of hadronic decays τ → hντ ,

with h = π, ρ, or a1, the ansatz is restricted to purely vectorial

currents. The matrix element is

Gτh√2

∑

λ=R,L

gλ 〈 Ψω(ντ ) | γµ | Ψλ(τ) 〉 Jhµ (3)

with the hadronic current Jhµ . The neutrino chirality ω is

uniquely determined from λ. The spectrum depends only on a

single parameter ξh

dnΓ

dx1dx2 . . . dxn= f (~x) + ξhPτg (~x) , (4)

with f and g being channel-dependent functions of the n

observables ~x = (x1, x2, . . . , xn) (see Ref. 2). The parameter ξh

is related to the couplings through

ξh = |gL|2 − |gR|2 . (5)

ξh is the negative of the chirality of the τ neutrino in these

decays. In the Standard Model, ξh = 1. Also included in the

Data Listings for ξh are measurements of the neutrino helicity

which coincide with ξh, if the neutrino is massless (ASNER

00, ACKERSTAFF 97R, AKERS 95P, ALBRECHT 93C, and

ALBRECHT 90I).

Combination of Measurements: The individual measure-

ments are combined, taking into account the correlations be-

tween the parameters. In a first fit, universality between the two

leptonic decays, and between all hadronic decays, is assumed.

A second fit is made without these assumptions. The results

of the two fits are provided as OUR FIT in the Data Listings

below in the tables whose title includes “(e or mu)” or “(all

hadronic modes),” and “(e),” “(mu)” etc., respectively. The

measurements show good agreement with the Standard Model.

The χ2 values with respect to the Standard model predictions

are 24.1 for 41 degrees of freedom and 26.8 for 56 degrees of

freedom, respectively. The correlations are reduced through this

combination to less than 20%, with the exception of ρ and η

which are correlated by +23%, for the fit with universality and

by +70% for τ → µνµντ .

Model-independent Analysis: From the Michel parameters,

limits can be derived on the couplings gκελ without further

model assumptions. In the Standard model gVLL = 1 (leptonic

decays), and gL = 1 (hadronic decays) and all other couplings

vanish. First, the partial decay widths have to be compared

to the Standard Model predictions to derive limits on the

normalization of the couplings Ax = G2τx/G2

F with Fermi’s

constant GF :

Ae = 1.0029 ± 0.0046 ,

Aµ = 0.981 ± 0.018 ,

Aπ = 1.0020± 0.0073 . (6)

Then limits on the couplings (95% CL) can be extracted (see

Ref. 3 and Ref. 4). Without the assumption of universality, the

limits given in Table 1 are derived.


Table 1: Coupling constants gγεµ. 95% confi-

dence level experimental limits. The limits in-clude the quoted values of Ae, Aµ, and Aπ andassume Aρ = Aa1

= 1.

τ → eνeντ

|gSRR| < 0.70 |gV

RR| < 0.17 |gTRR| ≡ 0

|gSLR| < 0.99 |gV

LR| < 0.13 |gTLR| < 0.082

|gSRL| < 2.01 |gV

RL| < 0.52 |gTRL| < 0.51

|gSLL| < 2.01 |gV

LL| < 1.005 |gTLL| ≡ 0

τ → µνµντ

|gSRR| < 0.72 |gV

RR| < 0.18 |gTRR| ≡ 0

|gSLR| < 0.95 |gV

LR| < 0.12 |gTLR| < 0.079

|gSRL| < 2.01 |gV

RL| < 0.52 |gTRL| < 0.51

|gSLL| < 2.01 |gV

LL| < 1.005 |gTLL| ≡ 0

τ → πντ

|gVR | < 0.15 |gV

L | > 0.992

τ → ρντ

|gVR | < 0.10 |gV

L | > 0.995

τ → a1ντ

|gVR | < 0.16 |gV

L | > 0.987

Model-dependent Interpretation: More stringent limits can

be derived assuming specific models. For example, in the frame-

work of a two Higgs doublet model, the measurements corre-

spond to a limit of mH± > 1.9 GeV × tan β on the mass of the

charged Higgs boson, or a limit of 253 GeV on the mass of the

second W boson in left-right symmetric models for arbitrary

mixing (both 95% CL). See Ref. 4 and Ref. 5.

Footnotes and References

1. F. Scheck, Phys. Reports 44, 187 (1978);W. Fetscher and H.J. Gerber in Precision Tests of the

Standard Model, edited by P. Langacker, World Scientific,1993;A. Stahl, Physics with τ Leptons, Springer Tracts in ModernPhysics.

2. M. Davier et al., Phys. Lett. B306, 411 (1993).

3. OPAL Collab., K. Ackerstaff et al., Eur. Phys. J. C8, 3(1999).

4. A. Stahl, Nucl. Phys. (Proc. Supp.) B76, 173 (1999).

5. M.-T. Dova et al., Phys. Rev. D58, 015005 (1998);T. Hebbeker and W. Lohmann, Z. Phys. C74, 399 (1997);A. Pich and J.P. Silva, Phys. Rev. D52, 4006 (1995).

ρ(e or µ) PARAMETERρ(e or µ) PARAMETERρ(e or µ) PARAMETERρ(e or µ) PARAMETER(V−A) theory predi ts ρ = 0.75.VALUE EVTS DOCUMENT ID TECN COMMENT0.745±0.008 OUR FIT0.745±0.008 OUR FIT0.745±0.008 OUR FIT0.745±0.008 OUR FIT0.749±0.008 OUR AVERAGE0.749±0.008 OUR AVERAGE0.749±0.008 OUR AVERAGE0.749±0.008 OUR AVERAGE0.742±0.014±0.006 81k HEISTER 01E ALEP 19911995 LEP runs0.775±0.023±0.020 36k ABREU 00L DLPH 19921995 runs0.781±0.028±0.018 46k ACKERSTAFF 99D OPAL 19901995 LEP runs0.762±0.035 54k ACCIARRI 98R L3 19911995 LEP runs

0.731±0.031 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV0.72 ±0.09 ±0.03 2 ABE 97O SLD 19931995 SLC runs0.747±0.010±0.006 55k ALEXANDER 97F CLEO Eee m= 10.6 GeV0.79 ±0.10 ±0.10 3732 FORD 87B MAC Eee m= 29 GeV0.71 ±0.09 ±0.03 1426 BEHRENDS 85 CLEO e+ e− near (4S)• • • We do not use the following data for averages, ts, limits, et . • • •0.735±0.013±0.008 31k AMMAR 97B CLEO Repl. by ALEXAN-DER 97F0.794±0.039±0.031 18k ACCIARRI 96H L3 Repl. by ACCIARRI 98R0.732±0.034±0.020 8.2k 3 ALBRECHT 95 ARG Eee m= 9.510.6 GeV0.738±0.038 4 ALBRECHT 95C ARG Repl. by ALBRECHT 980.751±0.039±0.022 BUSKULIC 95D ALEP Repl. by HEISTER 01E0.742±0.035±0.020 8000 ALBRECHT 90E ARG Eee m= 9.410.6 GeV1Combined t to ARGUS tau de ay parameter measurements in ALBRECHT 98, AL-BRECHT 95C, ALBRECHT 93G, and ALBRECHT 94E. ALBRECHT 98 use tau pairevents of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), and their harged onjugates.2ABE 97O assume η = 0 in their t. Letting η vary in the t gives a ρ value of 0.69 ±0.13 ± 0.05.3Value is from a simultaneous t for the ρ and η de ay parameters to the lepton energyspe trum. Not independent of ALBRECHT 90E ρ(e or µ) value whi h assumes η = 0.Result is strongly orrelated with ALBRECHT 95C.4 Combined t to ARGUS tau de ay parameter measurements in ALBRECHT 95C, AL-BRECHT 93G, and ALBRECHT 94E.ρ(e) PARAMETERρ(e) PARAMETERρ(e) PARAMETERρ(e) PARAMETER(V−A) theory predi ts ρ = 0.75.VALUE EVTS DOCUMENT ID TECN COMMENT0.747±0.010 OUR FIT0.747±0.010 OUR FIT0.747±0.010 OUR FIT0.747±0.010 OUR FIT0.744±0.010 OUR AVERAGE0.744±0.010 OUR AVERAGE0.744±0.010 OUR AVERAGE0.744±0.010 OUR AVERAGE0.747±0.019±0.014 44k HEISTER 01E ALEP 19911995 LEP runs0.744±0.036±0.037 17k ABREU 00L DLPH 19921995 runs0.779±0.047±0.029 25k ACKERSTAFF 99D OPAL 19901995 LEP runs0.68 ±0.04 ±0.07 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV0.71 ±0.14 ±0.05 ABE 97O SLD 19931995 SLC runs0.747±0.012±0.004 34k ALEXANDER 97F CLEO Eee m= 10.6 GeV0.735±0.036±0.020 4.7k 2 ALBRECHT 95 ARG Eee m= 9.510.6 GeV0.79 ±0.08 ±0.06 3230 3 ALBRECHT 93G ARG Eee m= 9.410.6 GeV0.64 ±0.06 ±0.07 2753 JANSSEN 89 CBAL Eee m= 9.410.6 GeV0.62 ±0.17 ±0.14 1823 FORD 87B MAC Eee m= 29 GeV0.60 ±0.13 699 BEHRENDS 85 CLEO e+ e− near (4S)0.72 ±0.10 ±0.11 594 BACINO 79B DLCO Eee m= 3.57.4 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.732±0.014±0.009 19k AMMAR 97B CLEO Repl. by ALEXAN-DER 97F0.793±0.050±0.025 BUSKULIC 95D ALEP Repl. by HEISTER 01E0.747±0.045±0.028 5106 ALBRECHT 90E ARG Repl. by ALBRECHT 951ALBRECHT 98 use tau pair events of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), andtheir harged onjugates.2ALBRECHT 95 use tau pair events of the type τ− τ+ → (ℓ− νℓ ντ )(h+ h− h+(π0 )ντ ) and their harged onjugates.3ALBRECHT 93G use tau pair events of the type τ− τ+ → (µ− νµ ντ ) (e+ νe ντ ) andtheir harged onjugates.ρ(µ) PARAMETERρ(µ) PARAMETERρ(µ) PARAMETERρ(µ) PARAMETER(V−A) theory predi ts ρ = 0.75.VALUE EVTS DOCUMENT ID TECN COMMENT0.763±0.020 OUR FIT0.763±0.020 OUR FIT0.763±0.020 OUR FIT0.763±0.020 OUR FIT0.770±0.022 OUR AVERAGE0.770±0.022 OUR AVERAGE0.770±0.022 OUR AVERAGE0.770±0.022 OUR AVERAGE0.776±0.045±0.019 46k HEISTER 01E ALEP 19911995 LEP runs0.999±0.098±0.045 22k ABREU 00L DLPH 19921995 runs0.777±0.044±0.016 27k ACKERSTAFF 99D OPAL 19901995 LEP runs0.69 ±0.06 ±0.06 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV0.54 ±0.28 ±0.14 ABE 97O SLD 19931995 SLC runs0.750±0.017±0.045 22k ALEXANDER 97F CLEO Eee m= 10.6 GeV0.76 ±0.07 ±0.08 3230 ALBRECHT 93G ARG Eee m= 9.410.6 GeV0.734±0.055±0.027 3041 ALBRECHT 90E ARG Eee m= 9.410.6 GeV0.89 ±0.14 ±0.08 1909 FORD 87B MAC Eee m= 29 GeV0.81 ±0.13 727 BEHRENDS 85 CLEO e+ e− near (4S)• • • We do not use the following data for averages, ts, limits, et . • • •0.747±0.048±0.044 13k AMMAR 97B CLEO Repl. by ALEXAN-DER 97F0.693±0.057±0.028 BUSKULIC 95D ALEP Repl. by HEISTER 01E1ALBRECHT 98 use tau pair events of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), andtheir harged onjugates.ξ(e or µ) PARAMETERξ(e or µ) PARAMETERξ(e or µ) PARAMETERξ(e or µ) PARAMETER(V−A) theory predi ts ξ = 1.VALUE EVTS DOCUMENT ID TECN COMMENT0.985±0.030 OUR FIT0.985±0.030 OUR FIT0.985±0.030 OUR FIT0.985±0.030 OUR FIT0.981±0.031 OUR AVERAGE0.981±0.031 OUR AVERAGE0.981±0.031 OUR AVERAGE0.981±0.031 OUR AVERAGE0.986±0.068±0.031 81k HEISTER 01E ALEP 19911995 LEP runs0.929±0.070±0.030 36k ABREU 00L DLPH 19921995 runs0.98 ±0.22 ±0.10 46k ACKERSTAFF 99D OPAL 19901995 LEP runs0.70 ±0.16 54k ACCIARRI 98R L3 19911995 LEP runs1.03 ±0.11 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV1.05 ±0.35 ±0.04 2 ABE 97O SLD 19931995 SLC runs1.007±0.040±0.015 55k ALEXANDER 97F CLEO Eee m= 10.6 GeV

754754754754LeptonParti le Listingsτ

• • • We do not use the following data for averages, ts, limits, et . • • •0.94 ±0.21 ±0.07 18k ACCIARRI 96H L3 Repl. by ACCIARRI 98R0.97 ±0.14 3 ALBRECHT 95C ARG Repl. by ALBRECHT 981.18 ±0.15 ±0.16 BUSKULIC 95D ALEP Repl. by HEISTER 01E0.90 ±0.15 ±0.10 3230 4 ALBRECHT 93G ARG Eee m= 9.410.6 GeV1Combined t to ARGUS tau de ay parameter measurements in ALBRECHT 98, AL-BRECHT 95C, ALBRECHT 93G, and ALBRECHT 94E. ALBRECHT 98 use tau pairevents of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), and their harged onjugates.2ABE 97O assume η = 0 in their t. Letting η vary in the t gives a ξ value of 1.02 ±0.36 ± 0.05.3Combined t to ARGUS tau de ay parameter measurements in ALBRECHT 95C, AL-BRECHT 93G, and ALBRECHT 94E. ALBRECHT 95C uses events of the type τ− τ+ →(ℓ− νℓ ντ ) (h+ h− h+ ντ ) and their harged onjugates.4ALBRECHT 93G measurement determines ∣∣ξ∣∣ for the ase ξ(e) = ξ(µ), but the authorspoint out that other LEP experiments determine the sign to be positive.

ξ(e) PARAMETERξ(e) PARAMETERξ(e) PARAMETERξ(e) PARAMETER(V−A) theory predi ts ξ = 1.VALUE EVTS DOCUMENT ID TECN COMMENT0.994±0.040 OUR FIT0.994±0.040 OUR FIT0.994±0.040 OUR FIT0.994±0.040 OUR FIT1.00 ±0.04 OUR AVERAGE1.00 ±0.04 OUR AVERAGE1.00 ±0.04 OUR AVERAGE1.00 ±0.04 OUR AVERAGE1.011±0.094±0.038 44k HEISTER 01E ALEP 19911995 LEP runs1.01 ±0.12 ±0.05 17k ABREU 00L DLPH 19921995 runs1.13 ±0.39 ±0.14 25k ACKERSTAFF 99D OPAL 19901995 LEP runs1.11 ±0.20 ±0.08 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV1.16 ±0.52 ±0.06 ABE 97O SLD 19931995 SLC runs0.979±0.048±0.016 34k ALEXANDER 97F CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.03 ±0.23 ±0.09 BUSKULIC 95D ALEP Repl. by HEISTER 01E1ALBRECHT 98 use tau pair events of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), andtheir harged onjugates.ξ(µ) PARAMETERξ(µ) PARAMETERξ(µ) PARAMETERξ(µ) PARAMETER(V−A) theory predi ts ξ = 1.VALUE EVTS DOCUMENT ID TECN COMMENT1.030±0.059 OUR FIT1.030±0.059 OUR FIT1.030±0.059 OUR FIT1.030±0.059 OUR FIT1.06 ±0.06 OUR AVERAGE1.06 ±0.06 OUR AVERAGE1.06 ±0.06 OUR AVERAGE1.06 ±0.06 OUR AVERAGE1.030±0.120±0.050 46k HEISTER 01E ALEP 19911995 LEP runs1.16 ±0.19 ±0.06 22k ABREU 00L DLPH 19921995 runs0.79 ±0.41 ±0.09 27k ACKERSTAFF 99D OPAL 19901995 LEP runs1.26 ±0.27 ±0.14 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV0.75 ±0.50 ±0.14 ABE 97O SLD 19931995 SLC runs1.054±0.069±0.047 22k ALEXANDER 97F CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.23 ±0.22 ±0.10 BUSKULIC 95D ALEP Repl. by HEISTER 01E1ALBRECHT 98 use tau pair events of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), andtheir harged onjugates.η(e or µ) PARAMETERη(e or µ) PARAMETERη(e or µ) PARAMETERη(e or µ) PARAMETER(V−A) theory predi ts η = 0.VALUE EVTS DOCUMENT ID TECN COMMENT0.013±0.020 OUR FIT0.013±0.020 OUR FIT0.013±0.020 OUR FIT0.013±0.020 OUR FIT0.015±0.021 OUR AVERAGE0.015±0.021 OUR AVERAGE0.015±0.021 OUR AVERAGE0.015±0.021 OUR AVERAGE0.012±0.026±0.004 81k HEISTER 01E ALEP 19911995 LEP runs−0.005±0.036±0.037 ABREU 00L DLPH 19921995 runs0.027±0.055±0.005 46k ACKERSTAFF 99D OPAL 19901995 LEP runs0.27 ±0.14 54k ACCIARRI 98R L3 19911995 LEP runs−0.13 ±0.47 ±0.15 ABE 97O SLD 19931995 SLC runs−0.015±0.061±0.062 31k AMMAR 97B CLEO Eee m= 10.6 GeV0.03 ±0.18 ±0.12 8.2k ALBRECHT 95 ARG Eee m= 9.510.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.25 ±0.17 ±0.11 18k ACCIARRI 96H L3 Repl. by ACCIARRI 98R−0.04 ±0.15 ±0.11 BUSKULIC 95D ALEP Repl. by HEISTER 01Eη(µ) PARAMETERη(µ) PARAMETERη(µ) PARAMETERη(µ) PARAMETER(V−A) theory predi ts η = 0.VALUE EVTS DOCUMENT ID TECN COMMENT0.094±0.073 OUR FIT0.094±0.073 OUR FIT0.094±0.073 OUR FIT0.094±0.073 OUR FIT0.17 ±0.15 OUR AVERAGE0.17 ±0.15 OUR AVERAGE0.17 ±0.15 OUR AVERAGE0.17 ±0.15 OUR AVERAGE Error in ludes s ale fa tor of 1.2.0.160±0.150±0.060 46k HEISTER 01E ALEP 19911995 LEP runs0.72 ±0.32 ±0.15 ABREU 00L DLPH 19921995 runs−0.59 ±0.82 ±0.45 1 ABE 97O SLD 19931995 SLC runs0.010±0.149±0.171 13k 2 AMMAR 97B CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.010±0.065±0.001 27k 3 ACKERSTAFF 99D OPAL 19901995 LEP runs−0.24 ±0.23 ±0.18 BUSKULIC 95D ALEP Repl. by HEISTER 01E1Highly orrelated ( orr. = 0.92) with ABE 97O ρ(µ) measurement.2Highly orrelated ( orr. = 0.949) with AMMAR 97B ρ(µ) value.3ACKERSTAFF 99D result is dominated by a onstraint on η from the OPAL measure-ments of the τ lifetime and B(τ− → µ− νµ ντ ) assuming lepton universality for thetotal oupling strength.

(δξ)(e or µ) PARAMETER(δξ)(e or µ) PARAMETER(δξ)(e or µ) PARAMETER(δξ)(e or µ) PARAMETER(V−A) theory predi ts (δξ) = 0.75.VALUE EVTS DOCUMENT ID TECN COMMENT0.746±0.021 OUR FIT0.746±0.021 OUR FIT0.746±0.021 OUR FIT0.746±0.021 OUR FIT0.744±0.022 OUR AVERAGE0.744±0.022 OUR AVERAGE0.744±0.022 OUR AVERAGE0.744±0.022 OUR AVERAGE0.776±0.045±0.024 81k HEISTER 01E ALEP 19911995 LEP runs0.779±0.070±0.028 36k ABREU 00L DLPH 19921995 runs0.65 ±0.14 ±0.07 46k ACKERSTAFF 99D OPAL 19901995 LEP runs0.70 ±0.11 54k ACCIARRI 98R L3 19911995 LEP runs0.63 ±0.09 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV0.88 ±0.27 ±0.04 2 ABE 97O SLD 19931995 SLC runs0.745±0.026±0.009 55k ALEXANDER 97F CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.81 ±0.14 ±0.06 18k ACCIARRI 96H L3 Repl. by ACCIARRI 98R0.65 ±0.12 3 ALBRECHT 95C ARG Repl. by ALBRECHT 980.88 ±0.11 ±0.07 BUSKULIC 95D ALEP Repl. by HEISTER 01E1Combined t to ARGUS tau de ay parameter measurements in ALBRECHT 98, AL-BRECHT 95C, ALBRECHT 93G, and ALBRECHT 94E. ALBRECHT 98 use tau pairevents of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), and their harged onjugates.2ABE 97O assume η = 0 in their t. Letting η vary in the t gives a (δξ) value of0.87 ± 0.27 ± 0.04.3Combined t to ARGUS tau de ay parameter measurements in ALBRECHT 95C, AL-BRECHT 93G, and ALBRECHT 94E. ALBRECHT 95C uses events of the type τ− τ+ →(ℓ− νℓ ντ ) (h+ h− h+ ντ ) and their harged onjugates.(δξ)(e) PARAMETER(δξ)(e) PARAMETER(δξ)(e) PARAMETER(δξ)(e) PARAMETER(V−A) theory predi ts (δξ) = 0.75.VALUE EVTS DOCUMENT ID TECN COMMENT0.734±0.028 OUR FIT0.734±0.028 OUR FIT0.734±0.028 OUR FIT0.734±0.028 OUR FIT0.731±0.029 OUR AVERAGE0.731±0.029 OUR AVERAGE0.731±0.029 OUR AVERAGE0.731±0.029 OUR AVERAGE0.778±0.066±0.024 44k HEISTER 01E ALEP 19911995 LEP runs0.85 ±0.12 ±0.04 17k ABREU 00L DLPH 19921995 runs0.72 ±0.31 ±0.14 25k ACKERSTAFF 99D OPAL 19901995 LEP runs0.56 ±0.14 ±0.06 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV0.85 ±0.43 ±0.08 ABE 97O SLD 19931995 SLC runs0.720±0.032±0.010 34k ALEXANDER 97F CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.11 ±0.17 ±0.07 BUSKULIC 95D ALEP Repl. by HEISTER 01E1ALBRECHT 98 use tau pair events of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), andtheir harged onjugates.(δξ)(µ) PARAMETER(δξ)(µ) PARAMETER(δξ)(µ) PARAMETER(δξ)(µ) PARAMETER(V−A) theory predi ts (δξ) = 0.75.VALUE EVTS DOCUMENT ID TECN COMMENT0.778±0.037 OUR FIT0.778±0.037 OUR FIT0.778±0.037 OUR FIT0.778±0.037 OUR FIT0.79 ±0.04 OUR AVERAGE0.79 ±0.04 OUR AVERAGE0.79 ±0.04 OUR AVERAGE0.79 ±0.04 OUR AVERAGE0.786±0.066±0.028 46k HEISTER 01E ALEP 19911995 LEP runs0.86 ±0.13 ±0.04 22k ABREU 00L DLPH 19921995 runs0.63 ±0.23 ±0.05 27k ACKERSTAFF 99D OPAL 19901995 LEP runs0.73 ±0.18 ±0.10 1 ALBRECHT 98 ARG Eee m= 9.510.6 GeV0.82 ±0.32 ±0.07 ABE 97O SLD 19931995 SLC runs0.786±0.041±0.032 22k ALEXANDER 97F CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.71 ±0.14 ±0.06 BUSKULIC 95D ALEP Repl. by HEISTER 01E1ALBRECHT 98 use tau pair events of the type τ− τ+ → (ℓ− νℓ ντ )(π+π0 ντ ), andtheir harged onjugates.ξ(π) PARAMETERξ(π) PARAMETERξ(π) PARAMETERξ(π) PARAMETER(V−A) theory predi ts ξ(π) = 1.VALUE EVTS DOCUMENT ID TECN COMMENT0.993±0.022 OUR FIT0.993±0.022 OUR FIT0.993±0.022 OUR FIT0.993±0.022 OUR FIT0.994±0.023 OUR AVERAGE0.994±0.023 OUR AVERAGE0.994±0.023 OUR AVERAGE0.994±0.023 OUR AVERAGE0.994±0.020±0.014 27k HEISTER 01E ALEP 19911995 LEP runs0.81 ±0.17 ±0.02 ABE 97O SLD 19931995 SLC runs1.03 ±0.06 ±0.04 2.0k COAN 97 CLEO Eee m= 10.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •0.987±0.057±0.027 BUSKULIC 95D ALEP Repl. by HEISTER 01E0.95 ±0.11 ±0.05 1 BUSKULIC 94D ALEP 1990+1991 LEP run1Superseded by BUSKULIC 95D.ξ(ρ) PARAMETERξ(ρ) PARAMETERξ(ρ) PARAMETERξ(ρ) PARAMETER(V−A) theory predi ts ξ(ρ) = 1.VALUE EVTS DOCUMENT ID TECN COMMENT0.994±0.008 OUR FIT0.994±0.008 OUR FIT0.994±0.008 OUR FIT0.994±0.008 OUR FIT0.994±0.009 OUR AVERAGE0.994±0.009 OUR AVERAGE0.994±0.009 OUR AVERAGE0.994±0.009 OUR AVERAGE0.987±0.012±0.011 59k HEISTER 01E ALEP 19911995 LEP runs0.99 ±0.12 ±0.04 ABE 97O SLD 19931995 SLC runs0.995±0.010±0.003 66k ALEXANDER 97F CLEO Eee m= 10.6 GeV1.022±0.028±0.030 1.7k 1 ALBRECHT 94E ARG Eee m= 9.410.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.045±0.058±0.032 BUSKULIC 95D ALEP Repl. by HEISTER 01E1.03 ±0.11 ±0.05 2 BUSKULIC 94D ALEP 1990+1991 LEP run1ALBRECHT 94E measure the square of this quantity and use the sign determined byALBRECHT 90I to obtain the quoted result.2 Superseded by BUSKULIC 95D.


ξ(a1) PARAMETERξ(a1) PARAMETERξ(a1) PARAMETERξ(a1) PARAMETER(V−A) theory predi ts ξ(a1) = 1.VALUE EVTS DOCUMENT ID TECN COMMENT1.001±0.027 OUR FIT1.001±0.027 OUR FIT1.001±0.027 OUR FIT1.001±0.027 OUR FIT1.002±0.028 OUR AVERAGE1.002±0.028 OUR AVERAGE1.002±0.028 OUR AVERAGE1.002±0.028 OUR AVERAGE1.000±0.016±0.024 35k 1 HEISTER 01E ALEP 19911995 LEP runs1.02 ±0.13 ±0.03 17.2k ASNER 00 CLEO Eee m= 10.6 GeV1.29 ±0.26 ±0.11 7.4k 2 ACKERSTAFF 97R OPAL 19921994 LEP runs0.85 +0.15−0.17 ±0.05 ALBRECHT 95C ARG Eee m= 9.510.6 GeV1.25 ±0.23 +0.15

−0.08 7.5k ALBRECHT 93C ARG Eee m= 9.410.6 GeV• • • We do not use the following data for averages, ts, limits, et . • • •1.08 +0.46

−0.41 +0.14−0.25 2.6k 3 AKERS 95P OPAL Repl. by ACKER-STAFF 97R0.937±0.116±0.064 BUSKULIC 95D ALEP Repl. by HEISTER 01E1HEISTER 01E quote 1.000 ± 0.016 ± 0.013 ± 0.020 where the errors are statisti al,systemati , and an un ertainty due to the nal state model. We ombine the systemati error and model un ertainty.2ACKERSTAFF 97R obtain this result with a model independent t to the hadroni stru -ture fun tions. Fitting with the model of Kuhn and Santamaria (ZPHY C48C48C48C48, 445 (1990))gives 0.87 ± 0.16 ± 0.04, and with the model of of Isgur et al. (PR D39D39D39D39,1357 (1989))they obtain 1.20 ± 0.21 ± 0.14.3AKERS 95P obtain this result with a model independent t to the hadroni stru turefun tions. Fitting with the model of Kuhn and Santamaria (ZPHY C48C48C48C48, 445 (1990))gives 0.87 ± 0.27+0.05

−0.06, and with the model of of Isgur et al. (PR D39D39D39D39,1357 (1989))they obtain 1.10 ± 0.31+0.13−0.14.

ξ(all hadroni modes) PARAMETERξ(all hadroni modes) PARAMETERξ(all hadroni modes) PARAMETERξ(all hadroni modes) PARAMETER(V−A) theory predi ts ξ = 1.VALUE EVTS DOCUMENT ID TECN COMMENT0.995±0.007 OUR FIT0.995±0.007 OUR FIT0.995±0.007 OUR FIT0.995±0.007 OUR FIT0.997±0.007 OUR AVERAGE0.997±0.007 OUR AVERAGE0.997±0.007 OUR AVERAGE0.997±0.007 OUR AVERAGE0.992±0.007±0.008 102k 1 HEISTER 01E ALEP 19911995 LEP runs0.997±0.027±0.011 39k 2 ABREU 00L DLPH 19921995 runs1.02 ±0.13 ±0.03 17.2k 3 ASNER 00 CLEO Eee m= 10.6 GeV1.032±0.031 37k 4 ACCIARRI 98R L3 19911995 LEP runs0.93 ±0.10 ±0.04 ABE 97O SLD 19931995 SLC runs1.29 ±0.26 ±0.11 7.4k 5 ACKERSTAFF 97R OPAL 19921994 LEP runs0.995±0.010±0.003 66k 6 ALEXANDER 97F CLEO Eee m= 10.6 GeV1.03 ±0.06 ±0.04 2.0k 7 COAN 97 CLEO Eee m= 10.6 GeV1.017±0.039 8 ALBRECHT 95C ARG Eee m= 9.510.6 GeV1.25 ±0.23 +0.15−0.08 7.5k 9 ALBRECHT 93C ARG Eee m= 9.410.6 GeV

• • • We do not use the following data for averages, ts, limits, et . • • •0.970±0.053±0.011 14k 10 ACCIARRI 96H L3 Repl. by ACCIARRI 98R1.08 +0.46−0.41 +0.14

−0.25 2.6k 11 AKERS 95P OPAL Repl. by ACKER-STAFF 97R1.006±0.032±0.019 12 BUSKULIC 95D ALEP Repl. by HEISTER 01E1.022±0.028±0.030 1.7k 13 ALBRECHT 94E ARG Eee m= 9.410.6 GeV0.99 ±0.07 ±0.04 14 BUSKULIC 94D ALEP 1990+1991 LEP run1HEISTER 01E quote 0.992 ± 0.007 ± 0.006 ± 0.005 where the errors are statisti al,systemati , and an un ertainty due to the nal state model. We ombine the systemati error and model un ertainty. They use τ → πντ , τ → K ντ , τ → ρντ , and τ →a1 ντ de ays.2ABREU 00L use τ− → h− ≥ 0π0 ντ de ays.3ASNER 00 use τ− → π− 2π0 ντ de ays.4ACCIARRI 98R use τ → πντ , τ → K ντ , and τ → ρντ de ays.5ACKERSTAFF 97R use τ → a1 ντ de ays.6ALEXANDER 97F use τ → ρντ de ays.7COAN 97 use h+ h− energy orrelations.8Combined t to ARGUS tau de ay parameter measurements in ALBRECHT 95C, AL-BRECHT 93G, and ALBRECHT 94E.9Uses τ → a1 ντ de ays. Repla ed by ALBRECHT 95C.10ACCIARRI 96H use τ → πντ , τ → K ντ , and τ → ρντ de ays.11AKERS 95P use τ → a1 ντ de ays.12BUSKULIC 95D use τ → πντ , τ → ρντ , and τ → a1 ντ de ays.13ALBRECHT 94E measure the square of this quantity and use the sign determined byALBRECHT 90I to obtain the quoted result. Uses τ → a1 ντ de ays. Repla ed byALBRECHT 95C.14BUSKULIC 94D use τ → πντ and τ → ρντ de ays. Superseded by BUSKULIC 95D.τ REFERENCESτ REFERENCESτ REFERENCESτ REFERENCESAAIJ 15AI JHEP 1502 121 R. Aaij et al. (LHCb Collab.)LEES 15G PR D91 051103 J.P. Lees et al. (Babar)ABLIKIM 14D PR D90 012001 M. Ablikim et al. (BES III Collab.)BELOUS 14 PRL 112 031801 K. Belous et al. (BELLE Collab.)RYU 14 PR D89 072009 S. Ryu et al. (BELLE Collab.)AAIJ 13AH PL B724 36 R. Aaij et al. (LHCb Collab.)MIYAZAKI 13 PL B719 346 Y. Miyazaki et al. (BELLE Collab.)LEES 12M PR D85 031102 J.P. Lees et al. (BABAR Collab.)Also PR D85 099904 (errat.) J.P. Lees et al. (BABAR Collab.)LEES 12X PR D86 092010 J.P. Lees et al. (BABAR Collab.)LEES 12Y PR D86 092013 J.P. Lees et al. (BABAR Collab.)PDG 12 PR D86 010001 J. Beringer et al. (PDG Collab.)DEL-AMO-SA... 11E PR D83 032002 P. del Amo San hez et al. (BABAR Collab.)MIYAZAKI 11 PL B699 251 Y. Miyazaki et al. (BELLE Collab.)AUBERT 10B PRL 104 021802 B. Aubert et al. (BABAR Collab.)AUBERT 10F PRL 105 051602 B. Aubert et al. (BABAR Collab.)HAYASAKA 10 PL B687 139 K. Hayasaka et al. (BELLE Collab.)LEE 10 PR D81 113007 M.J. Lee et al. (BELLE Collab.)

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(ALEPH Collab.)BERGFELD 97 PRL 79 2406 T. Bergfeld et al. (CLEO Collab.)BONVICINI 97 PRL 79 1221 G. Bonvi ini et al. (CLEO Collab.)BUSKULIC 97C ZPHY C74 263 D. Buskuli et al. (ALEPH Collab.)COAN 97 PR D55 7291 T.E. Coan et al. (CLEO Collab.)EDWARDS 97 PR D55 R3919 K.W. Edwards et al. (CLEO Collab.)EDWARDS 97B PR D56 R5297 K.W. Edwards et al. (CLEO Collab.)ESCRIBANO 97 PL B395 369 R. Es ribano, E. Masso (BARC, PARIT)ABREU 96B PL B365 448 P. Abreu et al. (DELPHI Collab.)ACCIARRI 96H PL B377 313 M. A iarri et al. (L3 Collab.)ACCIARRI 96K PL B389 187 M. A iarri et al. (L3 Collab.)ALAM 96 PRL 76 2637 M.S. Alam et al. (CLEO Collab.)ALBRECHT 96E PRPL 276 223 H. Albre ht et al. (ARGUS Collab.)ALEXANDER 96D PL B369 163 G. Alexander et al. (OPAL Collab.)ALEXANDER 96E PL B374 341 G. Alexander et al. (OPAL Collab.)ALEXANDER 96S PL B388 437 G. Alexander et al. (OPAL Collab.)BAI 96 PR D53 20 J.Z. Bai et al. (BES Collab.)BALEST 96 PL B388 402 R. Balest et al. (CLEO Collab.)

756756756756Lepton Parti le Listingsτ , Heavy Charged Lepton Sear hesBARTELT 96 PRL 76 4119 J.E. Bartelt et al. (CLEO Collab.)BUSKULIC 96 ZPHY C70 579 D. Buskuli et al. (ALEPH Collab.)BUSKULIC 96C ZPHY C70 561 D. Buskuli et al. (ALEPH Collab.)COAN 96 PR D53 6037 T.E. Coan et al. (CLEO Collab.)ABE 95Y PR D52 4828 K. Abe et al. (SLD Collab.)ABREU 95T PL B357 715 P. Abreu et al. (DELPHI Collab.)ABREU 95U PL B359 411 P. Abreu et al. (DELPHI Collab.)ACCIARRI 95 PL B345 93 M. A iarri et al. (L3 Collab.)ACCIARRI 95F PL B352 487 M. A iarri et al. (L3 Collab.)AKERS 95F ZPHY C66 31 R. Akers et al. (OPAL Collab.)AKERS 95I ZPHY C66 543 R. Akers et al. (OPAL Collab.)AKERS 95P ZPHY C67 45 R. Akers et al. (OPAL Collab.)AKERS 95Y ZPHY C68 555 R. Akers et al. (OPAL Collab.)ALBRECHT 95 PL B341 441 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 95C PL B349 576 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 95G ZPHY C68 25 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 95H ZPHY C68 215 H. Albre ht et al. (ARGUS Collab.)BALEST 95C PRL 75 3809 R. Balest et al. (CLEO Collab.)BERNABEU 95 NP B436 474 J. Bernabeu et al.BUSKULIC 95C PL B346 371 D. Buskuli et al. (ALEPH Collab.)BUSKULIC 95D PL B346 379 D. Buskuli et al. (ALEPH Collab.)Also PL B363 265 (erratum) D. Buskuli et al. (ALEPH Collab.)ABREU 94K PL B334 435 P. Abreu et al. (DELPHI Collab.)AKERS 94E PL B328 207 R. Akers et al. (OPAL Collab.)AKERS 94G PL B339 278 R. Akers et al. (OPAL Collab.)ALBRECHT 94E PL B337 383 H. Albre ht et al. (ARGUS Collab.)ARTUSO 94 PRL 72 3762 M. Artuso et al. (CLEO Collab.)BARTELT 94 PRL 73 1890 J.E. Bartelt et al. (CLEO Collab.)BATTLE 94 PRL 73 1079 M. Battle et al. (CLEO Collab.)BAUER 94 PR D50 13 D.A. Bauer et al. (TPC/2gamma Collab.)BUSKULIC 94D PL B321 168 D. Buskuli et al. (ALEPH Collab.)BUSKULIC 94E PL B332 209 D. Buskuli et al. (ALEPH Collab.)BUSKULIC 94F PL B332 219 D. Buskuli et al. (ALEPH Collab.)GIBAUT 94B PRL 73 934 D. Gibaut et al. (CLEO Collab.)ADRIANI 93M PRPL 236 1 O. Adriani et al. (L3 Collab.)ALBRECHT 93C ZPHY C58 61 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 93G PL B316 608 H. Albre ht et al. (ARGUS Collab.)BALEST 93 PR D47 R3671 R. Balest et al. (CLEO Collab.)BEAN 93 PRL 70 138 A. Bean et al. (CLEO Collab.)BORTOLETTO 93 PRL 71 1791 D. Bortoletto et al. (CLEO Collab.)ESCRIBANO 93 PL B301 419 R. Es ribano, E. Masso (BARC)PROCARIO 93 PRL 70 1207 M. Pro ario et al. (CLEO Collab.)ABREU 92N ZPHY C55 555 P. Abreu et al. (DELPHI Collab.)ACTON 92F PL B281 405 D.P. A ton et al. (OPAL Collab.)ACTON 92H PL B288 373 P.D. A ton et al. (OPAL Collab.)AKERIB 92 PRL 69 3610 D.S. Akerib et al. (CLEO Collab.)Also PRL 71 3395 (erratum) D.S. Akerib et al. (CLEO Collab.)ALBRECHT 92D ZPHY C53 367 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 92K ZPHY C55 179 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 92M PL B292 221 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 92Q ZPHY C56 339 H. Albre ht et al. (ARGUS Collab.)AMMAR 92 PR D45 3976 R. Ammar et al. (CLEO Collab.)ARTUSO 92 PRL 69 3278 M. Artuso et al. (CLEO Collab.)BAI 92 PRL 69 3021 J.Z. Bai et al. (BES Collab.)BATTLE 92 PL B291 488 M. Battle et al. (CLEO Collab.)BUSKULIC 92J PL B297 459 D. Buskuli et al. (ALEPH Collab.)DECAMP 92C ZPHY C54 211 D. De amp et al. (ALEPH Collab.)ADEVA 91F PL B265 451 B. Adeva et al. (L3 Collab.)ALBRECHT 91D PL B260 259 H. Albre ht et al. (ARGUS Collab.)ALEXANDER 91D PL B266 201 G. Alexander et al. (OPAL Collab.)ANTREASYAN 91 PL B259 216 D. Antreasyan et al. (Crystal Ball Collab.)GRIFOLS 91 PL B255 611 J.A. Grifols, A. Mendez (BARC)ABACHI 90 PR D41 1414 S. Aba hi et al. (HRS Collab.)ALBRECHT 90E PL B246 278 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 90I PL B250 164 H. Albre ht et al. (ARGUS Collab.)BEHREND 90 ZPHY C46 537 H.J. Behrend et al. (CELLO Collab.)BOWCOCK 90 PR D41 805 T.J.V. Bow o k et al. (CLEO Collab.)DELAGUILA 90 PL B252 116 F. del Aguila, M. Sher (BARC, WILL)GOLDBERG 90 PL B251 223 M. Goldberg et al. (CLEO Collab.)WU 90 PR D41 2339 D.Y. Wu et al. (Mark II Collab.)ABACHI 89B PR D40 902 S. Aba hi et al. (HRS Collab.)BEHREND 89B PL B222 163 H.J. Behrend et al. (CELLO Collab.)JANSSEN 89 PL B228 273 H. Janssen et al. (Crystal Ball Collab.)KLEINWORT 89 ZPHY C42 7 C. Kleinwort et al. (JADE Collab.)ADEVA 88 PR D38 2665 B. Adeva et al. (Mark-J Collab.)ALBRECHT 88B PL B202 149 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 88L ZPHY C41 1 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 88M ZPHY C41 405 H. Albre ht et al. (ARGUS Collab.)AMIDEI 88 PR D37 1750 D. Amidei et al. (Mark II Collab.)BEHREND 88 PL B200 226 H.J. Behrend et al. (CELLO Collab.)BRAUNSCH... 88C ZPHY C39 331 W. Brauns hweig et al. (TASSO Collab.)KEH 88 PL B212 123 S. Keh et al. (Crystal Ball Collab.)TSCHIRHART 88 PL B205 407 R. Ts hirhart et al. (HRS Collab.)ABACHI 87B PL B197 291 S. Aba hi et al. (HRS Collab.)ABACHI 87C PRL 59 2519 S. Aba hi et al. (HRS Collab.)ADLER 87B PRL 59 1527 J. Adler et al. (Mark III Collab.)AIHARA 87B PR D35 1553 H. Aihara et al. (TPC Collab.)AIHARA 87C PRL 59 751 H. Aihara et al. (TPC Collab.)ALBRECHT 87L PL B185 223 H. Albre ht et al. (ARGUS Collab.)ALBRECHT 87P PL B199 580 H. Albre ht et al. (ARGUS Collab.)BAND 87 PL B198 297 H.R. Band et al. (MAC Collab.)BAND 87B PRL 59 415 H.R. Band et al. (MAC Collab.)BARINGER 87 PRL 59 1993 P. Baringer et al. (CLEO Collab.)BEBEK 87C PR D36 690 C. Bebek et al. (CLEO Collab.)BURCHAT 87 PR D35 27 P.R. Bur hat et al. (Mark II Collab.)BYLSMA 87 PR D35 2269 B.G. Bylsma et al. (HRS Collab.)COFFMAN 87 PR D36 2185 D.M. Coman et al. (Mark III Collab.)DERRICK 87 PL B189 260 M. Derri k et al. (HRS Collab.)FORD 87 PR D35 408 W.T. Ford et al. (MAC Collab.)FORD 87B PR D36 1971 W.T. Ford et al. (MAC Collab.)GAN 87 PRL 59 411 K.K. Gan et al. (Mark II Collab.)GAN 87B PL B197 561 K.K. Gan et al. (Mark II Collab.)AIHARA 86E PRL 57 1836 H. Aihara et al. (TPC Collab.)BARTEL 86D PL B182 216 W. Bartel et al. (JADE Collab.)PDG 86 PL 170B 1 M. Aguilar-Benitez et al. (CERN, CIT+)RUCKSTUHL 86 PRL 56 2132 W. Ru kstuhl et al. (DELCO Collab.)SCHMIDKE 86 PRL 57 527 W.B. S hmidke et al. (Mark II Collab.)YELTON 86 PRL 56 812 J.M. Yelton et al. (Mark II Collab.)ALTHOFF 85 ZPHY C26 521 M. Altho et al. (TASSO Collab.)ASH 85B PRL 55 2118 W.W. Ash et al. (MAC Collab.)BALTRUSAIT... 85 PRL 55 1842 R.M. Baltrusaitis et al. (Mark III Collab.)BARTEL 85F PL 161B 188 W. Bartel et al. (JADE Collab.)BEHRENDS 85 PR D32 2468 S. Behrends et al. (CLEO Collab.)BELTRAMI 85 PRL 54 1775 I. Beltrami et al. (HRS Collab.)BERGER 85 ZPHY C28 1 C. Berger et al. (PLUTO Collab.)BURCHAT 85 PRL 54 2489 P.R. Bur hat et al. (Mark II Collab.)FERNANDEZ 85 PRL 54 1624 E. Fernandez et al. (MAC Collab.)MILLS 85 PRL 54 624 G.B. Mills et al. (DELCO Collab.)AIHARA 84C PR D30 2436 H. Aihara et al. (TPC Collab.)BEHREND 84 ZPHY C23 103 H.J. Behrend et al. (CELLO Collab.)MILLS 84 PRL 52 1944 G.B. Mills et al. (DELCO Collab.)BEHREND 83C PL 127B 270 H.J. Behrend et al. (CELLO Collab.)

SILVERMAN 83 PR D27 1196 D.J. Silverman, G.L. Shaw (UCI)BEHREND 82 PL 114B 282 H.J. Behrend et al. (CELLO Collab.)BLOCKER 82B PRL 48 1586 C.A. Blo ker et al. (Mark II Collab.)BLOCKER 82D PL 109B 119 C.A. Blo ker et al. (Mark II Collab.) JFELDMAN 82 PRL 48 66 G.J. Feldman et al. (Mark II Collab.)HAYES 82 PR D25 2869 K.G. Hayes et al. (Mark II Collab.)BERGER 81B PL 99B 489 C. Berger et al. (PLUTO Collab.)DORFAN 81 PRL 46 215 J.M. Dorfan et al. (Mark II Collab.)BRANDELIK 80 PL 92B 199 R. Brandelik et al. (TASSO Collab.)ZHOLENTZ 80 PL 96B 214 A.A. Zholents et al. (NOVO)Also SJNP 34 814 A.A. Zholents et al. (NOVO)Translated from YAF 34 1471.BACINO 79B PRL 42 749 W.J. Ba ino et al. (DELCO Collab.)KIRKBY 79 SLAC-PUB-2419 J. Kirkby (SLAC) JBatavia Lepton Photon Conferen e.BACINO 78B PRL 41 13 W.J. Ba ino et al. (DELCO Collab.) JAlso Tokyo Conf. 249 J. Kirz (STON)Also PL 96B 214 A.A. Zholents et al. (NOVO)BRANDELIK 78 PL 73B 109 R. Brandelik et al. (DASP Collab.) JFELDMAN 78 Tokyo Conf. 777 G.J. Feldman (SLAC) JJAROS 78 PRL 40 1120 J. Jaros et al. (LGW Collab.)PERL 75 PRL 35 1489 M.L. Perl et al. (LBL, SLAC)OTHER RELATED PAPERSOTHER RELATED PAPERSOTHER RELATED PAPERSOTHER RELATED PAPERSDAVIER 06 RMP 78 1043 M. Davier, A. Ho ker, Z. Zhang (LALO, PARIN+)RAHAL-CAL... 98 IJMP A13 695 G. Rahal-Callot (ETH)GENTILE 96 PRPL 274 287 S. Gentile, M. Pohl (ROMAI, ETH)WEINSTEIN 93 ARNPS 43 457 A.J. Weinstein, R. Stroynowski (CIT, SMU)PERL 92 RPP 55 653 M.L. Perl (SLAC)PICH 90 MPL A5 1995 A. Pi h (VALE)BARISH 88 PRPL 157 1 B.C. Barish, R. Stroynowski (CIT)GAN 88 IJMP A3 531 K.K. Gan, M.L. Perl (SLAC)HAYES 88 PR D38 3351 K.G. Hayes, M.L. Perl (SLAC)PERL 80 ARNPS 30 299 M.L. Perl (SLAC)Heavy Charged Lepton Sear hesCharged Heavy Lepton MASS LIMITSCharged Heavy Lepton MASS LIMITSCharged Heavy Lepton MASS LIMITSCharged Heavy Lepton MASS LIMITSSequential Charged Heavy Lepton (L±) MASS LIMITSSequential Charged Heavy Lepton (L±) MASS LIMITSSequential Charged Heavy Lepton (L±) MASS LIMITSSequential Charged Heavy Lepton (L±) MASS LIMITSThese experiments assumed that a fourth generation L± de ayed to a fourth generationνL (or L0) where νL was stable, or that L± de ays to a light νℓ via mixing.See the \Quark and Lepton Compositeness, Sear hes for" Listings for limits on radia-tively de aying ex ited leptons, i.e. ℓ∗ → ℓγ. See the \WIMPs and other Parti leSear hes" se tion for heavy harged parti le sear h limits in whi h the harged parti le ould be a lepton.VALUE (GeV) CL% DOCUMENT ID TECN COMMENT

>100.8>100.8>100.8>100.8 95 ACHARD 01B L3 De ay to νW>101.9 95 ACHARD 01B L3 mL − mL0 > 15 GeV• • • We do not use the following data for averages, ts, limits, et . • • •> 81.5 95 ACKERSTAFF 98C OPAL Assumed mL± − mL0 > 8.4GeV> 80.2 95 ACKERSTAFF 98C OPAL mL0 >mL± and L± → νW< 48 or > 61 95 1 ACCIARRI 96G L3> 63.9 95 ALEXANDER 96P OPAL De ay to massless ν's> 63.5 95 BUSKULIC 96S ALEP mL − mL0 > 7 GeV> 65 95 BUSKULIC 96S ALEP De ay to massless ν'snone 10225 2 AHMED 94 CNTR H1 Collab. at HERAnone 12.629.6 95 KIM 91B AMY Massless ν assumed> 44.3 95 AKRAWY 90G OPALnone 0.510 95 3 RILES 90 MRK2 For (mL0 -mL0)> 0.250.4GeV> 8 4 STOKER 89 MRK2 For (mL+ − mL0)= 0.4 GeV> 12 4 STOKER 89 MRK2 For mL0=0.9 GeVnone 18.427.6 95 5 ABE 88 VNS> 25.5 95 6 ADACHI 88B TOPZnone 1.522.0 95 BEHREND 88C CELL> 41 90 7 ALBAJAR 87B UA1> 22.5 95 8 ADEVA 85 MRKJ> 18.0 95 9 BARTEL 83 JADEnone 414.5 95 10 BERGER 81B PLUT> 15.5 95 11 BRANDELIK 81 TASS> 13. 12 AZIMOV 80> 16. 95 13 BARBER 80B CNTR> 0.490 14 ROTHE 69 RVUE1ACCIARRI 96G assumes LEP result that the asso iated neutral heavy lepton mass > 40GeV.2The AHMED 94 limits are from a sear h for neutral and harged sequential heavy leptonsat HERA via the de ay hannels L− → e γ, L− → νW−, L− → e Z ; and L0 → ν γ,L0 → e−W+, L− → νZ , where the W de ays to ℓνℓ, or to jets, and Z de ays to

ℓ+ ℓ− or jets.3RILES 90 limits were the result of a spe ial analysis of the data in the ase where the massdieren e mL− − mL0 was allowed to be quite small, where L0 denotes the neutrinointo whi h the sequential harged lepton de ays. With a slightly redu ed mL± range,the mass dieren e extends to about 4 GeV.4 STOKER 89 (Mark II at PEP) gives bounds on harged heavy lepton (L+) mass forthe generalized ase in whi h the orresponding neutral heavy lepton (L0) in the SU(2)doublet is not of negligible mass.5ABE 88 sear h for L+ and L− → hadrons looking for a oplanar jets. The bound isvalid for mν < 10 GeV.6ADACHI 88B sear h for hadroni de ays giving a oplanar events with large missing energy.E mee = 52 GeV.

757757757757See key on page 601 Lepton Parti le ListingsHeavy Charged Lepton Sear hes, Neutrino Properties7Assumes asso iated neutrino is approximately massless.8ADEVA 85 analyze one-isolated-muon data and sensitive to τ <10 nanose . AssumeB(lepton) = 0.30. E m = 4047 GeV.9BARTEL 83 limit is from PETRA e+ e− experiment with average E m = 34.2 GeV.10BERGER 81B is DESY DORIS and PETRA experiment. Looking for e+ e− → L+ L−.11BRANDELIK 81 is DESY-PETRA experiment. Looking for e+ e− → L+L−.12AZIMOV 80 estimated probabilities forM + N type events in e+ e− → L+ L− dedu ingsemi-hadroni de ay multipli ities of L from e+ e− annihilation data at E m = (2/3)mL.Obtained above limit omparing these with e+ e− data (BRANDELIK 80).13BARBER 80B looked for e+ e− → L+ L−, L → ν+L X with MARK-J at DESY-PETRA.14ROTHE 69 examines previous data on µ pair produ tion and π and K de ays.Stable Charged Heavy Lepton (L±) MASS LIMITSStable Charged Heavy Lepton (L±) MASS LIMITSStable Charged Heavy Lepton (L±) MASS LIMITSStable Charged Heavy Lepton (L±) MASS LIMITSVALUE (GeV) CL% DOCUMENT ID TECN>102.6>102.6>102.6>102.6 95 ACHARD 01B L3• • • We do not use the following data for averages, ts, limits, et . • • •> 28.2 95 15 ADACHI 90C TOPZnone 18.542.8 95 AKRAWY 90O OPAL> 26.5 95 DECAMP 90F ALEPnone mµ36.3 95 SODERSTROM90 MRK215ADACHI 90C put lower limits on the mass of stable harged parti les with ele tri hargeQ satisfying 2/3 < Q/e < 4/3 and with spin 0 or 1/2. We list here the spe ial ase fora stable harged heavy lepton.Charged Long-Lived Heavy Lepton MASS LIMITSCharged Long-Lived Heavy Lepton MASS LIMITSCharged Long-Lived Heavy Lepton MASS LIMITSCharged Long-Lived Heavy Lepton MASS LIMITSVALUE (GeV) CL% DOCUMENT ID TECN CHG COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •>574 95 CHATRCHYAN13AB CMS Leptons singlet model>102.0 95 ABBIENDI 03L OPAL pair produ ed in e+ e−> 0.1 16 ANSORGE 73B HBC − Long-livednone 0.554.5 17 BUSHNIN 73 CNTR − Long-livednone 0.20.92 18 BARNA 68 CNTR − Long-livednone 0.971.03 18 BARNA 68 CNTR − Long-lived16ANSORGE 73B looks for ele tron pair produ tion and ele tron-like Bremsstrahlung.17BUSHNIN 73 is SERPUKHOV 70 GeV p experiment. Masses assume mean life above7 × 10−10 and 3 × 10−8 respe tively. Cal ulated from ross se tion (see \ChargedQuasi-Stable Lepton Produ tion Dierential Cross Se tion" below) and 30 GeV muonpair produ tion data.18BARNA 68 is SLAC photoprodu tion experiment.Doubly-Charged Heavy Lepton MASS LIMITSDoubly-Charged Heavy Lepton MASS LIMITSDoubly-Charged Heavy Lepton MASS LIMITSDoubly-Charged Heavy Lepton MASS LIMITSVALUE (GeV) CL% DOCUMENT ID TECN CHG• • • We do not use the following data for averages, ts, limits, et . • • •none 19 GeV 90 19 CLARK 81 SPEC ++19CLARK 81 is FNAL experiment with 209 GeV muons. Bounds apply to µP whi h ouples with full weak strength to muon. See also se tion on \Doubly-Charged LeptonProdu tion Cross Se tion."Doubly-Charged Lepton Produ tion Cross Se tionDoubly-Charged Lepton Produ tion Cross Se tionDoubly-Charged Lepton Produ tion Cross Se tionDoubly-Charged Lepton Produ tion Cross Se tion(µN S attering)(µN S attering)(µN S attering)(µN S attering)VALUE ( m2) EVTS DOCUMENT ID TECN CHG• • • We do not use the following data for averages, ts, limits, et . • • •<6. × 10−38 0 20 CLARK 81 SPEC ++20CLARK 81 is FNAL experiment with 209 GeV muon. Looked for µ+nu leon → µ0P X,

µ0P → µ+µ− νµ and µ+ n → µ++P X, µ++P → 2µ+ νµ. Above limits are for σ×BRtaken from their mass-dependen e plot gure 2.REFERENCES FOR Heavy Charged Lepton Sear hesREFERENCES FOR Heavy Charged Lepton Sear hesREFERENCES FOR Heavy Charged Lepton Sear hesREFERENCES FOR Heavy Charged Lepton Sear hesCHATRCHYAN 13AB JHEP 1307 122 S. Chatr hyan et al. (CMS Collab.)ABBIENDI 03L PL B572 8 G. Abbiendi et al. (OPAL Collab.)ACHARD 01B PL B517 75 P. A hard et al. (L3 Collab.)ACKERSTAFF 98C EPJ C1 45 K. A kersta et al. (OPAL Collab.)ACCIARRI 96G PL B377 304 M. A iarri et al. (L3 Collab.)ALEXANDER 96P PL B385 433 G. Alexander et al. (OPAL Collab.)BUSKULIC 96S PL B384 439 D. Buskuli et al. (ALEPH Collab.)AHMED 94 PL B340 205 T. Ahmed et al. (H1 Collab.)KIM 91B IJMP A6 2583 G.N. Kim et al. (AMY Collab.)ADACHI 90C PL B244 352 I. Ada hi et al. (TOPAZ Collab.)AKRAWY 90G PL B240 250 M.Z. Akrawy et al. (OPAL Collab.)AKRAWY 90O PL B252 290 M.Z. Akrawy et al. (OPAL Collab.)DECAMP 90F PL B236 511 D. De amp et al. (ALEPH Collab.)RILES 90 PR D42 1 K. Riles et al. (Mark II Collab.)SODERSTROM 90 PRL 64 2980 E. Soderstrom et al. (Mark II Collab.)STOKER 89 PR D39 1811 D.P. Stoker et al. (Mark II Collab.)ABE 88 PRL 61 915 K. Abe et al. (VENUS Collab.)ADACHI 88B PR D37 1339 I. Ada hi et al. (TOPAZ Collab.)BEHREND 88C ZPHY C41 7 H.J. Behrend et al. (CELLO Collab.)ALBAJAR 87B PL B185 241 C. Albajar et al. (UA1 Collab.)ADEVA 85 PL 152B 439 B. Adeva et al. (Mark-J Collab.)Also PRPL 109 131 B. Adeva et al. (Mark-J Collab.)BARTEL 83 PL 123B 353 W. Bartel et al. (JADE Collab.)BERGER 81B PL 99B 489 C. Berger et al. (PLUTO Collab.)BRANDELIK 81 PL 99B 163 R. Brandelik et al. (TASSO Collab.)CLARK 81 PRL 46 299 A.R. Clark et al. (UCB, LBL, FNAL+)Also PR D25 2762 W.H. Smith et al. (LBL, FNAL, PRIN)AZIMOV 80 JETPL 32 664 Y.I. Azimov, V.A. Khoze (PNPI)Translated from ZETFP 32 677.BARBER 80B PRL 45 1904 D.P. Barber et al. (Mark-J Collab.)BRANDELIK 80 PL 92B 199 R. Brandelik et al. (TASSO Collab.)ANSORGE 73B PR D7 26 R.E. Ansorge et al. (CAVE)BUSHNIN 73 NP B58 476 Y.B. Bushnin et al. (SERP)Also PL 42B 136 S.V. Golovkin et al. (SERP)ROTHE 69 NP B10 241 K.W. Rothe, A.M. Wolsky (PENN)BARNA 68 PR 173 1391 A. Barna et al. (SLAC, STAN)

OTHER RELATED PAPERSOTHER RELATED PAPERSOTHER RELATED PAPERSOTHER RELATED PAPERSPERL 81 SLAC-PUB-2752 M.L. Perl (SLAC)Physi s in Collision Conferen e.Neutrino PropertiesINTRODUCTION TO THE NEUTRINOPROPERTIES LISTINGS

Revised August 2013 by P. Vogel (Caltech) and A. Piepke(University of Alabama).

The following Listings concern measurements of various

properties of neutrinos. Nearly all of the measurements, all

of which so far are limits, actually concern superpositions of

the mass eigenstates νi, which are in turn related to the weak

eigenstates νℓ, via the neutrino mixing matrix

|νℓ〉 =∑

i

Uℓi |νi〉 .

In the analogous case of quark mixing via the CKM matrix,

the smallness of the off-diagonal terms (small mixing angles)

permits a “dominant eigenstate” approximation. However, the

results of neutrino oscillation searches show that the mixing

matrix contains two large mixing angles and a third angle that

is not exceedingly small. We cannot, therefore, associate any

particular state |νi〉 with any particular lepton label e, µ or τ .

Nevertheless, note that in the standard labeling the |ν1〉 has

the largest |νe〉 component (∼ 2/3), |ν2〉 contains ∼ 1/3 of the

|νe〉 component and |ν3〉 contains only a small ∼ 2.5% |νe〉component.

Neutrinos are produced in weak decays with a definite lep-

ton flavor, and are typically detected by the charged current

weak interaction again associated with a specific lepton fla-

vor. Hence, the listings for the neutrino mass that follow are

separated into the three associated charged lepton categories.

Other properties (mean lifetime, magnetic moment, charge and

charge radius) are no longer separated this way. If needed, the

associated lepton flavor is reported in the footnotes.

Measured quantities (mass-squared, magnetic moments,

mean lifetimes, etc.) all depend upon the mixing parameters

|Uℓi|2, but to some extent also on experimental conditions (e.g.,

on energy resolution). Most of these observables, in particular

mass-squared, cannot distinguish between Dirac and Majorana

neutrinos, and are unaffected by CP phases.

Direct neutrino mass measurements are usually based on

the analysis of the kinematics of charged particles (leptons,

pions) emitted together with neutrinos (flavor states) in various

weak decays. The most sensitive neutrino mass measurement

to date, involving electron type antineutrinos, is based on

fitting the shape of the beta spectrum. The quantity 〈m2β〉 =∑

i |Uei|2m2νi

is determined or constrained, where the sum is

over all mass eigenvalues mνithat are too close together to be

resolved experimentally. If the energy resolution is better than

∆m2ij ≡ m2

νi− m2

νj, the corresponding heavier mνi

and mixing

758758758758LeptonParti le ListingsNeutrino Propertiesparameter could be determined by fitting the resulting spectral

anomaly (step or kink).

A limit on 〈m2β〉 implies an upper limit on the minimum

value m2min of m2

νi, independent of the mixing parameters Uei:

m2min ≤ 〈m2

β〉. However, if and when the value of 〈m2β〉 is

determined then its combination with the results derived from

neutrino oscillations that give us the values of the neutrino

mass-squared differences ∆m2ij ≡ m2

i − m2j and the mixing

parameters |Uei|2, the individual neutrino mass squares m2νj

=

〈m2β〉 −

∑i |Uei|2∆m2

ij can be determined.

So far solar, reactor, atmospheric and accelerator neutrino

oscillation experiments can be consistently described using

three active neutrino flavors, i.e. two mass splittings and three

mixing angles. However, several experiments with radioactive

sources, reactors, and accelerators imply the possible existence

of one or more non-interacting neutrino species that might be

observable since they couple weakly to the flavor neutrinos |νl〉.Combined three neutrino analyses determine the squared

mass differences and all three mixing angles to within reasonable

accuracy. For given |∆m2ij | a limit on 〈m2

β〉 from beta decay

defines an upper limit on the maximum value mmax of mνi:

m2max ≤ 〈m2

β〉 +∑

i<j |∆m2ij |. The analysis of the low energy

beta decay of tritium, combined with the oscillation results, thus

limits all active neutrino masses. Traditionally, experimental

neutrino mass limits obtained from pion decay π+ → µ+ + νµ

or the shape of the spectrum of decay products of the τ lepton

did not distinguish between flavor and mass eigenstates. These

results are reported as limits of the µ and τ based neutrino

mass. After the determination of the |∆m2ij |’s and the mixing

angles θij , the corresponding neutrino mass limits are no longer

competitive with those derived from low energy beta decays.

The spread of arrival times of the neutrinos from SN1987A,

coupled with the measured neutrino energies, provided a time-

of-flight limit on a quantity similar to 〈mβ〉 ≡√

〈m2β〉. This

statement, clothed in various degrees of sophistication, has

been the basis for a very large number of papers. The resulting

limits, however, are no longer comparable with the limits from

tritium beta decay.

Constraint on the sum of the neutrino masses can be

obtained from the analysis of the cosmic microwave background

anisotropy, combined with the galaxy redshift surveys and

other data. These limits are reported in a separate table ( Sum

of Neutrino Masses, mtot). Discussion concerning the model

dependence of this limit is continuing.

ν MASS (ele tron based)ν MASS (ele tron based)ν MASS (ele tron based)ν MASS (ele tron based)Those limits given below are for the square root of m2(e)νe ≡

∑i∣∣Uei

∣∣2m2νi . Limits that ome from the kinemati s of 3Hβ− ν de ay are thesquare roots of the limits for m2(e)

νe . Obtained from the measurementsreported in the Listings for \ν Mass Squared," below.VALUE (eV) CL% DOCUMENT ID TECN COMMENT< 2 OUR EVALUATION< 2 OUR EVALUATION< 2 OUR EVALUATION< 2 OUR EVALUATION< 2.05< 2.05< 2.05< 2.05 95 1 ASEEV 11 SPEC 3H β de ay< 2.3 95 2 KRAUS 05 SPEC 3H β de ay

• • • We do not use the following data for averages, ts, limits, et . • • •

< 5.8 95 3 PAGLIAROLI 10 ASTR SN1987A<21.7 90 4 ARNABOLDI 03A BOLO 187Re β-de ay< 5.7 95 5 LOREDO 02 ASTR SN1987A< 2.5 95 6 LOBASHEV 99 SPEC 3H β de ay< 2.8 95 7 WEINHEIMER 99 SPEC 3H β de ay< 4.35 95 8 BELESEV 95 SPEC 3H β de ay<12.4 95 9 CHING 95 SPEC 3Hβ de ay<92 95 10 HIDDEMANN 95 SPEC 3H β de ay15 +32

−15 HIDDEMANN 95 SPEC 3H β de ay<19.6 95 KERNAN 95 ASTR SN 1987A< 7.0 95 11 STOEFFL 95 SPEC 3H β de ay< 7.2 95 12 WEINHEIMER 93 SPEC 3H β de ay<11.7 95 13 HOLZSCHUH 92B SPEC 3H β de ay<13.1 95 14 KAWAKAMI 91 SPEC 3H β de ay< 9.3 95 15 ROBERTSON 91 SPEC 3H β de ay<14 95 AVIGNONE 90 ASTR SN 1987A<16 SPERGEL 88 ASTR SN 1987A17 to 40 16 BORIS 87 SPEC 3Hβ de ay1ASEEV 11 report the analysis of the entire beta endpoint data, taken with the Troitskintegrating ele trostati spe trometer between 1997 and 2002 (some of the earlier runswere reje ted), using a windowless gaseous tritium sour e. The tted value of mν , basedon the method of Feldman and Cousins, is obtained from the upper limit of the t form2

ν . Previous analysis problems were resolved by areful monitoring of the tritium gas olumn density. Supersedes LOBASHEV 99 and BELESEV 95.2KRAUS 05 is a ontinuation of the work reported in WEINHEIMER 99. This result rep-resents the nal analysis of data taken from 1997 to 2001. Various sour es of systemati un ertainties have been identied and quantied. The ba kground has been redu ed ompared to the initial running period. A spe tral anomaly at the endpoint, reported inLOBASHEV 99, was not observed.3PAGLIAROLI 10 is riti al of the likelihood method used by LOREDO 02.4ARNABOLDI 03A etal . report kinemati al neutrino mass limit using β-de ay of 187Re.Bolometri AgReO4 mi ro- alorimeters are used. Mass bound is substantially weakerthan those derived from tritium β-de ays but has dierent systemati un ertainties.5 LOREDO 02 updates LOREDO 89.6 LOBASHEV 99 report a new measurement whi h ontinues the work reported in BELE-SEV 95. This limit depends on phenomenologi al t parameters used to derive their bestt to m2ν , making unambiguous interpretation diÆ ult. See the footnote under \ν MassSquared."7WEINHEIMER 99 presents two analyses whi h ex lude the spe tral anomaly and resultin an a eptable m2

ν. We report the most onservative limit, but the other is nearly thesame. See the footnote under \ν Mass Squared."8BELESEV 95 (Mos ow) use an integral ele trostati spe trometer with adiabati mag-neti ollimation and a gaseous tritium sour es. A t to a normal Kurie plot above1830018350 eV (to avoid a low-energy anomaly) plus a mono hromati line 715 eVbelow the endpoint yields m2

ν= −4.1 ± 10.9 eV2, leading to this Bayesian limit.9CHING 95 quotes results previously given by SUN 93; no experimental details are given.A possible explanation for onsistently negative values of m2

νis given.10HIDDEMANN 95 (Muni h) experiment uses atomi tritium embedded in a metal-dioxidelatti e. Bayesian limit al ulated from the weighted mean m2

ν = 221 ± 4244 eV2 fromthe two runs listed below.11 STOEFFL 95 (LLNL) result is the Bayesian limit obtained from the m2ν errors givenbelow but with m2

νset equal to 0. The anomalous endpoint a umulation leads to avalue of m2

ν whi h is negative by more than 5 standard deviations.12WEINHEIMER 93 (Mainz) is a measurement of the endpoint of the tritium β spe trumusing an ele trostati spe trometer with a magneti guiding eld. The sour e is mole ulartritium frozen onto an aluminum substrate.13HOLZSCHUH 92B (Zuri h) result is obtained from the measurementm2ν =−24±48±61(1σ errors), in eV2, using the PDG pres ription for onversion to a limit in mν .14KAWAKAMI 91 (Tokyo) experiment uses tritium-labeled ara hidi a id. This result is theBayesian limit obtained from the m2

ν limit with the errors ombined in quadrature. Thiswas also done in ROBERTSON 91, although the authors report a dierent pro edure.15ROBERTSON 91 (LANL) experiment uses gaseous mole ular tritium. The result is instrong disagreement with the earlier laims by the ITEP group [LUBIMOV 80, BORIS 87(+ BORIS 88 erratum) that mν lies between 17 and 40 eV. However, the probability ofa positive m2 is only 3% if statisti al and systemati error are ombined in quadrature.16 See also omment in BORIS 87B and erratum in BORIS 88.ν MASS SQUARED (ele tron based)ν MASS SQUARED (ele tron based)ν MASS SQUARED (ele tron based)ν MASS SQUARED (ele tron based)Given troubling systemati s whi h result in improbably negative estima-tors of m2(e)

νe ≡∑

i∣∣Uei

∣∣2 m2νi , in many experiments, we use onlyKRAUS 05 and LOBASHEV 99 for our average.VALUE (eV2) CL% DOCUMENT ID TECN COMMENT

− 0.6 ± 1.9 OUR AVERAGE− 0.6 ± 1.9 OUR AVERAGE− 0.6 ± 1.9 OUR AVERAGE− 0.6 ± 1.9 OUR AVERAGE− 0.67± 2.53 1 ASEEV 11 SPEC 3H β de ay− 0.6 ± 2.2 ± 2.1 2 KRAUS 05 SPEC 3H β de ay

759759759759See key on page 601 Lepton Parti le ListingsNeutrino Properties• • • We do not use the following data for averages, ts, limits, et . • • •

− 1.9 ± 3.4 ± 2.2 3 LOBASHEV 99 SPEC 3H β de ay− 3.7 ± 5.3 ± 2.1 4 WEINHEIMER 99 SPEC 3H β de ay− 22 ± 4.8 5 BELESEV 95 SPEC 3H β de ay129 ±6010 6 HIDDEMANN 95 SPEC 3H β de ay313 ±5994 6 HIDDEMANN 95 SPEC 3H β de ay−130 ± 20 ±15 95 7 STOEFFL 95 SPEC 3H β de ay− 31 ± 75 ±48 8 SUN 93 SPEC 3Hβ de ay− 39 ± 34 ±15 9 WEINHEIMER 93 SPEC 3H β de ay− 24 ± 48 ±61 10 HOLZSCHUH 92B SPEC 3H β de ay− 65 ± 85 ±65 11 KAWAKAMI 91 SPEC 3H β de ay−147 ± 68 ±41 12 ROBERTSON 91 SPEC 3H β de ay1ASEEV 11 report the analysis of the entire beta endpoint data, taken with the Troitsk in-tegrating ele trostati spe trometer between 1997 and 2002, using a windowless gaseoustritium sour e. The analysis does not use the two additional t parameters (see LOBA-SHEV 99) for a step-like stru ture near the endpoint. Using only the runs where thetritium gas olumn density was arefully monitored the need for su h parameters waseliminated. Supersedes LOBASHEV 99 and BELESEV 95.2KRAUS 05 is a ontinuation of the work reported in WEINHEIMER 99. This resultrepresents the nal analysis of data taken from 1997 to 2001. Problems with signif-i antly negative squared neutrino masses, observed in some earlier experiments, havebeen resolved in this work.3 LOBASHEV 99 report a new measurement whi h ontinues the work reported in BELE-SEV 95. The data were orre ted for ele tron trapping ee ts in the sour e, eliminatingthe dependen e of the tted neutrino mass on the t interval. The analysis assuminga pure beta spe trum yields signi antly negative tted m2

ν ≈ −(2010) eV2. Thisproblem is attributed to a dis rete spe tral anomaly of about 6 × 10−11 intensity witha time-dependent energy of 515 eV below the endpoint. The data analysis a ountsfor this anomaly by introdu ing two extra phenomenologi al t parameters resulting ina best t of m2ν=−1.9 ± 3.4 ± 2.2 eV2 whi h is used to derive a neutrino mass limit.However, the introdu tion of phenomenologi al t parameters whi h are orrelated withthe derived m2

ν limit makes unambiguous interpretation of this result diÆ ult.4WEINHEIMER 99 is a ontinuation of the work reported in WEINHEIMER 93 . Usinga lower temperature of the frozen tritium sour e eliminated the dewetting of the T2lm, whi h introdu ed a dependen e of the tted neutrino mass on the t interval inthe earlier work. An indi ation for a spe tral anomaly reported in LOBASHEV 99 hasbeen seen, but its time dependen e does not agree with LOBASHEV 99. Two analyses,whi h ex lude the spe tral anomaly either by hoi e of the analysis interval or by using aparti ular data set whi h does not exhibit the anomaly, result in a eptable m2νts andare used to derive the neutrino mass limit published by the authors. We list the most onservative of the two.5BELESEV 95 (Mos ow) use an integral ele trostati spe trometer with adiabati mag-neti ollimation and a gaseous tritium sour es. This value omes from a t to a normalKurie plot above 1830018350 eV (to avoid a low-energy anomaly), in luding the ee tsof an apparent peak 715 eV below the endpoint.6HIDDEMANN 95 (Muni h) experiment uses atomi tritium embedded in a metal-dioxidelatti e. They quote measurements from two data sets.7 STOEFFL 95 (LLNL) uses a gaseous sour e of mole ular tritium. An anomalous pileupof events at the endpoint leads to the negative value for m2

ν. The authors a knowledgethat \the negative value for the best t of m2

ν has no physi al meaning" and dis usspossible explanations for this ee t.8 SUN 93 uses a tritiated hydro arbon sour e. See also CHING 95.9WEINHEIMER 93 (Mainz) is a measurement of the endpoint of the tritium β spe trumusing an ele trostati spe trometer with a magneti guiding eld. The sour e is mole ulartritium frozen onto an aluminum substrate.10HOLZSCHUH 92B (Zuri h) sour e is a monolayer of tritiated hydro arbon.11KAWAKAMI 91 (Tokyo) experiment uses tritium-labeled ara hidi a id.12ROBERTSON 91 (LANL) experiment uses gaseous mole ular tritium. The result is instrong disagreement with the earlier laims by the ITEP group [LUBIMOV 80, BORIS 87(+ BORIS 88 erratum) that mν lies between 17 and 40 eV. However, the probability ofa positive m2ν is only 3% if statisti al and systemati error are ombined in quadrature.

ν MASS (ele tron based)ν MASS (ele tron based)ν MASS (ele tron based)ν MASS (ele tron based)These are measurement of mν (in ontrast to mν , given above). Themasses an be dierent for a Dira neutrino in the absen e of CPT in-varian e. The possible distin tion between ν and ν properties is usuallyignored elsewhere in these Listings.VALUE (eV) CL% DOCUMENT ID TECN COMMENT<460 68 YASUMI 94 CNTR 163Ho de ay<225 95 SPRINGER 87 CNTR 163Ho de ay

ν MASS (muon based)ν MASS (muon based)ν MASS (muon based)ν MASS (muon based)Limits given below are for the square root of m2(e)νµ

≡∑

i∣∣Uµi

∣∣2 m2νi .In some of the COSM papers listed below, the authors did not distinguishbetween weak and mass eigenstates.OUR EVALUATION is based on OUR AVERAGE for the π± mass and theASSAMAGAN 96 value for the muon momentum for the π+ de ay at rest.The limit is al ulated using the unied lassi al analysis of FELDMAN 98for a Gaussian distribution near a physi al boundary. WARNING: sin e

m2(e)νµ

is al ulated from the dieren es of large numbers, it and the orresponding limits are extraordinarily sensitive to small hanges in thepion mass, the de ay muon momentum, and their errors. For example,the limits obtained using JECKELMANN 94, LENZ 98, and the weightedaverages are 0.15, 0.29, and 0.19 MeV, respe tively.VALUE (MeV) CL% DOCUMENT ID TECN COMMENT<0.19 (CL = 90%) OUR EVALUATION<0.19 (CL = 90%) OUR EVALUATION<0.19 (CL = 90%) OUR EVALUATION<0.19 (CL = 90%) OUR EVALUATION<0.17 90 1 ASSAMAGAN 96 SPEC m2

ν= −0.016 ± 0.023


<0.15 2 DOLGOV 95 COSM Nu leosynthesis<0.48 3 ENQVIST 93 COSM Nu leosynthesis<0.3 4 FULLER 91 COSM Nu leosynthesis<0.42 4 LAM 91 COSM Nu leosynthesis<0.50 90 5 ANDERHUB 82 SPEC m2

ν= −0.14 ± 0.20

<0.65 90 CLARK 74 ASPK Kµ3 de ay1ASSAMAGAN 96 measurement of pµ from π+ → µ+ ν at rest ombined with JECK-ELMANN 94 Solution B pion mass yields m2ν = −0.016 ± 0.023 with orrespondingBayesian limit listed above. If Solution A is used, m2

ν= −0.143 ± 0.024 MeV2. Re-pla es ASSAMAGAN 94.2DOLGOV 95 removes earlier assumptions (DOLGOV 93) about thermal equilibrium belowTQCD for wrong-heli ity Dira neutrinos (ENQVIST 93, FULLER 91) to set more strin-gent limits.3 ENQVIST 93 bases limit on the fa t that thermalized wrong-heli ity Dira neutrinoswould speed up expansion of early universe, thus redu ing the primordial abundan e.FULLER 91 exploits the same me hanism but in the older al ulation obtains a largerprodu tion rate for these states, and hen e a lower limit. Neutrino lifetime assumed toex eed nu leosynthesis time, ∼ 1 s.4Assumes neutrino lifetime >1 s. For Dira neutrinos only. See also ENQVIST 93.5ANDERHUB 82 kinemati s is insensitive to the pion mass.

ν MASS (tau based)ν MASS (tau based)ν MASS (tau based)ν MASS (tau based)The limits given below are the square roots of limits for m2(e)ντ

≡∑

i∣∣Uτi

∣∣2 m2νi .In some of the ASTR and COSM papers listed below, the authors did notdistinguish between weak and mass eigenstates.VALUE (MeV) CL% EVTS DOCUMENT ID TECN COMMENT

< 18.2< 18.2< 18.2< 18.2 95 1 BARATE 98F ALEP 19911995 LEP runs• • • We do not use the following data for averages, ts, limits, et . • • •

< 28 95 2 ATHANAS 00 CLEO Eee m= 10.6 GeV< 27.6 95 3 ACKERSTAFF 98T OPAL 19901995 LEP runs< 30 95 473 4 AMMAR 98 CLEO Eee m = 10.6 GeV< 60 95 5 ANASTASSOV 97 CLEO Eee m= 10.6 GeV< 0.37 or >22 6 FIELDS 97 COSM Nu leosynthesis< 68 95 7 SWAIN 97 THEO mτ , ττ , τ partialwidths< 29.9 95 8 ALEXANDER 96M OPAL 19901994 LEP runs<149 9 BOTTINO 96 THEO π, µ, τ leptoni de ays<1 or >25 10 HANNESTAD 96C COSM Nu leosynthesis< 71 95 11 SOBIE 96 THEO mτ , ττ , B(τ− →e− νe ντ )< 24 95 25 12 BUSKULIC 95H ALEP 19911993 LEP runs< 0.19 13 DOLGOV 95 COSM Nu leosynthesis< 3 14 SIGL 95 ASTR SN 1987A< 0.4 or > 30 15 DODELSON 94 COSM Nu leosynthesis< 0.1 or > 50 16 KAWASAKI 94 COSM Nu leosynthesis155225 17 PERES 94 THEO π,K ,µ,τ weak de ays< 32.6 95 113 18 CINABRO 93 CLEO Eee m ≈ 10.6 GeV< 0.3 or > 35 19 DOLGOV 93 COSM Nu leosynthesis< 0.74 20 ENQVIST 93 COSM Nu leosynthesis< 31 95 19 21 ALBRECHT 92M ARG Eee m= 9.410.6 GeV< 0.3 22 FULLER 91 COSM Nu leosynthesis< 0.5 or > 25 23 KOLB 91 COSM Nu leosynthesis< 0.42 22 LAM 91 COSM Nu leosynthesis1BARATE 98F result based on kinemati s of 2939 τ− → 2π−π+ ντ and 52 τ− →3π− 2π+(π0)ντ de ays. If possible 2.5% ex ited a1 de ay is in luded in 3-prong sampleanalysis, limit in reases to 19.2 MeV.2ATHANAS 00 bound omes from analysis of τ− → π−π+π−π0 ντ de ays.3ACKERSTAFF 98T use τ → 5π± ντ de ays to obtain a limit of 43.2 MeV (95%CL).They ombine this with ALEXANDER 96M value using τ → 3h± ντ de ays to obtainquoted limit.4AMMAR 98 limit omes from analysis of τ− → 3π− 2π+ ντ and τ− → 2π−π+2π0 ντde ay modes.5ANASTASSOV 97 derive limit by omparing their mτ measurement (whi h depends onmντ

) to BAI 96 mτ threshold measurement.

760760760760Lepton Parti le ListingsNeutrino Properties6FIELDS 97 limit for a Dira neutrino. For a Majorana neutrino the mass region < 0.93or >31 MeV is ex luded. These bounds assume Nν <4 from nu leosynthesis; a widerex luded region o urs with a smaller Nν upper limit.7 SWAIN 97 derive their limit from the Standard Model relationships between the tau mass,lifetime, bran hing fra tions for τ− → e− νe ντ , τ− → µ− νµντ , τ− → π− ντ , andτ− → K− ντ , and the muon mass and lifetime by assuming lepton universality and usingworld average values. Limit is redu ed to 48 MeV when the CLEO τ mass measurement(BALEST 93) is in luded; see CLEO's more re ent mντ

limit (ANASTASSOV 97).Consideration of mixing with a fourth generation heavy neutrino yields sin2θL < 0.016(95%CL).8ALEXANDER 96M bound omes from analyses of τ− → 3π− 2π+ ντ and τ− →h− h− h+ ντ de ays.9BOTTINO 96 assumes three generations of neutrinos with mixing, nds onsisten y withmassless neutrinos with no mixing based on 1995 data for masses, lifetimes, and leptoni partial widths.10HANNESTAD 96C limit is on the mass of a Majorana neutrino. This bound assumesNν < 4 from nu leosynthesis. A wider ex luded region o urs with a smaller Nν up-per limit. This paper is the orre ted version of HANNESTAD 96; see the erratum:HANNESTAD 96B.11 SOBIE 96 derive their limit from the Standard Model relationship between the tau mass,lifetime, and leptoni bran hing fra tion, and the muon mass and lifetime, by assuminglepton universality and using world average values.12BUSKULIC 95H bound omes from a two-dimensional t of the visible energy and in-variant mass distribution of τ → 5π (π0 )ντ de ays. Repla ed by BARATE 98F.13DOLGOV 95 removes earlier assumptions (DOLGOV 93) about thermal equilibrium belowTQCD for wrong-heli ity Dira neutrinos (ENQVIST 93, FULLER 91) to set more strin-gent limits. DOLGOV 96 argues that a possible window near 20 MeV is ex luded.14 SIGL 95 ex lude massive Dira or Majorana neutrinos with lifetimes between 10−3 and108 se onds if the de ay produ ts are predominantly γ or e+ e−.15DODELSON 94 al ulate onstraints on ντ mass and lifetime from nu leosynthesis for4 generi de ay modes. Limits depend strongly on de ay mode. Quoted limit is valid forall de ay modes of Majorana neutrinos with lifetime greater than about 300 s. For Dira neutrinos limits hange to < 0.3 or > 33.16KAWASAKI 94 ex luded region is for Majorana neutrino with lifetime >1000 s. Otherlimits are given as a fun tion of ντ lifetime for de ays of the type ντ → νµφ where φis a Nambu-Goldstone boson.17PERES 94 used PDG 92 values for parameters to obtain a value onsistent with mixing.Reexamination by BOTTINO 96 whi h in luded radiative orre tions and 1995 PDGparameters resulted in two allowed regions, m3 < 70 MeV and 140 MeV m3 < 149MeV.18CINABRO 93 bound omes from analysis of τ− → 3π− 2π+ ντ and τ− →2π−π+2π0 ντ de ay modes.19DOLGOV 93 assumes neutrino lifetime >100 s. For Majorana neutrinos, the low masslimit is 0.5 MeV. KAWANO 92 points out that these bounds an be over ome for a Dira neutrino if it possesses a magneti moment. See also DOLGOV 96.20ENQVIST 93 bases limit on the fa t that thermalized wrong-heli ity Dira neutrinoswould speed up expansion of early universe, thus redu ing the primordial abundan e.FULLER 91 exploits the same me hanism but in the older al ulation obtains a largerprodu tion rate for these states, and hen e a lower limit. Neutrino lifetime assumed toex eed nu leosynthesis time, ∼ 1 s.21ALBRECHT 92M reports measurement of a slightly lower τ mass, whi h has the ee tof redu ing the ντ mass reported in ALBRECHT 88B. Bound is from analysis of τ− →3π− 2π+ ντ mode.22Assumes neutrino lifetime >1 s. For Dira neutrinos. See also ENQVIST 93.23KOLB 91 ex lusion region is for Dira neutrino with lifetime >1 s; other limits are given.SUM OF NEUTRINO MASSES

Revised January 2016 by K.A. Olive (University of Minnesota).

The limits on low mass (mν<∼ 1 MeV) neutrinos apply to

mtot given by

mtot =∑

ν

(gν/2)mν ,

where gν is the number of spin degrees of freedom for ν

plus ν: gν = 4 for neutrinos with Dirac masses; gν = 2 for

Majorana neutrinos. Stable neutrinos in this mass range make

a contribution to the total energy density of the Universe which

is given by

ρν = mtotnν = mtot(3/11)nγ ,

where the factor 3/11 is the ratio of (light) neutrinos to photons.

Writing Ων = ρν/ρc, where ρc is the critical energy density of

the Universe, and using nγ = 412 cm−3, we have

Ωνh2 = mtot/(94 eV) .

While an upper limit to the matter density of Ωmh2 < 0.12

would constrain mtot < 11 eV, much stronger constraints are

obtained from a combination of observations of the CMB, the

amplitude of density fluctuations on smaller scales from the

clustering of galaxies and the Lyman-α forest, baryon acoustic

oscillations, and new Hubble parameter data. These combine

to give an upper limit of around 0.2 eV, and may, in the near

future, be able to provide a lower bound on the sum of the

neutrino masses.SUM OF THE NEUTRINO MASSES, mtotSUM OF THE NEUTRINO MASSES, mtotSUM OF THE NEUTRINO MASSES, mtotSUM OF THE NEUTRINO MASSES, mtot(Dened in the above note), of ee tively stable neutrinos (i.e., thosewith mean lives greater than or equal to the age of the universe). Thesepapers assumed Dira neutrinos. When ne essary, we have generalizedthe results reported so they apply to mtot. For other limits, see SZA-LAY 76, VYSOTSKY 77, BERNSTEIN 81, FREESE 84, SCHRAMM 84,and COWSIK 85.VALUE (eV) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

< 0.15 95 1 PALANQUE-... 15 COSM SDSS/BOSS< 0.12 95 2 PALANQUE-... 15A COSM SDSS/BOSS< 0.23 95 3 ADE 14 COSM Plan k0.320±0.081 4 BATTYE 14 COSM0.35 ±0.10 5 BEUTLER 14 COSM BOSS0.22 +0.09

−0.10 6 COSTANZI 14 COSM< 0.22 95 7 GIUSARMA 14 COSM0.32 ±0.11 8 HOU 14 COSM< 0.26 95 9 LEISTEDT 14 COSM< 0.18 95 10 RIEMER-SOR...14 COSM< 0.24 68 11 MORESCO 12 COSM< 0.29 95 12 XIA 12 COSM< 0.81 95 13 SAITO 11 COSM SDSS< 0.44 95 14 HANNESTAD 10 COSM< 0.6 95 15 SEKIGUCHI 10 COSM< 0.28 95 16 THOMAS 10 COSM< 1.1 17 ICHIKI 09 COSM< 1.3 95 18 KOMATSU 09 COSM WMAP< 1.2 19 TERENO 09 COSM< 0.33 20 VIKHLININ 09 COSM< 0.28 21 BERNARDIS 08 COSM< 0.172.3 22 FOGLI 07 COSM< 0.42 95 23 KRISTIANSEN 07 COSM< 0.632.2 24 ZUNCKEL 07 COSM< 0.24 95 25 CIRELLI 06 COSM< 0.62 95 26 HANNESTAD 06 COSM< 1.2 27 SANCHEZ 06 COSM< 0.17 95 25 SELJAK 06 COSM< 2.0 95 28 ICHIKAWA 05 COSM< 0.75 29 BARGER 04 COSM< 1.0 30 CROTTY 04 COSM< 0.7 31 SPERGEL 03 COSM WMAP< 0.9 32 LEWIS 02 COSM< 4.2 33 WANG 02 COSM CMB< 2.7 34 FUKUGITA 00 COSM< 5.5 35 CROFT 99 ASTR Ly α power spe <180 SZALAY 74 COSM<132 COWSIK 72 COSM<280 MARX 72 COSM<400 GERSHTEIN 66 COSM1Constrains the total mass of neutrinos using the Lyman α forest power spe trum ob-tained by BOSS. The analysis in ludes CMB data from Plan k, WMAP, ACT, andSPT. Limit improves to 0.14 when BAO data are in luded. Superseded by PALANQUE-DELABROUILLE 15A.2 Constrains the total mass of neutrinos using the Lyman-α forest power spe trum obtainedby BOSS. The analysis in ludes CMB data from Plank, ACT, and SPT.Limit is un hangedwhen BAO data are in luded. Supersedes PALANQUE-DELABROUILLE 15.3Constrains the total mass of neutrinos from Plan k CMB data along with WMAP polar-ization, high L, and BAO data.4 Finite neutrino mass t to resolve dis repan y between CMB and lensing measurements.5 Fit to the total mass of neutrinos from BOSS data along with WMAP CMB data anddata from other BAO onstraints and weak lensing.6 Fit to the total mass of neutrinos from Plan k CMB data along with BAO.7Constrains the total mass of neutrinos from Plan k CMB data ombined with baryona ousti os illation data from BOSS and HST data on the Hubble parameter.8 Fit based on the SPT-SZ survey ombined with CMB, BAO, and H0 data.9Constraints the total mass of neutrinos (marginalizing over the ee tive number of neu-trino spe ies) from CMB, CMB lensing, BAO, and galaxy lustering data.

761761761761See key on page 601 LeptonParti le ListingsNeutrino Properties10Constrains the total mass of neutrinos from Plan k CMB data ombined with baryona ousti os illation data from BOSS, 6dFGS, SDSS, WiggleZ data on the galaxy powerspe trum, and HST data on the Hubble parameter. The limit is in reased to 0.25 eV ifa lower bound to the sum of neutrino masses of 0.04 eV is assumed.11Constrains the total mass of neutrinos from observational Hubble parameter data withseven-year WMAP data and the most re ent estimate of H0.12Constrains the total mass of neutrinos from the CFHTLS ombined with seven-yearWMAP data and a prior on the Hubble parameter. Limit is relaxed to 0.41 eV whensmall s ales ae ted by non-linearities are removed.13Constrains the total mass of neutrinos from the Sloan Digital Sky Survey and the ve-yearWMAP data.14Constrains the total mass of neutrinos from the 7-year WMAP data in luding SDSSand HST data. Limit relaxes to 1.19 eV when CMB data is used alone. SupersedesHANNESTAD 06.15Constrains the total mass of neutrinos from a ombination of CMB data, a re ent mea-surement of H0 (SHOES), and baryon a ousti os illation data from SDSS.16Constrains the total mass of neutrinos from SDSS MegaZ LRG DR7 galaxy lusteringdata ombined with CMB, HST, supernovae and baryon a ousti os illation data. Limitrelaxes to 0.47 eV when the equation of state parameter, w 6= 1.17Constrains the total mass of neutrinos from weak lensing measurements when ombinedwith CMB. Limit improves to 0.54 eV when supernovae and baryon a ousti os illationobservations are in luded. Assumes CDM model.18Constrains the total mass of neutrinos from ve-year WMAP data. Limit improves to 0.67eV when supernovae and baryon a ousti os illation observations are in luded. Limitsquoted assume the CDM model. Supersedes SPERGEL 07.19Constrains the total mass of neutrinos from weak lensing measurements when ombinedwith CMB. Limit improves to 0.03 < mν < 0.54 eV when supernovae and baryona ousti os illation observations are in luded. The slight preferen e for massive neutrinosat the two-sigma level disappears when systemati errors are taken into a ount. AssumesCDM model.20Constrains the total mass of neutrinos from re ent Chandra X-ray observations of galaxy lusters when ombined with CMB, supernovae, and baryon a ousti os illation measure-ments. Assumes at universe and onstant dark-energy equation of state, w.21Constraints the total mass of neutrinos from re ent CMB and SOSS LRG power spe trumdata along with bias mass relations from SDSS, DEEP2, and Lyman-Break Galaxies. Itassumes CDM model. Limit degrades to 0.59 eV in a more general wCDM model.22Constrains the total mass of neutrinos from neutrino os illation experiments and osmo-logi al data. The most onservative limit uses only WMAP three-year data, while themost stringent limit in ludes CMB, large-s ale stru ture, supernova, and Lyman-alphadata.23Constrains the total mass of neutrinos from re ent CMB, large s ale stru ture, SN1a, andbaryon a ousti os illation data. The limit relaxes to 1.75 when WMAP data alone is usedwith no prior. Paper shows results with several ombinations of data sets. SupersedesKRISTIANSEN 06.24Constrains the total mass of neutrinos from the CMB and the large s ale stru ture data.The most onservative limit is obtained when generi initial onditions are allowed.25Constrains the total mass of neutrinos from re ent CMB, large s ale stru ture, Lyman-alpha forest, and SN1a data.26Constrains the total mass of neutrinos from re ent CMB and large s ale stru ture data.See also GOOBAR 06. Superseded by HANNESTAD 10.27Constrains the total mass of neutrinos from the CMB and the nal 2dF Galaxy RedshiftSurvey.28Constrains the total mass of neutrinos from the CMB experiments alone, assuming CDMUniverse. FUKUGITA 06 show that this result is un hanged by the 3-year WMAP data.29Constrains the total mass of neutrinos from the power spe trum of u tuations derivedfrom the Sloan Digital Sky Survey and the 2dF galaxy redshift survey, WMAP and 27other CMB experiments and measurements by the HST Key proje t.30Constrains the total mass of neutrinos from the power spe trum of u tuations derivedfrom the Sloan Digital Sky Survey, the 2dF galaxy redshift survey, WMAP and ACBAR.The limit is strengthened to 0.6 eV when measurements by the HST Key proje t andsupernovae data are in luded.31Constrains the fra tional ontribution of neutrinos to the total matter density in theUniverse from WMAP data ombined with other CMB measurements, the 2dfGRS data,and Lyman α data. The limit does not noti eably hange if the Lyman α data are notused.32 LEWIS 02 onstrains the total mass of neutrinos from the power spe trum of u tuationsderived from the CMB, HST Key proje t, 2dF galaxy redshift survey, supernovae type Ia,and BBN.33WANG 02 onstrains the total mass of neutrinos from the power spe trum of u tuationsderived from the CMB and other osmologi al data sets su h as galaxy lustering andthe Lyman α forest.34 FUKUGITA 00 is a limit on neutrino masses from stru ture formation. The onstraint isbased on the lustering s ale σ8 and the COBE normalization and leads to a onservativelimit of 0.9 eV assuming 3 nearly degenerate neutrinos. The quoted limit is on the sumof the light neutrino masses.35CROFT 99 result based on the power spe trum of the Ly α forest. If matter < 0.5,the limit is improved to mν < 2.4 (matter/0.171) eV.Limits on MASSES of Light Stable Right-Handed νLimits on MASSES of Light Stable Right-Handed νLimits on MASSES of Light Stable Right-Handed νLimits on MASSES of Light Stable Right-Handed ν(with ne essarily suppressed intera tion strengths)(with ne essarily suppressed intera tion strengths)(with ne essarily suppressed intera tion strengths)(with ne essarily suppressed intera tion strengths)VALUE (eV) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<100200 1 OLIVE 82 COSM Dira ν

<2002000 1 OLIVE 82 COSM Majorana ν1Depending on intera tion strength GR where GR <GF .

Limits on MASSES of Heavy Stable Right-Handed νLimits on MASSES of Heavy Stable Right-Handed νLimits on MASSES of Heavy Stable Right-Handed νLimits on MASSES of Heavy Stable Right-Handed ν(with ne essarily suppressed intera tion strengths)(with ne essarily suppressed intera tion strengths)(with ne essarily suppressed intera tion strengths)(with ne essarily suppressed intera tion strengths)VALUE (GeV) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

> 10 1 OLIVE 82 COSM GR/GF <0.1>100 1 OLIVE 82 COSM GR/GF <0.011These results apply to heavy Majorana neutrinos and are summarized by the equation:mν >1.2 GeV (GF /GR ). The bound saturates, and if GR is too small no mass rangeis allowed.

ν CHARGEν CHARGEν CHARGEν CHARGEVALUE (units: ele tron harge) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<2.1× 10−12 90 1 CHEN 14A TEXO Nu lear rea tor<1.5× 10−12 90 2 STUDENIKIN 14 Nu lear rea tor<3.7× 10−12 90 3 GNINENKO 07 RVUE Nu lear rea tor<2 × 10−14 4 RAFFELT 99 ASTR Red giant luminosity<6 × 10−14 5 RAFFELT 99 ASTR Solar ooling<4 × 10−4 6 BABU 94 RVUE BEBC beam dump<3 × 10−4 7 DAVIDSON 91 RVUE SLAC e− beam dump<2 × 10−15 8 BARBIELLINI 87 ASTR SN 1987A<1 × 10−13 9 BERNSTEIN 63 ASTR Solar energy losses1CHEN 14A use the Multi-Conguration RRPA method to analyze rea tor νe s atteringon Ge atoms with 300 eV re oil energy threshold to obtain this limit.2 STUDENIKIN 14 uses the limit on µν from BEDA 13 and the 2.8 keV threshold of theele tron re oil energy to obtain this limit.3GNINENKO 07 use limit on νe magneti moment from LI 03B to derive this result. Thelimit is onsiderably weaker than the limits on the harge of νe and νe from variousastrophysi s onsiderations.4This RAFFELT 99 limit applies to all neutrino avors whi h are light enough (<5 keV)to be emitted from globular- luster red giants.5This RAFFELT 99 limit is derived from the helioseismologi al limit on a new energy-loss hannel of the Sun, and applies to all neutrino avors whi h are light enough (<1 keV)to be emitted from the sun.6BABU 94 use COOPER-SARKAR 92 limit on ν magneti moment to derive quotedresult. It applies to ντ .7DAVIDSON 91 use data from early SLAC ele tron beam dump experiment to derive harge limit as a fun tion of neutrino mass. It applies to ντ .8 Exa t BARBIELLINI 87 limit depends on assumptions about the intergala ti or gala ti magneti elds and about the dire t distan e and time through the eld. It applies to νe .9The limit applies to all avors.

ν (MEAN LIFE) / MASSν (MEAN LIFE) / MASSν (MEAN LIFE) / MASSν (MEAN LIFE) / MASSMeasures [∑ ∣∣Uℓ j ∣∣2 j mj]−1, where the sum is over mass eigenstateswhi h annot be resolved experimentally. Some of the limits onstrain theradiative de ay and are based on the limit of the orresponding photon ux. Other apply to the de ay of a heavier neutrino into the lighter oneand a Majoron or other invisible parti le. Many of these limits apply toany ν within the indi ated mass range.Limits on the radiative de ay are either dire tly based on the limits of the orresponding photon ux, or are derived from the limits on the neutrinomagneti moments. In the later ase the transition rate for νi → νj + γis onstrained by ij = 1τ ij

= (m2i−m2

j)3m3

i

µ2ij where µij is the neutrinotransition moment in the mass eigenstates basis. Typi ally, the limits onlifetime based on the magneti moments are many orders of magnitudemore restri tive than limits based on the nonobservation of photons.VALUE (s/eV) CL% DOCUMENT ID TECN COMMENT> 15.4> 15.4> 15.4> 15.4 90 1 KRAKAUER 91 CNTR νµ, νµ at LAMPF> 7 × 109> 7 × 109> 7 × 109> 7 × 109 2 RAFFELT 85 ASTR> 300> 300> 300> 300 90 3 REINES 74 CNTR νe• • • We do not use the following data for averages, ts, limits, et . • • •

> 105 − 1010 95 4 CECCHINI 11 ASTR ν2→ ν1 radiative de ay90 5 MIRIZZI 07 CMB radiative de ay90 6 MIRIZZI 07 CIB radiative de ay7 WONG 07 CNTR Rea tor νe> 0.11 90 8 XIN 05 CNTR Rea tor νe9 XIN 05 CNTR Rea tor νe> 0.004 90 10 AHARMIM 04 SNO quasidegen. ν masses> 4.4 × 10−5 90 10 AHARMIM 04 SNO hierar hi al ν masses& 100 95 11 CECCHINI 04 ASTR Radiative de ay for νmass > 0.01 eV> 0.067 90 12 EGUCHI 04 KLND quasidegen. ν masses> 1.1 × 10−3 90 12 EGUCHI 04 KLND hierar hi al ν masses> 8.7 × 10−5 99 13 BANDYOPA... 03 FIT nonradiative de ay≥ 4200 90 14 DERBIN 02B CNTR Solar pp and Be ν

> 2.8 × 10−5 99 15 JOSHIPURA 02B FIT nonradiative de ay

762762762762LeptonParti le ListingsNeutrino Properties16 DOLGOV 99 COSM17 BILLER 98 ASTR mν= 0.051 eV> 2.8 × 1015 18,19 BLUDMAN 92 ASTR mν < 50 eVnone 10−12 − 5× 104 20 DODELSON 92 ASTR mν=1300 keV< 10−12 or > 5× 104 20 DODELSON 92 ASTR mν=1300 keV21 GRANEK 91 COSM De aying L0> 6.4 90 22 KRAKAUER 91 CNTR νe at LAMPF> 1.1 × 1015 23 WALKER 90 ASTR mν= 0.03 ∼ 2 MeV> 6.3 × 1015 19,24 CHUPP 89 ASTR mν < 20 eV> 1.7 × 1015 19 KOLB 89 ASTR mν < 20 eV25 RAFFELT 89 RVUE ν (Dira , Majorana)26 RAFFELT 89B ASTR> 8.3 × 1014 27 VONFEILIT... 88 ASTR> 22 68 28 OBERAUER 87 νR (Dira )> 38 68 28 OBERAUER 87 ν (Majorana)> 59 68 28 OBERAUER 87 νL (Dira )> 30 68 KETOV 86 CNTR ν (Dira )> 20 68 KETOV 86 CNTR ν (Majorana)29 BINETRUY 84 COSM mν ∼ 1 MeV> 0.11 90 30 FRANK 81 CNTR ν ν LAMPF> 2 × 1021 31 STECKER 80 ASTR mν= 10100 eV> 1.0 × 10−2 90 30 BLIETSCHAU 78 HLBC νµ, CERN GGM> 1.7 × 10−2 90 30 BLIETSCHAU 78 HLBC νµ, CERN GGM< 3 × 10−11 32 FALK 78 ASTR mν <10 MeV> 2.2 × 10−3 90 30 BARNES 77 DBC ν, ANL 12-ft33 COWSIK 77 ASTR> 3. × 10−3 90 30 BELLOTTI 76 HLBC ν, CERN GGM> 1.3 × 10−2 90 30 BELLOTTI 76 HLBC ν, CERN GGM1KRAKAUER 91 quotes the limit τ/mν1 > (0.75a2 + 21.65a + 26.3) s/eV, where ais a parameter des ribing the asymmetry in the neutrino de ay dened as dNγ

/d osθ= (1/2)(1 + a osθ) The parameter a= 0 for a Majorana neutrino, but an vary from−1 to 1 for a Dira neutrino. The bound given by the authors is the most onservative(whi h applies for a= − 1).2RAFFELT 85 limit on the radiative de ay is from solar x- and γ-ray uxes. Limit dependson ν ux from pp, now established from GALLEX and SAGE to be > 0.5 of expe tation.3REINES 74 looked for ν of nonzero mass de aying radiatively to a neutral of lesser mass+ γ. Used liquid s intillator dete tor near ssion rea tor. Finds lab lifetime 6 × 107 sor more. Above value of (mean life)/mass assumes average ee tive neutrino energy of0.2 MeV. To obtain the limit 6× 107 s REINES 74 assumed that the full νe rea tor ux ould be responsible for yielding de ays with photon energies in the interval 0.1 MeV 0.5 MeV. This represents some overestimate so their lower limit is an over-estimate ofthe lab lifetime (VOGEL 84). If so, OBERAUER 87 may be omparable or better.4CECCHINI 11 sear h for radiative de ays of solar neutrinos into visible photons duringthe 2006 total solar e lipse. The range of (mean life)/mass values orresponds to a rangeof ν1 masses between 10−4 and 0.1 eV.5MIRIZZI 07 determine a limit on the neutrino radiative de ay from analysis of the maxi-mum allowed distortion of the CMB spe trum as measured by the COBE/FIRAS. For thede ay ν2 → ν1 the lifetime limit is . 4× 1020 s for mmin . 0.14 eV. For transitionwith the ∣∣m31∣∣ mass dieren e the lifetime limit is ∼ 2 × 1019 s for mmin . 0.14eV and ∼ 5× 1020 s for mmin & 0.14 eV.6MIRIZZI 07 determine a limit on the neutrino radiative de ay from analysis of the osmi infrared ba kground (CIB) using the Spitzer Observatory data. For transition with the∣∣m31∣∣ mass dieren e they obtain the lifetime limit ∼ 1020 s for mmin . 0.14 eV.7WONG 07 use their limit on the neutrino magneti moment together with the assumedexperimental value of m213 ∼ 2×10−3 eV2 to obtain τ13/m31 > 3.2×1027 s/eV3 forthe radiative de ay in the ase of the inverted mass hierar hy. Similarly to RAFFELT 89this limit an be violated if ele tri and magneti moments are equal to ea h other.Analogous, but numeri ally somewhat dierent limits are obtained for τ23 and τ21.8XIN 05 sear h for the γ from radiative de ay of νe produ ed by the ele tron apture on51Cr. No events were seen and the limit on τ/mν was derived. This is a weaker limiton the de ay of νe than KRAKAUER 91.9XIN 05 use their limit on the neutrino magneti moment of νe together with the assumedexperimental value of m21,3 ∼ 2×10−3 eV2 to obtain τ13/m31 > 1×1023 s/eV3 forthe radiative de ay in the ase of the inverted mass hierar hy. Similarly to RAFFELT 89this limit an be violated if ele tri and magneti moments are equal to ea h other.Analogous, but numeri ally somewhat dierent limits are obtained for τ23 and τ21.Again, this limit is spe i for νe .10AHARMIM 04 obtained these results from the solar νe ux limit set by the SNO mea-surement assuming ν2 de ay through nonradiative pro ess ν2 → ν1X , where X is aMajoron or other invisible parti le. Limits are given for the ases of quasidegenerate andhierar hi al neutrino masses.11CECCHINI 04 obtained this bound through the observations performed on the o asionof the 21 June 2001 total solar e lipse, looking for visible photons from radiative de aysof solar neutrinos. Limit is a τ/mν2 in ν2 → ν1 γ. Limit ranges from ∼ 100 to107 s/eV for 0.01 < mν1 < 0.1 eV.12EGUCHI 04 obtained these results from the solar νe ux limit set by the KamLANDmeasurement assuming ν2 de ay through nonradiative pro ess ν2 → ν1X , where X isa Majoron or other invisible parti le. Limits are given for the ases of quasidegenerateand hierar hi al neutrino masses.13The ratio of the lifetime over the mass derived by BANDYOPADHYAY 03 is for ν2. Theyobtained this result using the following solar-neutrino data: total rates measured in Cland Ga experiments, the Super-Kamiokande's zenith-angle spe tra, and SNO's day andnight spe tra. They assumed that ν1 is the lowest mass, stable or nearly stable neutrino

state and ν2 de ays through nonradiative Majoron emission pro ess, ν2 → ν1 + J, orthrough nonradiative pro ess with all the nal state parti les being sterile. The best tis obtained in the region of the LMA solution.14DERBIN 02B (also BACK 03B) obtained this bound for the radiative de ay from theresults of ba kground measurements with Counting Test Fa ility (the prototype of theBorexino dete tor). The laboratory gamma spe trum is given as dNγ/d osθ= (1/2) (1 +α osθ) with α=0 for a Majorana neutrino, and α varying to −1 to 1 for a Dira neutrino.The listed bound is for the ase of α=0. The most onservative bound 1.5×103 s eV−1is obtained for the ase of α=−1.15The ratio of the lifetime over the mass derived by JOSHIPURA 02B is for ν2. Theyobtained this result from the total rates measured in all solar neutrino experiments.They assumed that ν1 is the lowest mass, stable or nearly stable neutrino state and ν2de ays through nonradiative pro ess like Majoron emission de ay, ν2 → ν′1 + J whereν′1 state is sterile. The exa t limit depends on the spe i solution of the solar neutrinoproblem. The quoted limit is for the LMA solution.16DOLGOV 99 pla es limits in the (Majorana) τ -asso iated ν mass-lifetime plane based onnu leosynthesis. Results would be onsiderably modied if neutrino os illations exist.17BILLER 98 use the observed TeV γ-ray spe tra to set limits on the mean life of anyradiatively de aying neutrino between 0.05 and 1 eV. Curve shows τν/Bγ > 0.15×1021 sat 0.05 eV, > 1.2× 1021 s at 0.17 eV, > 3× 1021 s at 1 eV, where Bγ is the bran hingratio to photons.18BLUDMAN 92 sets additional limits by this method for higher mass ranges. Cosmologi allimits are also obtained.19 Limit on the radiative de ay based on nonobservation of γ's in oin iden e with ν's fromSN 1987A.20DODELSON 92 range is for wrong-heli ity keV mass Dira ν's from the ore of neutronstar in SN 1987A de aying to ν's that would have intera ted in KAM2 or IMB dete tors.21GRANEK 91 onsiders heavy neutrino de ays to γ νL and 3νL, where mνL <100 keV.Lifetime is al ulated as a fun tion of heavy neutrino mass, bran hing ratio into γ νL,and mνL.22KRAKAUER 91 quotes the limit for νe , τ/mν > (0.3a2 + 9.8a + 15.9) s/eV, wherea is a parameter des ribing the asymmetry in the radiative neutrino de ay dened asdNγ

/d osθ = (1/2)(1 + a osθ) a= 0 for a Majorana neutrino, but an vary from −1to 1 for a Dira neutrino. The bound given by the authors is the most onservative(whi h applies for a= − 1).23WALKER 90 uses SN 1987A γ ux limits after 289 days.24CHUPP 89 should be multiplied by a bran hing ratio (about 1) and a dete tion eÆ ien y(about 1/4), and pertains to radiative de ay of any neutrino to a lighter or sterile neutrino.25RAFFELT 89 uses KYULDJIEV 84 to obtain τm3 > 3 × 1018 s eV3 (based on νe e− ross se tions). The bound for the radiative de ay is not valid if ele tri and magneti transition moments are equal for Dira neutrinos.26RAFFELT 89B analyze stellar evolution and ex lude the region 3 × 1012 < τm3< 3× 1021 s eV3.27Model-dependent theoreti al analysis of SN 1987A neutrinos. Quoted limit is for[∑

j∣∣Uℓ j ∣∣2 j mj]−1, where ℓ=µ, τ . Limit is 3.3× 1014 s/eV for ℓ=e.28OBERAUER 87 looks for photons and e+ e− pairs from radiative de ays of rea torneutrinos.29BINETRUY 84 nds τ < 108 s for neutrinos in a radiation-dominated universe.30These experiments look for νk → νj γ or νk → νj γ.31 STECKER 80 limit based on UV ba kground; result given is τ > 4×1022 s at mν=20 eV.32FALK 78 nds lifetime onstraints based on supernova energeti s.33COWSIK 77 onsiders variety of s enarios. For neutrinos produ ed in the big bang,present limits on opti al photon ux require τ > 1023 s for mν ∼ 1 eV. See alsoCOWSIK 79 and GOLDMAN 79.

ν MAGNETIC MOMENTν MAGNETIC MOMENTν MAGNETIC MOMENTν MAGNETIC MOMENTThe oupling of neutrinos to an ele tromagneti eld is a hara terizedby a 3×3 matrix λ of the magneti (µ) and ele tri (d) dipole moments(λ = µ - id). For Majorana neutrinos the matrix λ is antisymmetri and only transition moments are allowed, while for Dira neutrinos λ isa general 3×3 matrix. In the standard ele troweak theory extended toin lude neutrino masses (see FUJIKAWA 80) µν = 3eGFmν/(8π2√2) =3.2 × 10−19(mν/eV)µB , i.e. it is unobservably small given the knownsmall neutrino masses. In more general models there is no longer a propor-tionality between neutrino mass and its magneti moment, even thoughonly massive neutrinos have nonvanishing magneti moments without netuning.Laboratory bounds on λ are obtained via elasti ν-e s attering, where thes attered neutrino is not observed. The ombinations of matrix elementsof λ that are onstrained by various experiments depend on the initialneutrino avor and on its propagation between sour e and dete tor (e.g.,solar νe and rea tor νe do not onstrain the same ombinations). Thelistings below therefore identify the initial neutrino avor.Other limits, e.g. from various stellar ooling pro esses, apply to all neu-trino avors. Analogous avor independent, but weaker, limits are ob-tained from the analysis of e+ e− → ν ν γ ollider experiments.

763763763763See key on page 601 Lepton Parti le ListingsNeutrino PropertiesVALUE (10−10 µB ) CL% DOCUMENT ID TECN COMMENT< 0.29< 0.29< 0.29< 0.29 90 1 BEDA 13 CNTR Rea tor νe< 6.8< 6.8< 6.8< 6.8 90 2 AUERBACH 01 LSND νe e, νµ e s attering< 3900< 3900< 3900< 3900 90 3 SCHWIENHO...01 DONU ντ e− → ντ e−• • • We do not use the following data for averages, ts, limits, et . • • •

< 0.022 90 4 ARCEO-DIAZ 15 ASTR Red giants< 0.1 95 5 CORSICO 14 ASTR< 0.05 95 6 MILLER-BER...14B ASTR< 0.045 95 7 VIAUX 13A ASTR Globular luster M5< 0.32 90 8 BEDA 10 CNTR Rea tor νe< 2.2 90 9 DENIZ 10 TEXO Rea tor νe< 0.0110.027 10 KUZNETSOV 09 ASTR νL → νR in SN1987A< 0.54 90 11 ARPESELLA 08A BORX Solar ν spe trum shape< 0.58 90 12 BEDA 07 CNTR Rea tor νe< 0.74 90 13 WONG 07 CNTR Rea tor νe< 0.9 90 14 DARAKTCH... 05 Rea tor νe< 130 90 15 XIN 05 CNTR Rea tor νe< 37 95 16 GRIFOLS 04 FIT Solar 8B ν (SNO NC)< 3.6 90 17 LIU 04 SKAM Solar ν spe trum shape< 1.1 90 18 LIU 04 SKAM Solar ν spe trum shape(LMA region)< 5.5 90 19 BACK 03B CNTR Solar pp and Be ν

< 1.0 90 20 DARAKTCH... 03 Rea tor νe< 1.3 90 21 LI 03B CNTR Rea tor νe< 2 90 22 GRIMUS 02 FIT solar + rea tor (Majo-rana ν)<80000 90 23 TANIMOTO 00 RVUE e+ e− → ν ν γ

< 0.010.04 24 AYALA 99 ASTR νL → νR in SN 1987A< 1.5 90 25 BEACOM 99 SKAM ν spe trum shape< 0.03 26 RAFFELT 99 ASTR Red giant luminosity< 4 27 RAFFELT 99 ASTR Solar ooling<44000 90 ABREU 97J DLPH e+ e− → ν ν γ at LEP<33000 90 28 ACCIARRI 97Q L3 e+ e− → ν ν γ at LEP< 0.62 29 ELMFORS 97 COSM Depolarization in earlyuniverse plasma<27000 95 30 ESCRIBANO 97 RVUE (Z → ν ν) at LEP< 30 90 VILAIN 95B CHM2 νµ e → νµ e<55000 90 GOULD 94 RVUE e+ e− → ν ν γ at LEP< 1.9 95 31 DERBIN 93 CNTR Rea tor ν e → ν e< 5400 90 32 COOPER-... 92 BEBC ντ e− → ντ e−< 2.4 90 33 VIDYAKIN 92 CNTR Rea tor ν e → ν e<56000 90 DESHPANDE 91 RVUE e+ e− → ν ν γ

< 100 95 34 DORENBOS... 91 CHRM νµ e → νµ e< 8.5 90 AHRENS 90 CNTR νµ e → νµ e< 10.8 90 35 KRAKAUER 90 CNTR LAMPF ν e → ν e< 7.4 90 35 KRAKAUER 90 CNTR LAMPF (νµ, νµ )eelast.< 0.02 36 RAFFELT 90 ASTR Red giant luminosity< 0.1 37 RAFFELT 89B ASTR Cooling helium stars38 FUKUGITA 88 COSM Primordial magn. elds<40000 90 39 GROTCH 88 RVUE e+ e− → ν ν γ

≤ .3 37 RAFFELT 88B ASTR He burning stars< 0.11 37 FUKUGITA 87 ASTR Cooling helium stars< 0.0006 40 NUSSINOV 87 ASTR Cosmi EM ba k-grounds< 0.10.2 MORGAN 81 COSM 4He abundan e< 0.85 BEG 78 ASTR Stellar plasmons< 0.6 41 SUTHERLAND 76 ASTR Red giants + degener-ate dwarfs< 81 42 KIM 74 RVUE νµ e → νµ e< 1 BERNSTEIN 63 ASTR Solar ooling< 14 COWAN 57 CNTR Rea tor ν1BEDA 13 report νe e− s attering results, using the Kalinin Nu lear Power Plant and ashielded Ge dete tor. The re oil ele tron spe trum is analyzed between 2.5 and 55 keV.Supersedes BEDA 07. Supersedes BEDA 10. This is the most stringent limit on themagneti moment of rea tor νe .2AUERBACH 01 limit is based on the LSND νe and νµ ele tron s attering measurements.The limit is slightly more stringent than KRAKAUER 90.3 SCHWIENHORST 01 quote an experimental sensitivity of 4.9× 10−7.4ARCEO-DIAZ 15 onstrains the neutrino magneti moment from observation of the tipof the red giant bran h in the globular luster ω-Centauri.5 CORSICO 14 onstrains the neutrino magneti moment from observations of white drarfpulsations.6MILLER-BERTOLAMI 14B onstrains the neutrino magneti moment from observationsof the white dwarf luminosity fun tion of the Gala ti disk.7VIAUX 13A onstrains the neutrino magneti moment from observations of the globular luster M5.8BEDA 10 report νe e− s attering results, using the Kalinin Nu lear Power Plant and ashielded Ge dete tor. The re oil ele tron spe trum is analyzed between 2.9 and 45 keV.Supersedes BEDA 07. Superseded by BEDA 13.9DENIZ 10 observe rea tor νe e s attering with re oil kineti energies 38 MeV usingCsI(Tl) dete tors. The observed rate and spe tral shape are onsistent with the StandardModel predi tion, leading to the reported onstraint on νe magneti moment.

10KUZNETSOV 09 obtain a limit on the avor averaged magneti moment of Dira neu-trinos from the time averaged neutrino signal of SN1987A. Improves and supersedes theanalysis of BARBIERI 88 and AYALA 99.11ARPESELLA 08A obtained this limit using the shape of the re oil ele tron energy spe -trum from the Borexino 192 live days of solar neutrino data.12BEDA 07 performed sear h for ele tromagneti νe -e s attering at Kalininskaya nu learrea tor. A Ge dete tor with a tive and passive shield was used and the ele tron re oilspe trum between 3.0 and 61.3 keV analyzed. Superseded by BEDA 10.13WONG 07 performed sear h for non-standard νe -e s attering at the Kuo-Sheng nu learrea tor. Ge dete tor equipped with a tive anti-Compton shield is used. Most stringentlaboratory limit on magneti moment of rea tor νe . Supersedes LI 03B.14DARAKTCHIEVA 05 present the nal analysis of the sear h for non-standard νe -e s at-tering omponent at Bugey nu lear rea tor. Full kinemati al event re onstru tion ofboth the kineti energy above 700 keV and s attering angle of the re oil ele tron, byuse of TPC. Most stringent laboratory limit on magneti moment. Supersedes DARAK-TCHIEVA 03.15XIN 05 evaluated the νe ux at the Kuo-Sheng nu lear rea tor and sear hed for non-standard νe -e s attering. Ge dete tor equipped with a tive anti-Compton shield wasused. This laboratory limit on magneti moment is onsiderably less stringent than thelimits for rea tor νe , but is spe i to νe .16GRIFOLS 04 obtained this bound using the SNO data of the solar 8B neutrino uxmeasured with deuteron breakup. This bound applies to µe = (µ221 + µ222 + µ223)1/2.17 LIU 04 obtained this limit using the shape of the re oil ele tron energy spe trum from theSuper-Kamiokande-I 1496 days of solar neutrino data. Neutrinos are assumed to haveonly diagonal magneti moments, µν1 = µν2. This limit orresponds to the os illationparameters in the va uum os illation region.18 LIU 04 obtained this limit using the shape of the re oil ele tron energy spe trum fromthe Super-Kamiokande-I 1496 live-day solar neutrino data, by limiting the os illation pa-rameter region in the LMA region allowed by solar neutrino experiments plus KamLAND.µν1 = µν2 is assumed. In the LMA region, the same limit would be obtained even ifneutrinos have o-diagonal magneti moments.19BACK 03B obtained this bound from the results of ba kground measurements withCounting Test Fa ility (the prototype of the Borexino dete tor). Standard Solar Model ux was assumed. This µν an be dierent from the rea tor µν in ertain os illations enarios (see BEACOM 99).20DARAKTCHIEVA 03 sear hed for non-standard νe -e s attering omponent at Bugeynu lear rea tor. Full kinemati al event re onstru tion by use of TPC. Superseded byDARAKTCHIEVA 05.21 LI 03B used Ge dete tor in a tive shield near nu lear rea tor to test for nonstandard νe -es attering.22GRIMUS 02 obtain stringent bounds on all Majorana neutrino transition moments froma simultaneous t of LMA-MSW os illation parameters and transition moments to globalsolar neutrino data + rea tor data. Using only solar neutrino data, a 90% CL bound of6.3× 10−10µB is obtained.23TANIMOTO 00 ombined e+ e− → ν ν γ data from VENUS, TOPAZ, and AMY.24AYALA 99 improves the limit of BARBIERI 88.25BEACOM 99 obtain the limit using the shape, but not the absolute magnitude whi his ae ted by os illations, of the solar neutrino spe trum obtained by Superkamiokande(825 days). This µν an be dierent from the rea tor µν in ertain os illation s enarios.26RAFFELT 99 is an update of RAFFELT 90. This limit applies to all neutrino avorswhi h are light enough (< 5 keV) to be emitted from globular- luster red giants. Thislimit pertains equally to ele tri dipole moments and magneti transition moments, andit applies to both Dira and Majorana neutrinos.27RAFFELT 99 is essentially an update of BERNSTEIN 63, but is derived from the he-lioseismologi al limit on a new energy-loss hannel of the Sun. This limit applies to allneutrino avors whi h are light enough (<1 keV) to be emitted from the Sun. This limitpertains equally to ele tri dipole and magneti transition moments, and it applies toboth Dira and Majorana neutrinos.28ACCIARRI 97Q result applies to both dire t and transition magneti moments and forq2=0.29ELMFORS 97 al ulate the rate of depolarization in a plasma for neutrinos with a mag-neti moment and use the onstraints from a big-bang nu leosynthesis on additionaldegrees of freedom.30Applies to absolute value of magneti moment.31DERBIN 93 determine the ross se tion for 0.62.0 MeV ele tron energy as (1.28 ±0.63) × σweak. However, the (rea tor on rea tor o)/(rea tor o) is only ∼ 1/100.32COOPER-SARKAR 92 assume fDs /fπ = 2 and Ds , Ds produ tion ross se tion =2.6 µb to al ulate ν ux.33VIDYAKIN 92 limit is from a e νe elasti s attering experiment. No experimental detailsare given ex ept for the ross se tion from whi h this limit is derived. Signal/noise was1/10. The limit uses sin2θW = 0.23 as input.34DORENBOSCH 91 orre ts an in orre t statement in DORENBOSCH 89 that the νmagneti moment is < 1 × 10−9 at the 95%CL. DORENBOSCH 89 measures bothνµ e and ν e elasti s attering and assume µ(ν) = µ(ν).35KRAKAUER 90 experiment fully reported in ALLEN 93.36RAFFELT 90 limit applies for a diagonal magneti moment of a Dira neutrino, or for atransition magneti moment of a Majorana neutrino. In the latter ase, the same analysisgives < 1.4× 10−12. Limit at 95%CL obtained from δM .37 Signi ant dependen e on details of stellar models.38 FUKUGITA 88 nd magneti dipole moments of any two neutrino spe ies are boundedby µ < 10−16 [10−9 G/B0 where B0 is the present-day intergala ti eld strength.39GROTCH 88 ombined data from MAC, ASP, CELLO, and Mark J.

764764764764LeptonParti le ListingsNeutrino Properties40For mν = 8200 eV. NUSSINOV 87 examines transition magneti moments for νµ →νe and obtain < 3× 10−15 for mν > 16 eV and < 6× 10−14 for mν > 4 eV.41We obtain above limit from SUTHERLAND 76 using their limit f < 1/3.42KIM 74 is a theoreti al analysis of νµ rea tion data.NEUTRINO CHARGE RADIUS SQUAREDNEUTRINO CHARGE RADIUS SQUAREDNEUTRINO CHARGE RADIUS SQUAREDNEUTRINO CHARGE RADIUS SQUAREDWe report limits on the so- alled neutrino harge radius squared. Whilethe straight-forward denition of a neutrino harge radius has been provento be gauge-dependent and, hen e, unphysi al (LEE 77C), there have beenre ent attempts to dene a physi ally observable neutrino harge radius(BERNABEU 00, BERNABEU 02). The issue is still ontroversial (FU-JIKAWA 03, BERNABEU 03). A more general interpretation of the exper-imental results is that they are limits on ertain nonstandard ontributionsto neutrino s attering.VALUE (10−32 m2) CL% DOCUMENT ID TECN COMMENT

−2.1 to 3.3−2.1 to 3.3−2.1 to 3.3−2.1 to 3.3 90 1 DENIZ 10 TEXO Rea tor νe e• • • We do not use the following data for averages, ts, limits, et . • • •

−0.53 to 0.68 90 2 HIRSCH 03 νµ e s at.−8.2 to 9.9 90 3 HIRSCH 03 anomalous e+ e− → ν ν γ

−2.97 to 4.14 90 4 AUERBACH 01 LSND νe e → νe e−0.6 to 0.6 90 VILAIN 95B CHM2 νµ e elasti s at.0.9 ±2.7 ALLEN 93 CNTR LAMPF ν e → ν e

< 2.3 95 MOURAO 92 ASTR HOME/KAM2 ν rates< 7.3 90 5 VIDYAKIN 92 CNTR Rea tor ν e → ν e1.1 ±2.3 ALLEN 91 CNTR Repl. by ALLEN 93−1.1 ±1.0 6 AHRENS 90 CNTR νµ e elasti s at.−0.3 ±1.5 6 DORENBOS... 89 CHRM νµ e elasti s at.7 GRIFOLS 89B ASTR SN 1987A1DENIZ 10 observe rea tor νe e s attering with re oil kineti energies 38 MeV usingCsI(Tl) dete tors. The observed rate and spe tral shape are onsistent with the StandardModel predi tion, leading to the reported onstraint on νe harge radius.2Based on analysis of CCFR 98 results. Limit is on ⟨r2V ⟩ + ⟨r2A⟩. The CHARM II andE734 at BNL results are reanalyzed, and weaker bounds on the harge radius squaredthan previously published are obtained. The NuTeV result is dis ussed; when tentativelyinterpreted as νµ harge radius it implies ⟨r2V ⟩ + ⟨r2A⟩ = (4.20 ± 1.64) × 10 −33 m2.3Results of LEP-2 are interpreted as limits on the axial-ve tor harge radius squared ofa Majorana ντ . Slightly weaker limits for both ve tor and axial-ve tor harge radiussquared are obtained for the Dira ase, and somewhat weaker limits are obtained fromthe analysis of lower energy data (LEP-1.5 and TRISTAN).4AUERBACH 01 measure νe e elasti s attering with LSND dete tor. The ross se tionagrees with the Standard Model expe tation, in luding the harge and neutral urrentinterferen e. The 90% CL applies to the range shown.5VIDYAKIN 92 limit is from a e ν elasti s attering experiment. No experimental detailsare given ex ept for the ross se tion from whi h this limit is derived. Signal/noise was1/10. The limit uses sin2θW = 0.23 as input.6Result is obtained from reanalysis given in ALLEN 91, followed by our redu tion to obtain1 σ errors.7GRIFOLS 89B sets a limit of ⟨r2⟩

< 0.2× 10−32 m2 for right-handed neutrinos.REFERENCES FOR Neutrino PropertiesREFERENCES FOR Neutrino PropertiesREFERENCES FOR Neutrino PropertiesREFERENCES FOR Neutrino PropertiesARCEO-DIAZ 15 ASP 70 1 S. Ar eo-Diaz et al.PALANQUE-... 15 JCAP 1502 045 N. Palanque-Delabrouille et al.PALANQUE-... 15A JCAP 1511 011 N. Palanque-Delabrouille et al.ADE 14 AA 571 A16 P.A.R. Ade et al. (Plan k Collab.)BATTYE 14 PRL 112 051303 R.A. Battye, A. Moss (MCHS, NOTT)BEUTLER 14 MNRAS 444 3501 F. Beutler et al. (BOSS Collab.)CHEN 14A PR D90 011301 J.-W. Chen et al. (TEXONO Collab.)CORSICO 14 JCAP 1408 054 A.H. Corsi oCOSTANZI 14 JCAP 1410 081 M. Costanzi et al. (TRST, TRSTI)GIUSARMA 14 PR D90 043507 E. Giusarma et al.HOU 14 APJ 782 74 Z. Hou et al.LEISTEDT 14 PRL 113 041301 B. Leistedt, H.V. Peiris, L. VerdeMILLER-BER... 14B AA 562 A123 M.M. Miller Bertolami (MPIG, LAPL)RIEMER-SOR... 14 PR D89 103505 S. Riemer-Sorensen, D. Parkinson, T. M. DavisSTUDENIKIN 14 EPL 107 21001 A.I. StudenikinBEDA 13 PPNL 10 139 A.G. Beda et al. (GEMMA Collab.)VIAUX 13A PRL 111 231301 N. Viaux et al.MORESCO 12 JCAP 1207 053 M. Mores o et al.XIA 12 JCAP 1206 010 J.-Q. Xia et al.ASEEV 11 PR D84 112003 V.N. Aseev et al.CECCHINI 11 ASP 34 486 S. Ce hini et al.SAITO 11 PR D83 043529 S. Saito, M. Takada, A. TaruyaBEDA 10 PPNL 7 406 A.G. Beda et al. (GEMMA Collab.)DENIZ 10 PR D81 072001 M. Deniz et al. (TEXONO Collab.)HANNESTAD 10 JCAP 1008 001 S. Hannestad et al.PAGLIAROLI 10 ASP 33 287 G. Pagliaroli, F. Rossi-Torres, E. Vissani (INFN+)SEKIGUCHI 10 JCAP 1003 015 T. Sekigu hi et al.THOMAS 10 PRL 105 031301 S.A. Thomas, F.B. Abdalla, O. Lahav (LOUC)ICHIKI 09 PR D79 023520 K. I hiki, M. Takada, T. TakahashiKOMATSU 09 APJS 180 330 E. Komatsu et al.KUZNETSOV 09 IJMP A24 5977 A.V. Kuznetsov, N.V. Mikheev, A.A. Okrugin (YARO)TERENO 09 AA 500 657 I. Tereno et al.VIKHLININ 09 APJ 692 1060 A. Vikhlinin et al.ARPESELLA 08A PRL 101 091302 C. Arpesella et al. (Borexino Collab.)BERNARDIS 08 PR D78 083535 F. De Bernardis et al.BEDA 07 PAN 70 1873 A.G. Beda et al.Translated from YAF 70 1925.

FOGLI 07 PR D75 053001 G.L. Fogli et al.GNINENKO 07 PR D75 075014 S.N. Gninenko, N.V. Krasnikov, A. RubbiaKRISTIANSEN 07 PR D75 083510 J. Kristiansen, O. Elgaroy, H. DahleMIRIZZI 07 PR D76 053007 A. Mirizzi, D. Montanino, P.D. Serpi oSPERGEL 07 APJS 170 377 D.N. Spergel et al.WONG 07 PR D75 012001 H.T. Wong et al. (TEXONO Collab.)ZUNCKEL 07 JCAP 0708 004 C. Zun kel, P. FerreiraCIRELLI 06 JCAP 0612 013 M. Cirelli et al.FUKUGITA 06 PR D74 027302 M. Fukugita et al.GOOBAR 06 JCAP 0606 019 A. Goobar et al.HANNESTAD 06 JCAP 0611 016 S. Hannestad, G. RaeltKRISTIANSEN 06 PR D74 123005 J. Kristiansen, O. Elgaroy, H. EriksenSANCHEZ 06 MNRAS 366 189 A.G. San hez et al.SELJAK 06 JCAP 0610 014 U. Seljak, A. Slosar, P. M DonaldDARAKTCH... 05 PL B615 153 Z. Darakt hieva et al. (MUNU Collab.)ICHIKAWA 05 PR D71 043001 K. I hikawa, M. Fukugita, M. Kawasaki (ICRR)KRAUS 05 EPJ C40 447 Ch. Kraus et al.XIN 05 PR D72 012006 B. Xin et al. (TEXONO Collab.)AHARMIM 04 PR D70 093014 B. Aharmim et al. (SNO Collab.)BARGER 04 PL B595 55 V. Barger, D. Marfatia, A. TregreCECCHINI 04 ASP 21 183 S. Ce hini et al. (BGNA+)CROTTY 04 PR D69 123007 P. Crotty, J. Lesgourgues, S. PastorEGUCHI 04 PRL 92 071301 K. Egu hi et al. (KamLAND Collab.)GRIFOLS 04 PL B587 184 J.A. Grifols, E. Masso, S. Mohanty (BARC, AHMED)LIU 04 PRL 93 021802 D.W. Liu et al. (Super-Kamiokande Collab.)ARNABOLDI 03A PRL 91 161802 C. Arnaboldi et al.BACK 03B PL B563 35 H.O. Ba k et al. (Borexino Collab.)BANDYOPA... 03 PL B555 33 A. Bandyopadhyay, S. Choubey, S. Goswami (SAHA+)BERNABEU 03 hep-ph/0303202 J. Bernabeu, J. Papavassiliou, J. VidalDARAKTCH... 03 PL B564 190 Z. Darakt hieva et al. (MUNU Collab.)FUJIKAWA 03 hep-ph/0303188 K. Fujikawa, R. Shro kHIRSCH 03 PR D67 033005 M. Hirs h, E. Nardi, D. RestrepoLI 03B PRL 90 131802 H.B. Li et al. (TEXONO Collab.)SPERGEL 03 APJS 148 175 D.N. Spergel et al.BERNABEU 02 PRL 89 101802 J. Bernabeu, J. Papavassiliou, J. VidalAlso PRL 89 229902 (errat.) J. Bernabeu, J. Papavassiliou, J. VidalDERBIN 02B JETPL 76 409 A.V. Derbin, O.Ju. SmirnovTranslated from ZETFP 76 483.GRIMUS 02 NP B648 376 W. Grimus et al.JOSHIPURA 02B PR D66 113008 A.S. Joshipura, E. Masso, S. MohantyLEWIS 02 PR D66 103511 A. Lewis, S. BridleLOREDO 02 PR D65 063002 T.J. Loredo, D.Q. LambWANG 02 PR D65 123001 X. Wang, M. Tegmark, M. ZaldarriagaAUERBACH 01 PR D63 112001 L.B. Auerba h et al. (LSND Collab.)SCHWIENHO... 01 PL B513 23 R. S hwienhorst et al. (DONUT Collab.)ATHANAS 00 PR D61 052002 M. Athanas et al. (CLEO Collab.)BERNABEU 00 PR D62 113012 J. Bernabeu et al.FUKUGITA 00 PRL 84 1082 M. Fukugita, G.C. Liu, N. SugiyamaTANIMOTO 00 PL B478 1 N. Tanimoto et al.AYALA 99 PR D59 111901 A. Ayala, J.C. D'Olivo, M. TorresBEACOM 99 PRL 83 5222 J.F. Bea om, P. VogelCROFT 99 PRL 83 1092 R.A.C. Croft, W. Hu, R. DaveDOLGOV 99 NP B548 385 A.D. Dolgov et al.LOBASHEV 99 PL B460 227 V.M. Lobashev et al.RAFFELT 99 PRPL 320 319 G.G. RaeltWEINHEIMER 99 PL B460 219 Ch. Weinheimer et al.ACKERSTAFF 98T EPJ C5 229 K. A kersta et al. (OPAL Collab.)AMMAR 98 PL B431 209 R. Ammar et al. (CLEO Collab.)BARATE 98F EPJ C2 395 R. Barate et al. (ALEPH Collab.)BILLER 98 PRL 80 2992 S.D. Biller et al. (WHIPPLE Collab.)FELDMAN 98 PR D57 3873 G.J. Feldman, R.D. CousinsLENZ 98 PL B416 50 S. Lenz et al.ABREU 97J ZPHY C74 577 P. Abreu et al. (DELPHI Collab.)ACCIARRI 97Q PL B412 201 M. A iarri et al. (L3 Collab.)ANASTASSOV 97 PR D55 2559 A. Anastassov et al. (CLEO Collab.)Also PR D58 119903 (erratum)A. Anastassov et al. (CLEO Collab.)ELMFORS 97 NP B503 3 P. Elmfors et al.ESCRIBANO 97 PL B395 369 R. Es ribano, E. Masso (BARC, PARIT)FIELDS 97 ASP 6 169 B.D. Fields, K. Kainulainen, K.A. Olive (NDAM+)SWAIN 97 PR D55 R1 J. Swain, L. Taylor (NEAS)ALEXANDER 96M ZPHY C72 231 G. Alexander et al. (OPAL Collab.)ASSAMAGAN 96 PR D53 6065 K.A. Assamagan et al. (PSI, ZURI, VILL+)BAI 96 PR D53 20 J.Z. Bai et al. (BES Collab.)BOTTINO 96 PR D53 6361 A. Bottino et al.DOLGOV 96 PL B383 193 A.D. Dolgov, S. Pastor, J.W.F. Valle (IFIC, VALE)HANNESTAD 96 PRL 76 2848 S. Hannestad, J. Madsen (AARH)HANNESTAD 96B PRL 77 5148 (erratum) S. Hannestad, J. Madsen (AARH)HANNESTAD 96C PR D54 7894 S. Hannestad, J. Madsen (AARH)SOBIE 96 ZPHY C70 383 R.J. Sobie, R.K. Keeler, I. Lawson (VICT)BELESEV 95 PL B350 263 A.I. Belesev et al. (INRM, KIAE)BUSKULIC 95H PL B349 585 D. Buskuli et al. (ALEPH Collab.)CHING 95 IJMP A10 2841 C.R. Ching et al. (CST, BEIJT, CIAE)DOLGOV 95 PR D51 4129 A.D. Dolgov, K. Kainulainen, I.Z. Rothstein (MICH+)HIDDEMANN 95 JP G21 639 K.H. Hiddemann, H. Daniel, O. S hwentker (MUNT)KERNAN 95 NP B437 243 P.J. Kernan, L.M. Krauss (CASE)SIGL 95 PR D51 1499 G. Sigl, M.S. Turner (FNAL, EFI)STOEFFL 95 PRL 75 3237 W. Stoe, D.J. De man (LLNL)VILAIN 95B PL B345 115 P. Vilain et al. (CHARM II Collab.)ASSAMAGAN 94 PL B335 231 K.A. Assamagan et al. (PSI, ZURI, VILL+)BABU 94 PL B321 140 K.S. Babu, T.M. Gould, I.Z. Rothstein (BART+)DODELSON 94 PR D49 5068 S. Dodelson, G. Gyuk, M.S. Turner (FNAL, CHIC+)GOULD 94 PL B333 545 T.M. Gould, I.Z. Rothstein (JHU, MICH)JECKELMANN 94 PL B335 326 B. Je kelmann, P.F.A. Goudsmit, H.J. Leisi (WABRN+)KAWASAKI 94 NP B419 105 M. Kawasaki et al. (OSU)PERES 94 PR D50 513 O.L.G. Peres, V. Pleitez, R. Zukanovi h Fun halYASUMI 94 PL B334 229 S. Yasumi et al. (KEK, TSUK, KYOT+)ALLEN 93 PR D47 11 R.C. Allen et al. (UCI, LANL, ANL+)BALEST 93 PR D47 R3671 R. Balest et al. (CLEO Collab.)CINABRO 93 PRL 70 3700 D. Cinabro et al. (CLEO Collab.)DERBIN 93 JETPL 57 768 A.V. Derbin et al. (PNPI)Translated from ZETFP 57 755.DOLGOV 93 PRL 71 476 A.D. Dolgov, I.Z. Rothstein (MICH)ENQVIST 93 PL B301 376 K. Enqvist, H. Uibo (NORD)SUN 93 CJNP 15 261 H.C. Sun et al. (CIAE, CST, BEIJT)WEINHEIMER 93 PL B300 210 C. Weinheimer et al. (MANZ)ALBRECHT 92M PL B292 221 H. Albre ht et al. (ARGUS Collab.)BLUDMAN 92 PR D45 4720 S.A. Bludman (CFPA)COOPER-... 92 PL B280 153 A.M. Cooper-Sarkar et al. (BEBC WA66 Collab.)DODELSON 92 PRL 68 2572 S. Dodelson, J.A. Frieman, M.S. Turner (FNAL+)HOLZSCHUH 92B PL B287 381 E. Holzs huh, M. Frits hi, W. Kundig (ZURI)KAWANO 92 PL B275 487 L.H. Kawano et al. (CIT, UCSD, LLL+)MOURAO 92 PL B285 364 A.M. Mourao, J. Pulido, J.P. Ralston (LISB, LISBT+)PDG 92 PR D45 S1 K. Hikasa et al. (KEK, LBL, BOST+)VIDYAKIN 92 JETPL 55 206 G.S. Vidyakin et al. (KIAE)Translated from ZETFP 55 212.ALLEN 91 PR D43 R1 R.C. Allen et al. (UCI, LANL, UMD)DAVIDSON 91 PR D43 2314 S. Davidson, B.A. Campbell, D. Bailey (ALBE+)DESHPANDE 91 PR D43 943 N.G. Deshpande, K.V.L. Sarma (OREG, TATA)DORENBOS... 91 ZPHY C51 142 (erratum)J. Dorenbos h et al. (CHARM Collab.)FULLER 91 PR D43 3136 G.M. Fuller, R.A. Malaney (UCSD)GRANEK 91 IJMP A6 2387 H. Granek, B.H.J. M Kellar (MELB)

765765765765See key on page 601 Lepton Parti le ListingsNeutrino Properties, Number of Neutrino TypesKAWAKAMI 91 PL B256 105 H. Kawakami et al. (INUS, TOHOK, TINT+)KOLB 91 PRL 67 533 E.W. Kolb et al. (FNAL, CHIC)KRAKAUER 91 PR D44 R6 D.A. Krakauer et al. (LAMPF E225 Collab.)LAM 91 PR D44 3345 W.P. Lam, K.W. Ng (AST)ROBERTSON 91 PRL 67 957 R.G.H. Robertson et al. (LASL, LLL)AHRENS 90 PR D41 3297 L.A. Ahrens et al. (BNL, BROW, HIRO+)AVIGNONE 90 PR D41 682 F.T. Avignone, J.I. Collar (SCUC)KRAKAUER 90 PL B252 177 D.A. Krakauer et al. (LAMPF E225 Collab.)RAFFELT 90 PRL 64 2856 G.G. Raelt (MPIM)WALKER 90 PR D41 689 T.P. Walker (HARV)CHUPP 89 PRL 62 505 E.L. Chupp, W.T. Vestrand, C. Reppin (UNH, MPIM)DORENBOS... 89 ZPHY C41 567 J. Dorenbos h et al. (CHARM Collab.)GRIFOLS 89B PR D40 3819 J.A. Grifols, E. Masso (BARC)KOLB 89 PRL 62 509 E.W. Kolb, M.S. Turner (CHIC, FNAL)LOREDO 89 ANYAS 571 601 T.J. Loredo, D.Q. Lamb (CHIC)RAFFELT 89 PR D39 2066 G.G. Raelt (PRIN, UCB)RAFFELT 89B APJ 336 61 G. Raelt, D. Dearborn, J. Silk (UCB, LLL)ALBRECHT 88B PL B202 149 H. Albre ht et al. (ARGUS Collab.)BARBIERI 88 PRL 61 27 R. Barbieri, R.N. Mohapatra (PISA, UMD)BORIS 88 PRL 61 245 (erratum) S.D. Boris et al. (ITEP, ASCI)FUKUGITA 88 PRL 60 879 M. Fukugita et al. (KYOTU, MPIM, UCB)GROTCH 88 ZPHY C39 553 H. Grot h, R.W. Robinett (PSU)RAFFELT 88B PR D37 549 G.G. Raelt, D.S.P. Dearborn (UCB, LLL)SPERGEL 88 PL B200 366 D.N. Spergel, J.N. Bah all (IAS)VONFEILIT... 88 PL B200 580 F. von Feilitzs h, L. Oberauer (MUNT)BARBIELLINI 87 NAT 329 21 G. Barbiellini, G. Co oni (CERN)BORIS 87 PRL 58 2019 S.D. Boris et al. (ITEP, ASCI)Also PRL 61 245 (erratum) S.D. Boris et al. (ITEP, ASCI)BORIS 87B JETPL 45 333 S.D. Boris et al. (ITEP)Translated from ZETFP 45 267.FUKUGITA 87 PR D36 3817 M. Fukugita, S. Yazaki (KYOTU, TOKY)NUSSINOV 87 PR D36 2278 S. Nussinov, Y. Rephaeli (TELA)OBERAUER 87 PL B198 113 L.F. Oberauer, F. von Feilitzs h, R.L. MossbauerSPRINGER 87 PR A35 679 P.T. Springer et al. (LLNL)KETOV 86 JETPL 44 146 S.N. Ketov et al. (KIAE)Translated from ZETFP 44 114.COWSIK 85 PL 151B 62 R. Cowsik (TATA)RAFFELT 85 PR D31 3002 G.G. Raelt (MPIM)BINETRUY 84 PL 134B 174 P. Binetruy, G. Girardi, P. Salati (LAPP)FREESE 84 NP B233 167 K. Freese, D.N. S hramm (CHIC, FNAL)KYULDJIEV 84 NP B243 387 A.V. Kyuldjiev (SOFI)SCHRAMM 84 PL 141B 337 D.N. S hramm, G. Steigman (FNAL, BART)VOGEL 84 PR D30 1505 P. VogelANDERHUB 82 PL 114B 76 H.B. Anderhub et al. (ETH, SIN)OLIVE 82 PR D25 213 K.A. Olive, M.S. Turner (CHIC, UCSB)BERNSTEIN 81 PL 101B 39 J. Bernstein, G. Feinberg (STEV, COLU)FRANK 81 PR D24 2001 J.S. Frank et al. (LASL, YALE, MIT+)MORGAN 81 PL 102B 247 J.A. Morgan (SUSS)FUJIKAWA 80 PRL 45 963 K. Fujikawa, R. Shro k (STON)LUBIMOV 80 PL 94B 266 V.A. Lyubimov et al. (ITEP)STECKER 80 PRL 45 1460 F.W. Ste ker (NASA)COWSIK 79 PR D19 2219 R. Cowsik (TATA)GOLDMAN 79 PR D19 2215 T. Goldman, G.J. Stephenson (LASL)BEG 78 PR D17 1395 M.A.B. Beg, W.J. Mar iano, M. Ruderman (ROCK+)BLIETSCHAU 78 NP B133 205 J. Bliets hau et al. (Gargamelle Collab.)FALK 78 PL 79B 511 S.W. Falk, D.N. S hramm (CHIC)BARNES 77 PRL 38 1049 V.E. Barnes et al. (PURD, ANL)COWSIK 77 PRL 39 784 R. Cowsik (MPIM, TATA)LEE 77C PR D16 1444 B.W. Lee, R.E. Shro k (STON)VYSOTSKY 77 JETPL 26 188 M.I. Vysotsky, A.D. Dolgov, Y.B. Zeldovi h (ITEP)Translated from ZETFP 26 200.BELLOTTI 76 LNC 17 553 E. Bellotti et al. (MILA)SUTHERLAND 76 PR D13 2700 P. Sutherland et al. (PENN, COLU, NYU)SZALAY 76 AA 49 437 A.S. Szalay, G. Marx (EOTV)CLARK 74 PR D9 533 A.R. Clark et al. (LBL)KIM 74 PR D9 3050 J.E. Kim, V.S. Mathur, S. Okubo (ROCH)REINES 74 PRL 32 180 F. Reines, H.W. Sobel, H.S. Gurr (UCI)SZALAY 74 APAH 35 8 A.S. Szalay, G. Marx (EOTV)COWSIK 72 PRL 29 669 R. Cowsik, J. M Clelland (UCB)MARX 72 Nu Conf. Budapest G. Marx, A.S. Szalay (EOTV)GERSHTEIN 66 JETPL 4 120 S.S. Gershtein, Y.B. Zeldovi h (KIAM)Translated from ZETFP 4 189.BERNSTEIN 63 PR 132 1227 J. Bernstein, M. Ruderman, G. Feinberg (NYU+)COWAN 57 PR 107 528 C.L. Cowan, F. Reines (LANL)Number of Neutrino TypesThe neutrinos referred to in this se tion are those of the StandardSU(2)×U(1) Ele troweak Model possibly extended to allow nonzeroneutrino masses. Light neutrinos are those with m < mZ /2. Thelimits are on the number of neutrino mass eigenstates, in luding ν1,ν2, and ν3.

THE NUMBER OF LIGHT NEUTRINO TYPESFROM COLLIDER EXPERIMENTS

Revised March 2008 by D. Karlen (University of Victoria andTRIUMF).

The most precise measurements of the number of light

neutrino types, Nν , come from studies of Z production in e+e−

collisions. The invisible partial width, Γinv, is determined by

subtracting the measured visible partial widths, corresponding

to Z decays into quarks and charged leptons, from the total Z

width. The invisible width is assumed to be due to Nν light

neutrino species each contributing the neutrino partial width

Γν as given by the Standard Model. In order to reduce the

model dependence, the Standard Model value for the ratio of

the neutrino to charged leptonic partial widths, (Γν/Γℓ)SM =

1.991±0.001, is used instead of (Γν)SM to determine the number

of light neutrino types:

Nν =Γinv

Γℓ

(Γℓ

Γν

)

SM

. (1)

The combined result from the four LEP experiments is Nν =

2.984 ± 0.008 [1].

In the past, when only small samples of Z decays had been

recorded by the LEP experiments and by the Mark II at SLC,

the uncertainty in Nν was reduced by using Standard Model

fits to the measured hadronic cross sections at several center-

of-mass energies near the Z resonance. Since this method is

much more dependent on the Standard Model, the approach

described above is favored.

Before the advent of the SLC and LEP, limits on the

number of neutrino generations were placed by experiments at

lower-energy e+e− colliders by measuring the cross section of

the process e+e− → ννγ. The ASP, CELLO, MAC, MARK J,

and VENUS experiments observed a total of 3.9 events above

background [2], leading to a 95% CL limit of Nν < 4.8.

This process has a much larger cross section at center-of-mass

energies near the Z mass and has been measured at LEP by

the ALEPH, DELPHI, L3, and OPAL experiments [3]. These

experiments have observed several thousand such events, and

the combined result is Nν = 3.00 ± 0.08. The same process has

also been measured by the LEP experiments at much higher

center-of-mass energies, between 130 and 208 GeV, in searches

for new physics [4]. Combined with the lower energy data, the

result is Nν = 2.92 ± 0.05.

Experiments at pp colliders also placed limits on Nν by

determining the total Z width from the observed ratio of

W± → ℓ±ν to Z → ℓ+ℓ− events [5]. This involved a calculation

that assumed Standard Model values for the total W width and

the ratio of W and Z leptonic partial widths, and used an

estimate of the ratio of Z to W production cross sections.

Now that the Z width is very precisely known from the LEP

experiments, the approach is now one of those used to determine

the W width.

References

1. ALEPH, DELPHI, L3, OPAL, and SLD Collaborations, andLEP Electroweak Working Group, and SLD ElectroweakGroup, and SLD Heavy Flavour Group, Phys. Reports 427,257 (2006).

2. VENUS: K. Abe et al., Phys. Lett. B232, 431 (1989);ASP: C. Hearty et al., Phys. Rev. D39, 3207 (1989);CELLO: H.J. Behrend et al., Phys. Lett. B215, 186 (1988);MAC: W.T. Ford et al., Phys. Rev. D33, 3472 (1986);MARK J: H. Wu, Ph.D. Thesis, Univ. Hamburg (1986).

3. L3: M. Acciarri et al., Phys. Lett. B431, 199 (1998);DELPHI: P. Abreu et al., Z. Phys. C74, 577 (1997);OPAL: R. Akers et al., Z. Phys. C65, 47 (1995);ALEPH: D. Buskulic et al., Phys. Lett. B313, 520 (1993).

4. DELPHI: J. Abdallah et al., Eur. Phys. J. C38, 395 (2005);L3: P. Achard et al., Phys. Lett. B587, 16 (2004);

766766766766Lepton Parti le ListingsNumber of Neutrino TypesALEPH: A. Heister et al., Eur. Phys. J. C28, 1 (2003);OPAL: G. Abbiendi et al., Eur. Phys. J. C18, 253 (2000).

5. UA1: C. Albajar et al., Phys. Lett. B198, 271 (1987);UA2: R. Ansari et al., Phys. Lett. B186, 440 (1987).Number from e+ e− CollidersNumber from e+ e− CollidersNumber from e+ e− CollidersNumber from e+ e− CollidersNumber of Light ν TypesNumber of Light ν TypesNumber of Light ν TypesNumber of Light ν TypesVALUE DOCUMENT ID TECN2.9840±0.00822.9840±0.00822.9840±0.00822.9840±0.0082 1 LEP-SLC 06 RVUE

• • • We do not use the following data for averages, ts, limits, et . • • •3.00 ±0.05 2 LEP 92 RVUE1Combined t from ALEPH, DELPHI, L3 and OPAL Experiments.2 Simultaneous ts to all measured ross se tion data from all four LEP experiments.Number of Light ν Types from Dire t Measurement of Invisible Z WidthNumber of Light ν Types from Dire t Measurement of Invisible Z WidthNumber of Light ν Types from Dire t Measurement of Invisible Z WidthNumber of Light ν Types from Dire t Measurement of Invisible Z WidthIn the following, the invisible Z width is obtained from studies of single-photon eventsfrom the rea tion e+ e− → ν ν γ. All are obtained from LEP runs in the Eee m range88209 GeV.VALUE DOCUMENT ID TECN COMMENT2.92±0.05 OUR AVERAGE2.92±0.05 OUR AVERAGE2.92±0.05 OUR AVERAGE2.92±0.05 OUR AVERAGE Error in ludes s ale fa tor of 1.2.2.84±0.10±0.14 ABDALLAH 05B DLPH √s = 180209 GeV2.98±0.05±0.04 ACHARD 04E L3 1990-2000 LEP runs2.86±0.09 HEISTER 03C ALEP √s = 189209 GeV2.69±0.13±0.11 ABBIENDI,G 00D OPAL 1998 LEP run2.89±0.32±0.19 ABREU 97J DLPH 19931994 LEP runs3.23±0.16±0.10 AKERS 95C OPAL 19901992 LEP runs2.68±0.20±0.20 BUSKULIC 93L ALEP 19901991 LEP runs

• • • We do not use the following data for averages, ts, limits, et . • • •2.84±0.15±0.14 ABREU 00Z DLPH 19971998 LEP runs3.01±0.08 ACCIARRI 99R L3 19911998 LEP runs3.1 ±0.6 ±0.1 ADAM 96C DLPH √s = 130, 136 GeVLimits from Astrophysi s and CosmologyLimits from Astrophysi s and CosmologyLimits from Astrophysi s and CosmologyLimits from Astrophysi s and CosmologyEe tive Number of Light ν TypesEe tive Number of Light ν TypesEe tive Number of Light ν TypesEe tive Number of Light ν Types(\Light" means < about 1 MeV). The quoted values orrespond to Ne , where Ne= 3.046 in the Standard Model with Nν = 3. See also OLIVE 81. For a review oflimits based on Nu leosynthesis, Supernovae, and also on terrestial experiments, seeDENEGRI 90. Also see \Big-Bang Nu leosynthesis" in this Review.VALUE CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •3.3 ±0.5 95 1 ADE 14 COSM Plan k3.78+0.31

−0.30 2 COSTANZI 14 COSM3.29±0.31 3 HOU 14 COSM< 3.80 95 4 LEISTEDT 14 COSM< 4.10 95 5 MORESCO 12 COSM< 5.79 95 6 XIA 12 COSM< 4.08 95 MANGANO 11 COSM BBN0.9 < Nν < 8.2 7 ICHIKAWA 07 COSM3 < Nν < 7 95 8 CIRELLI 06 COSM2.7 < Nν < 4.6 95 9 HANNESTAD 06 COSM3.6 < Nν < 7.4 95 8 SELJAK 06 COSM< 4.4 10 CYBURT 05 COSM< 3.3 11 BARGER 03C COSM1.4 <Nν < 6.8 12 CROTTY 03 COSM1.9 <Nν < 6.6 12 PIERPAOLI 03 COSM2 < Nν < 4 LISI 99 COSM BBN< 4.3 OLIVE 99 COSM BBN< 4.9 COPI 97 Cosmology< 3.6 HATA 97B High D/H quasar abs.< 4.0 OLIVE 97 BBN; high 4He and 7Li< 4.7 CARDALL 96B COSM High D/H quasar abs.< 3.9 FIELDS 96 COSM BBN; high 4He and 7Li< 4.5 KERNAN 96 COSM High D/H quasar abs.< 3.6 OLIVE 95 BBN; ≥ 3 massless ν

< 3.3 WALKER 91 Cosmology< 3.4 OLIVE 90 Cosmology< 4 YANG 84 Cosmology< 4 YANG 79 Cosmology< 7 STEIGMAN 77 CosmologyPEEBLES 71 Cosmology<16 13 SHVARTSMAN69 CosmologyHOYLE 64 Cosmology

1Fit to the number of neutrino degrees of freedom from Plan k CMB data along withWMAP polarization, high L, and BAO data.2 Fit to the number of neutrinos degrees of freedom from Plan k CMB data along withBAO, shear and luster data.3 Fit based on the SPT-SZ survey ombined with CMB, BAO, and H0 data.4Constrains the number of neutrino degrees of freedom (marginalizing over the total mass)from CMB, CMB lensing, BAO, and galaxy lustering data.5 Limit on the number of light neutrino types from observational Hubble parameter datawith seven-year WMAP data, SPT, and the most re ent estimate of H0. Best t is3.45 ± 0.65.6 Limit on the number of light neutrino types from the CFHTLS ombined with seven-yearWMAP data and a prior on the Hubble parameter. Best t is 4.17+1.62−1.26. Limit isrelaxed to 3.98+2.02

−1.20 when small s ales ae ted by non-linearities are removed.7Constrains the number of neutrino types from re ent CMB and large s ale stru ture data.No priors on other osmologi al parameters are used.8Constrains the number of neutrino types from re ent CMB, large s ale stru ture, Lyman-alpha forest, and SN1a data. The slight preferen e for Nν > 3 omes mostly from theLyman-alpha forest data.9Constrains the number of neutrino types from re ent CMB and large s ale stru ture data.See also HAMANN 07.10 Limit on the number of neutrino types based on 4He and D/H abundan e assuming abaryon density xed to the WMAP data. Limit relaxes to 4.6 if D/H is not used or to5.8 if only D/H and the CMB are used. See also CYBURT 01 and CYBURT 03.11 Limit on the number of neutrino types based on ombination of WMAP data and big-bang nu leosynthesis. The limit from WMAP data alone is 8.3. See also KNELLER 01.Nν ≥ 3 is assumed to ompute the limit.12 95% onden e level range on the number of neutrino avors fromWMAP data ombinedwith other CMB measurements, the 2dfGRS data, and HST data.13 SHVARTSMAN 69 limit inferred from his equations.Number Coupling with Less Than Full Weak StrengthNumber Coupling with Less Than Full Weak StrengthNumber Coupling with Less Than Full Weak StrengthNumber Coupling with Less Than Full Weak StrengthVALUE DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •

<20 1 OLIVE 81C COSM<20 1 STEIGMAN 79 COSM1Limit varies with strength of oupling. See also WALKER 91.REFERENCES FOR Limits on Number of Neutrino TypesREFERENCES FOR Limits on Number of Neutrino TypesREFERENCES FOR Limits on Number of Neutrino TypesREFERENCES FOR Limits on Number of Neutrino TypesADE 14 AA 571 A16 P.A.R. Ade et al. (Plan k Collab.)COSTANZI 14 JCAP 1410 081 M. Costanzi et al. (TRST, TRSTI)HOU 14 APJ 782 74 Z. Hou et al.LEISTEDT 14 PRL 113 041301 B. Leistedt, H.V. Peiris, L. VerdeMORESCO 12 JCAP 1207 053 M. Mores o et al.XIA 12 JCAP 1206 010 J.-Q. Xia et al.MANGANO 11 PL B701 296 G. Mangano, P. Serpi oHAMANN 07 JCAP 0708 021 J. Hamann et al.ICHIKAWA 07 JCAP 0705 007 K. I hikawa, M. Kawasaki, F. TakahashiCIRELLI 06 JCAP 0612 013 M. Cirelli et al.HANNESTAD 06 JCAP 0611 016 S. Hannestad, G. RaeltLEP-SLC 06 PRPL 427 257 ALEPH, DELPHI, L3, OPAL, SLD and working groupsSELJAK 06 JCAP 0610 014 U. Seljak, A. Slosar, P. M DonaldABDALLAH 05B EPJ C38 395 J. Abdallah et al. (DELPHI Collab.)CYBURT 05 ASP 23 313 R.H. Cyburt et al.ACHARD 04E PL B587 16 P. A hard et al. (L3 Collab.)BARGER 03C PL B566 8 V. Barger et al.CROTTY 03 PR D67 123005 P. Crotty, J. Lesgourgues, S. PastorCYBURT 03 PL B567 227 R.H. Cyburt, B.D. Fields, K.A. OliveHEISTER 03C EPJ C28 1 A. Heister et al. (ALEPH Collab.)PIERPAOLI 03 MNRAS 342 L63 E. PierpaoliCYBURT 01 ASP 17 87 R.H. Cyburt, B.D. Fields, K.A. OliveKNELLER 01 PR D64 123506 J.P. Kneller et al.ABBIENDI,G 00D EPJ C18 253 G. Abbiendi et al. (OPAL Collab.)ABREU 00Z EPJ C17 53 P. Abreu et al. (DELPHI Collab.)ACCIARRI 99R PL B470 268 M. A iarri et al. (L3 Collab.)LISI 99 PR D59 123520 E. Lisi, S. Sarkar, F.L. VillanteOLIVE 99 ASP 11 403 K.A. Olive, D. ThomasABREU 97J ZPHY C74 577 P. Abreu et al. (DELPHI Collab.)COPI 97 PR D55 3389 C.J. Copi, D.N. S hramm, M.S. Turner (CHIC)HATA 97B PR D55 540 N. Hata et al. (OSU, PENN)OLIVE 97 ASP 7 27 K.A. Olive, D. Thomas (MINN, FLOR)ADAM 96C PL B380 471 W. Adam et al. (DELPHI Collab.)CARDALL 96B APJ 472 435 C.Y. Cardall, G.M. Fuller (UCSD)FIELDS 96 New Ast 1 77 B.D. Fields et al. (NDAM, CERN, MINN+)KERNAN 96 PR D54 3681 P.S. Kernan, S. Sarkar (CASE, OXFTP)AKERS 95C ZPHY C65 47 R. Akers et al. (OPAL Collab.)OLIVE 95 PL B354 357 K.A. Olive, G. Steigman (MINN, OSU)BUSKULIC 93L PL B313 520 D. Buskuli et al. (ALEPH Collab.)LEP 92 PL B276 247 LEP Collabs. (LEP, ALEPH, DELPHI, L3, OPAL)WALKER 91 APJ 376 51 T.P. Walker et al. (HSCA, OSU, CHIC+)DENEGRI 90 RMP 62 1 D. Denegri, B. Sadoulet, M. Spiro (CERN, UCB+)OLIVE 90 PL B236 454 K.A. Olive et al. (MINN, CHIC, OSU+)YANG 84 APJ 281 493 J. Yang et al. (CHIC, BART)OLIVE 81 APJ 246 557 K.A. Olive et al. (CHIC, BART)OLIVE 81C NP B180 497 K.A. Olive, D.N. S hramm, G. Steigman (EFI+)STEIGMAN 79 PRL 43 239 G. Steigman, K.A. Olive, D.N. S hramm (BART+)YANG 79 APJ 227 697 J. Yang et al. (CHIC, YALE, UVA)STEIGMAN 77 PL 66B 202 G. Steigman, D.N. S hramm, J.E. Gunn (YALE, CHIC+)PEEBLES 71 Physi al Cosmology P.Z. Peebles (PRIN)Prin eton Univ. Press (1971)SHVARTSMAN 69 JETPL 9 184 V.F. Shvartsman (MOSU)Translated from ZETFP 9 315.HOYLE 64 NAT 203 1108 F. Hoyle, R.J. Tayler (CAMB)

767767767767See key on page 601 Lepton Parti le ListingsDouble-β De ayDouble-β De ayOMITTED FROM SUMMARY TABLENEUTRINOLESS DOUBLE-β DECAY

Revised August 2015 by P. Vogel (Caltech) and A. Piepke(University of Alabama).

Observation of neutrinoless double-beta (0νββ) decay would

signal violation of total lepton number conservation. The pro-

cess can be mediated by an exchange of a light Majorana

neutrino, or by an exchange of other particles. However, the

existence of 0νββ-decay requires Majorana neutrino mass, no

matter what the actual mechanism is. As long as only a limit

on the lifetime is available, limits on the effective Majorana

neutrino mass, on the lepton-number violating right-handed

current or other possible mechanisms mediating 0νββ-decay

can be obtained, independently of the actual mechanism by as-

suming that one of these “new physics” possibilities dominates.

These limits are listed in the next three tables, together with a

claimed 0νββ-decay signal reported by part of the Heidelberg-

Moscow collaboration. There is tension between that claim and

several recent experiments which did not find evidence for 0νββ

decay.

In the following we assume that the exchange of light

Majorana neutrinos (mνi≤ 10 MeV) contributes dominantly

to the decay rate. Besides a dependence on the phase space

(G0ν) and the nuclear matrix element (M0ν), the observable

0νββ-decay rate is proportional to the square of the effective

Majorana mass 〈mββ〉, (T 0ν1/2)

−1 = G0ν · |M 0ν|2 · 〈mββ〉2, with

〈mββ〉2 = |∑

i U2eimνi

|2. The sum contains, in general, com-

plex CP-phases in U2ei, i.e., cancellations may occur. For three

neutrino flavors, there are three physical phases for Majorana

neutrinos. There is only one phase if neutrinos are Dirac parti-

cles. The two additional Majorana phase differences affect only

processes to which lepton-number-changing amplitudes con-

tribute. Given the general 3 × 3 mixing matrix for Majorana

neutrinos, one can construct other analogous lepton number

violating quantities, 〈mℓℓ′〉 =∑

i UℓiUℓ′imνi(l or l′ 6= e). How-

ever, these are currently much less constrained than 〈mββ〉.Nuclear structure calculations are needed to deduce 〈mββ〉

from the decay rate. While G0ν can be calculated, the compu-

tation of M0ν is subject to uncertainty. Comparing different

nuclear model evaluations indicates a factor ∼2 to 3 spread

in the calculated nuclear matrix elements. In addition, if the

effective value of the axial current coupling constant gA in

nuclei is substantially smaller than its single nucleon value

gA = 1.2723 ± 0.0023, the decay rate might be further reduced.

The particle physics quantities to be determined are thus nu-

clear model-dependent, so the half-life measurements are listed

first. Where possible, we reference the nuclear matrix elements

used in the subsequent analysis. Since rates for the more con-

ventional 2νββ decay serve to calibrate some nuclear models

(e.g. QRPA-based calculations), results for this process are

also given.

Oscillation experiments utilizing atmospheric-, accelerator-,

solar-, and reactor-produced neutrinos and anti-neutrinos yield

strong evidence that at least some neutrinos are massive.

However, these findings shed no light on the mass hierarchy

(i.e., on the sign of ∆m231), the absolute neutrino mass values

or the properties of neutrinos under CPT-conjugation (Dirac or

Majorana).

All confirmed oscillation experiments can be consistently de-

scribed using three interacting neutrino species with two mass

splittings and three mixing angles. Full three flavor analyses

such as e.g. [1] yield: |∆m231| = 2.48+0.05

−0.07 (2.38+0.05−0.06) × 10−3

eV2 and sin2 θ23 = 0.567+0.032−0.124 (0.573+0.025

−0.039) for the param-

eters observed in atmospheric and accelerator experiments,

where the values correspond to the normal (inverted) hi-

erarchies. Observations of solar νe and reactor νe lead to

∆m221 = 7.60+0.19

−0.18 × 10−5 eV2 and sin2 θ12 = 0.323 ± 0.016.

The investigation of reactor νe at ∼1.5 km baseline shows that

electron type neutrinos couple only weakly to the third mass

eigenstate with sin2 θ13 = 0.0226 ± 0.0012 (0.0229 ± 0.0012).

(All errors correspond to 1σ.)

Based on the 3-neutrino analysis: 〈mββ〉2 = | cos2 θ13

cos2 θ12m1+ei∆α21 cos2 θ13 sin2 θ12m2+ei∆α31 sin2 θ13m3|2, with

∆α21, ∆α31 denoting the physically relevant Majorana CP-

phase differences (possible Dirac phase δ is absorbed in these

∆α). Given the present knowledge of the neutrino oscillation

parameters one can derive the relation between the effective

Majorana mass and the mass of the lightest neutrino, as illus-

trated in the left panel of Fig. 1. The three mass hierarchies

allowed by the oscillation data: normal (m1 < m2 < m3), in-

verted (m3 < m1 < m2), and degenerate (m1 ≈ m2 ≈ m3),

result in different projections. The width of the innermost

hatched bands reflects the uncertainty introduced by the un-

known Majorana and Dirac phases. If the experimental errors

of the oscillation parameters are taken into account, then the

allowed areas are widened as shown by the outer bands of Fig. 1.

Because of the overlap of the different mass scenarios a measure-

ment of 〈mββ〉 in the degenerate or inversely hierarchical ranges

would not determine the hierarchy. The middle panel of Fig. 1

depicts the relation of 〈mββ〉 with the summed neutrino mass

mtot = m1 + m2 + m3, constrained by observational cosmology.

The oscillation data thus allow to test whether observed values

of 〈mββ〉 and mtot are consistent within the 3 neutrino frame-

work and the light neutrino-exchange dominance assumption.

The right hand panel of Fig. 1, finally, shows 〈mββ〉 as a

function of the kinematical mass 〈mβ〉 = [Σ|Uei|2m2νi

]1/2 deter-

mined through the analysis of the electron energy distribution

in low energy beta decays. The rather large intrinsic width of

the ββ-decay constraint essentially does not allow to positively

identify the inverted hierarchy, and thus the sign of ∆m231, even

in combination with these other observables. Naturally, if the

value of 〈mββ〉 ≤ 0.01 eV, but non-zero is ever established then

normal hierarchy becomes the only possible scenario.

768768768768LeptonParti le ListingsDouble-β De ay

Figure 1: The left panel shows the depen-dence of 〈mββ〉 on the absolute mass of the light-est neutrino mmin. The middle panel shows〈mββ〉 as a function of the summed neutrinomass mtot, while the right panel depicts 〈mββ〉as a function of the mass 〈mβ〉. In all panelsthe width of the hatched areas is due to theunknown Majorana phases and thus irreducible.The allowed areas given by the solid lines areobtained by taking into account the errors ofthe oscillation parameters (at 90% confidencelevel [1]) . The two sets of solid lines corre-spond to the normal (blue) and inverted(red)hierarchies. These sets merge into each otherfor 〈mββ〉 ≥ 0.1 eV, which corresponds to thedegenerate mass pattern.

It should be noted that systematic uncertainties of the

nuclear matrix elements are not folded into the mass projections

shown in Fig. 1. Taking this additional uncertainty into account

would further widen the allowed areas. The uncertainties in

oscillation parameters affect the width of the allowed bands in

an asymmetric manner, as shown in Fig. 1. For example, for

the degenerate mass pattern (〈mββ〉 ≥ 0.1 eV) the upper edge

is simply 〈mββ〉 ∼ m, where m is the common mass of the

degenerate multiplet, independent of the oscillation parameters,

while the lower edge is m cos(2θ12). Similar arguments explain

the other features of Fig. 1. The plots in Fig. 1 are based on a

3-neutrino analysis. If it turns out that additional, i.e. sterile

light neutrinos exist, the allowed regions would be modified

substantially.

If the neutrinoless double-beta decay is observed, it will be

possible to fix a range of absolute values of the masses mνi.

Unlike the direct neutrino mass measurements, however, a limit

on 〈mββ〉 does not allow one to constrain the individual mass

values mνieven when the mass differences ∆m2 are known.

Neutrino oscillation data imply, for the first time, the

existence of a lower limit ∼ 0.014 eV for the Majorana neutrino

mass for the inverted hierarchy mass pattern while 〈mββ〉 could,

by fine tuning, vanish in the case of the normal mass hierarchy.

Several new double beta searches have been proposed to probe

the interesting 〈mββ〉 mass range, with the prospect of full

coverage of the inverted mass hierarchy region within the next

decade.

The 0νββ decay mechanism discussed so far is not the

only way in which the decay can occur. Numerous other

possible scenarios have been proposed, however, all of them

requiring new physics. It will be a challenging task to decide

which mechanism was responsible once 0νββ decay is observed.

LHC experiments may reveal corresponding signatures for new

physics of lepton number violation. If lepton-number-violating

right-handed current weak interactions exist, their strength can

be characterized by the phenomenological coupling constants η

and λ (η describes the coupling between the right-handed lepton

current and left-handed quark current while λ describes the cou-

pling when both currents are right-handed). The 0νββ decay

rate then depends on 〈η〉 = η∑

i UeiVei and 〈λ〉 = λ∑

i UeiVei

that vanish for massless or unmixed neutrinos (Vℓj is a matrix

analogous to Uℓj but describing the mixing with the hypo-

thetical right-handed neutrinos). The observation of the single

electron spectra could, in principle, allow to distinguish this

mechanism of 0νββ from the light Majorana neutrino exchange

driven mode. The limits on 〈η〉 and 〈λ〉 are listed in a sepa-

rate table. The reader is cautioned that a number of earlier

experiments did not distinguish between η and λ. In addition,

see the section on Majoron searches for additional limits set by

these experiments.

References

1. D.V. Forero, M. Tortola, and J.W.F. Valle, Phys. Rev.D90, 093006 (2014) and private communication with M.Tortola.Half-life Measurements and Limits for Double-β De ayHalf-life Measurements and Limits for Double-β De ayHalf-life Measurements and Limits for Double-β De ayHalf-life Measurements and Limits for Double-β De ayIn most ases the transitions (Z,A) → (Z+2,A) + 2e− + (0 or 2) νe to the 0+ groundstate of the nal nu leus are listed. However, we also list transitions that in rease thenu lear harge (2e+, e+/EC and ECEC) and transitions to ex ited states of the nalnu lei (0+

i, 2+, and 2+

i). In the following Listings, only best or omparable limits orlifetimes for ea h isotope are reported and only those with T1/2 > 1020 years that arerelevant for parti le physi s. For 2ν de ay, whi h is well established, only measuredhalf-lives with the smallest (or omparable) error for ea h nu leus are reported.t1/2(1021 yr) CL% ISOTOPE TRANSITION METHOD DOCUMENT ID


> 26000 90 136Xe 0ν g.s.→ 2+1 KamLAND-Zen 1 ASAKURA 16> 26000 90 136Xe 0ν g.s.→ 2+2 KamLAND-Zen 2 ASAKURA 16> 24000 90 136Xe 0ν g.s.→ 0+1 KamLAND-Zen 3 ASAKURA 161.926 ± 0.094 76Ge 2ν g.s.→ g.s. GERDA 4 AGOSTINI 15A> 4000 90 130Te 0ν g.s.→ g.s. CUORE 5 ALFONSO 15(6.93 ± 0.04) × 10−3 100Mo 2ν NEMO-3 6 ARNOLD 15> 1100 90 100Mo 0ν NEMO-3 7 ARNOLD 152.165 ± 0.016 ± 0.059 136Xe 2ν g.s.→ g.s. EXO-200 8 ALBERT 14> 11000 90 136Xe 0ν g.s.→ g.s. EXO-200 9 ALBERT 14B> 1100 90 100Mo 0ν ⟨m⟩-driven NEMO-3 10 ARNOLD 14

769769769769See key on page 601 Lepton Parti le ListingsDouble-β De ay> 600 90 100Mo 0ν ⟨

λ⟩-driven NEMO-3 11 ARNOLD 14

> 1000 90 100Mo 0ν ⟨η⟩-driven NEMO-3 12 ARNOLD 140.107+0.046

−0.026 150Nd 0ν+2ν 0+→ 0+1 γ in Ge det. 13 KIDD 14> 21000 90 76Ge 0ν g.s.→ g.s. GERDA 14 AGOSTINI 13A> 0.13 90 96Ru 0ν+2ν 2β+, g.s Ge ounting 15 BELLI 13A> 19000 90 136Xe 0ν g.s.→ g.s. KamLAND-Zen 16 GANDO 13A9.2+5.5

−2.6 ± 1.3 78Kr 2ν2K g.s.→ g.s. BAKSAN 17 GAVRILYAK 13> 5.4 90 78Kr 0ν2K g.s.→ 2+ BAKSAN 18 GAVRILYAK 13> 940 90 130Te 0ν 0+ → 0+1 CUORICINO 19 ANDREOTTI 12> 1.0 90 106Cd 0ν ECEC, g.s. 106CdWO4 s int.20 BELLI 12A> 2.2 90 106Cd 0ν β+EC, g.s. 106CdWO4 s int.21 BELLI 12A> 1.2 90 106Cd 0ν 2β+, g.s. 106CdWO4 s int.22 BELLI 12A2.38 ± 0.02 ± 0.14 136Xe 2ν g.s.→ g.s. KamLAND-Zen 23 GANDO 12A0.7 ± 0.09 ± 0.11 130Te 2ν NEMO-3 24 ARNOLD 11> 130 90 130Te 0ν NEMO-3 25 ARNOLD 11> 1.3 90 112Sn 0ν 0+→ 0+3 γ Ge det. 26 BARABASH 11> 0.69 90 112Sn 0ν 0+→ 0+2 γ Ge det. 27 BARABASH 11> 1.3 90 112Sn 0ν 0+→ 0+1 γ Ge det. 28 BARABASH 11> 1.06 90 112Sn 0ν γ Ge det. 29 BARABASH 11(2.8 ± 0.1 ± 0.3)E-2 116Cd 2ν NEMO-3 30 BARABASH 11A(4.4+0.5

−0.4 ± 0.4)E-2 48Ca 2ν NEMO-3 31,32 BARABASH 11A(69 ± 9 ± 10)E-2 130Te 2ν NEMO-3 32,33 BARABASH 11A> 360 90 82Se 0ν NEMO-3 32,34 BARABASH 11A> 100 90 130Te 0ν NEMO-3 32,35 BARABASH 11A> 16 90 116Cd 0ν NEMO-3 32,36 BARABASH 11A> 0.32 90 64Zn 0ν ECEC, g.s. ZnWO4 s int. 37 BELLI 11D> 0.85 90 64Zn 0ν β+EC, g.s. ZnWO4 s int. 37 BELLI 11D> 0.11 90 106Cd 0ν 0+→ 4+ TGV2 det. 38 RUKHADZE 11(2.35 ± 0.14 ± 0.16)E-296Zr 2ν NEMO-3 39 ARGYRIADES 10> 9.2 90 96Zr 0ν NEMO-3 40 ARGYRIADES 10> 0.22 90 96Zr 0ν 0+→ 0+1 NEMO-3 41 ARGYRIADES 100.69+0.10

−0.08 ± 0.07 100Mo 2ν 0+ → 0+1 Ge oin . 42 BELLI 10> 18.0 90 150Nd 0ν NEMO-3 43 ARGYRIADES 09(9.11+0.25

−0.22 ± 0.63)E-3 150Nd 2ν NEMO-3 44 ARGYRIADES 09> 0.43 90 64Zn 0ν β+EC ZnW04 s int. 45 BELLI 09A> 0.11 90 64Zn 0ν ECEC ZnW04 s int. 46 BELLI 09A0.55+0.12

−0.09 100Mo 2ν+0ν 0+ → 0+1 Ge oin iden e 47 KIDD 09> 0.22 90 64Zn 0ν ZnWO4 s int. 48 BELLI 08> 1.1 90 114Cd 0ν 2β CdWO4 s int. 49 BELLI 08B> 58 90 48Ca 0ν CaF2 s int. 50 UMEHARA 080.57+0.13

−0.09 ± 0.08 100Mo 2ν 0+ → 0+1 NEMO-3 51 ARNOLD 07> 89 90 100Mo 0ν 0+ → 0+1 NEMO-3 52 ARNOLD 07> 160 90 100Mo 0ν 0+ → 2+ NEMO-3 53 ARNOLD 0722300+4400

−3100 76Ge 0ν Enri hed HPGe 54 KLAPDOR-K... 06A> 1800 90 130Te 0ν Cryog. det. 55 ARNABOLDI 05> 100 90 82Se 0ν NEMO-3 56 ARNOLD 05A(9.6 ± 0.3 ± 1.0)E-2 82Se 2ν NEMO-3 57 ARNOLD 05A> 140 90 82Se 0ν NEMO-3 58 ARNOLD 040.14+0.04

−0.02 ± 0.03 150Nd 0ν+2ν 0+→ 0+1 γ in Ge det. 59 BARABASH 04> 31 90 130Te 0ν 0+→ 2+ Cryog. det. 60 ARNABOLDI 03> 110 90 128Te 0ν Cryog. det. 61 ARNABOLDI 03(0.029+0.004

−0.003) 116Cd 2ν 116CdWO4 s int.62 DANEVICH 03> 170 90 116Cd 0ν 116CdWO4 s int.63 DANEVICH 03> 29 90 116Cd 0ν 0+→ 2+ 116CdWO4 s int.64 DANEVICH 03> 14 90 116Cd 0ν 0+→ 0+1 116CdWO4 s int.65 DANEVICH 03> 6 90 116Cd 0ν 0+→ 0+2 116CdWO4 s int.66 DANEVICH 03> 1.1 90 186W 0ν CdWO4 s int. 67 DANEVICH 03> 1.1 90 186W 0ν 0+→ 2+ CdWO4 s int. 68 DANEVICH 03>15700 90 76Ge 0ν Enri hed HPGe 69 AALSETH 02B> 58 90 134Xe 0ν Liquid Xe S int. 70 BERNABEI 02D> 1.3 90 160Gd 0ν Gd2SiO5:Ce 71 DANEVICH 01> 1.3 90 160Gd 0ν 0+→ 2+ Gd2SiO5:Ce 72 DANEVICH 01> 19000 90 76Ge 0ν Enri hed HPGe 73 KLAPDOR-K... 01(9.4 ± 3.2)E-3 96Zr 0ν+2ν Geo hem 74 WIESER 010.042+0.033

−0.013 48Ca 2ν Ge spe trometer 75 BRUDANIN 000.021+0.008−0.004 ± 0.002 96Zr 2ν NEMO-2 76 ARNOLD 99

> 2.8 90 82Se 0ν 0+ → 2+ NEMO-2 77 ARNOLD 98(6.75+0.37−0.42 ± 0.68)E-3 150Nd 2ν TPC 78 DESILVA 970.043+0.024−0.011 ± 0.014 48Ca 2ν TPC 79 BALYSH 960.026+0.009−0.005 116Cd 2ν 0+ → 0+ ELEGANT IV EJIRI 957200 ± 400 128Te 0ν+2ν Geo hem 80 BERNATOW... 922.0 ± 0.6 238U 0ν+2ν Radio hem 81 TURKEVICH 911800 ± 700 128Te 0ν+2ν Geo hem. 82 LIN 88B

1ASAKURA 16 use the KamLAND-Zen liquid s intillator alorimeter (136Xe 89.5 kg yr)to pla e a limit on the 0νββ-de ay into the rst ex ited state of the daughter nu lide.2ASAKURA 16 use the KamLAND-Zen liquid s intillator alorimeter (136Xe 89.5 kg yr)to pla e a limit on the 0νββ-de ay into the se ond ex ited state of the daughter nu lide.3ASAKURA 16 use the KamLAND-Zen liquid s intillator alorimeter (136Xe 89.5 kg yr)to pla e a limit on the 0νββ-de ay into the third ex ited state of the daughter nu lide.4AGOSTINI 15A use 17.9 kg yr exposure of the GERDA alorimeter to derive an improvedmeasurement of the 2νββ de ay half life of 76Ge.5ALFONSO 15 use the ombined exposure of the high resolution CUORICINO (19.75 kgyr) and CUORE-0 (9.8 kg yr) bolometers to onstru t a Bayesian limit on the 0νββde ay half life of 130Te.6ARNOLD 15 use the NEMO-3 tra king alorimeter with 34.3 kg yr exposure to determinethe 2νββ-half life of 100Mo. Supersedes ARNOLD 05A and ARNOLD 04.7ARNOLD 15 use the NEMO-3 tra king alorimeter with 34.3 kg yr exposure to determinethe limit of 0νββ-half life of 100Mo. Supersedes ARNOLD 2005A and BARABASH 11A.8ALBERT 14 use the EXO-200 tra king dete tor for a re-measurement of the 2νββ-halflife of 136Xe. A nu lear matrix element of 0.0218 ± 0.0003 MeV−1 is derived from thisdata. Supersedes ACKERMAN 11.9ALBERT 14B use 100 kg yr of exposure of the EXO-200 tra king alorimeter to pla e alower limit on the 0νββ-half life of 136Xe. Supersedes AUGER 12.10ARNOLD 14 use 34.7 kg yr of exposure of the NEMO-3 tra king alorimeter to derivea limit on the ⟨m⟩-driven (light neutrino mass) 0νββ-half life of 100Mo. SupersedesBARABASH 11A.11ARNOLD 14 use 34.7 kg yr of exposure of the NEMO-3 tra king alorimeter to derivea limit on the ⟨λ⟩-driven (right handed quark and lepton urrents) 0νββ-half life of100Mo.12ARNOLD 14 use 34.7 kg yr of exposure of the NEMO-3 tra king alorimeter to derive alimit on the ⟨

η⟩-driven (right handed quark urrent) 0νββ-half life of 100Mo.13KIDD 14 utilize two undergraound Ge dete tors to determine the in lusive double betade ay rate to the rst ex ited 0+1 state using γ-γ oin iden es.14AGOSTINI 13A use 21.6 kg yr of data, olle ted with GERDA dete tor array, to pla e alower limit on the 0νββ-half life of 76Ge. This result is in tension with the eviden e for0νββ-de ay reported in KLAPDOR-KLEINGROTHAUS 06A. This half-life limit ex eedsthe limit reported in KLAPDOR-KLEINGROTHAUS 01.15BELLI 13A use an underground Ge dete tor to sear h for the 2β+-de ay of 96Ru viathe intensity of the annihilation peak. This method annot distinguish two from zeroneutrino de ay.16GANDO 13A use the KamLAND dete tor to sear h for 0νββ-de ay of 136Xe based onan exposure of 89.5 kg yr. This result is in tension with the eviden e of 0νββ reportedin KLAPDOR-KLEINGROTHAUS 06A and earier referen es to that work. SupersedesGANDO 12A and is more sensitive than BERNABEI 02D.17GAVRILYAK 13 use a proportional ounter lled with Kr gas to sear h for the 2ν2Kde ay of 78Kr. Data with the enri hed and depleted Kr were used to determine signaland ba kground. A 2.5σ ex ess of events obtained with the enri hed sample is interpretedas an indi ation for the presen e of this de ay.18GAVRILYAK 13 use a proportional ounter lled with Kr gas to sear h for the 0ν2Kde ay of 78Kr into 2828 keV ex ited state of 78Se. This transition ould be subje t toresonant rate enhan ement. Data obtained with the enri hed and depleted Kr were usedto determine signal and ba kground.19ANDREOTTI 12 use high resolution TeO2 bolometri alorimeter to sear h for the 0νββde ay of 130Te leading to the ex ited 01+ state at 1793.5 keV.20BELLI 12A use 106CdWO4 215 g rystal s intillator to sear h for various ββ de aymodes. The limit for the ECEC mode is derived from the t to the ba kground spe trumin the 1.83.2 MeV energy interval in the run of 6590 hours. The same analysis providesseveral limits (∼ 25× 1020 years) for the ECEC mode leading to the ex ited 0+ and2+ states. Also a similar size limits for the possible resonan e pro ess populating statesat 2718 keV, 2741 keV, and 2748 keV were obtained.21BELLI 12A use 106CdWO4 215 g rystal s intillator to sear h for various ββ de ay modes.The limit for the ECβ+ mode is derived from the t to the ba kground spe trum in the2.03.0 MeV energy interval in the run of 6590 hours. The same analysis provides severallimits (∼ 0.51.3 × 1021 years) for the ECβ+ mode leading to the ex ited 0+ and 2+states.22BELLI 12A use 106CdWO4 215 g rystal s intillator to sear h for various ββ de ay modes.The limit for the β+β+ mode is derived from the t to the ba kground spe trum in the0.762.8 MeV energy interval in the run of 6590 hours. The same analysis provides thelimit (1.2× 1021 years) for the β+β+ mode leading to the rst ex ited 2+ state.23GANDO 12A use a modi ation of the existing KamLAND dete tor. The ββ de aysour e/dete tor is 13 tons of enri hed 136Xe-loaded s intillator ontained in an innerballoon. The 2νββ de ay rate is derived from the t to the spe trum between 0.5 and4.8 MeV. This result is in agreement with ACKERMAN 11.24ARNOLD 11 use enri hed 130Te in the NEMO-3 dete tor to measure the 2ν ββ de ayrate. This result is in agreement with, but more a urate than ARNABOLDI 03.25ARNOLD 11 use the NEMO-3 dete tor to obtain a limit for the 0ν ββ de ay.This resultis less signi ant than ARNABOLDI 05.26BARABASH 11 use 100 g of enri hed 112Sn to determine a limit for the ECEC 0νββde ay to the 0+3 state of 112Cd by sear hing for the de-ex itation γ with a Ge dete tor.This de ay mode is a andidate for resonant rate enhan ement.27BARABASH 11 use 100 g of enri hed 112Sn to determine a limit for the ECEC 0νββde ay to the 0+2 state of 112Cd by sear hing for the de-ex itation γ with a Ge dete tor.28BARABASH 11 use 100 g of enri hed 112Sn to determine a limit for the ECEC 0νββde ay to the 0+1 state of 112Cd by sear hing for the de-ex itation γ with a Ge dete tor.29BARABASH 11 use 100 g of enri hed 112Sn to determine a limit for the ECEC 0νββde ay to the ground state of 112Cd by sear hing for the de-ex itation γ with a Gedete tor.

770770770770LeptonParti le ListingsDouble-β De ay30Supersedes DANEVICH 03 and ARNOLD 96.31 Supersedes BRUDANIN 00 and BALYSH 96.32BARABASH 11A use the NEMO-3 dete tor to measure 2νββ rates and pla e limits on0νββ half lives for various nu lides.33 Supersedes ARNABOLDI 03.34 Supersedes ARNOLD 05A, ARNOLD 04, ARNOLD 98, and ELLIOTT 92.35 Less restri tive than ARNABOLDI 08.36 Less restri tive than DANEVICH 03.37BELLI 11D use ZnWO4 s intillator alorimeters to sear h for various ββ de ay modes of64Zn, 70Zn, 180W, and 186W.38RUKHADZE 11 uses 13.6 g of enri hed 106Cd to sear h for the neutrinoless ECEC de ayinto an ex ited state of 106Pd and its hara teristi γ-radiation using the TGV2 dete tor.This de ay mode is a andidate for resonant rate enhan ement, however, hindered bythe large spin dieren e.39ARGYRIADES 10 use 9.4 ± 0.2 g of 96Zr in NEMO-3 dete tor and identify its 2νββde ay. The result is in agreement and supersedes ARNOLD 99.40ARGYRIADES 10 use 9.4 ± 0.2 g of 96Zr in NEMO-3 dete tor and obtain a limit of the0νββ de ay. The result is in agreement and supersedes ARNOLD 99.41ARGYRIADES 10 use 9.4 ± 0.2 g of 96Zr in NEMO-3 dete tor and obtain a limit of the0νββ de ay into the rst ex ited 0+1 state in 96Mo.42BELLI 10 use enri hed 100Mo with 4 HP Ge dete tors to re ord the 590.8 and 539.5 keVγ rays from the de ay of the 0+1 state in 100Ru both in singles and oin iden es. Thisresult onrms the measurement of KIDD 09 and ARNOLD 07 and supersedes them.43ARGYRIADES 09 use the NEMO-3 tra king alorimeter ontaining 36.5 g of 150Nd,a total exposure of 924.7 days, to derive a limit for the 0νββ half-life. SupersedesDESILVA 97.44ARGYRIADES 09 use the NEMO-3 tra king alorimeter ontaining 36.5 g of 150Nd, atotal exposure of 924.7 days, to determine the value of the 2νββ half-life. This result isin marginal agreement, but has somewhat smaller error bars, than DESILVA 97.45BELLI 09A use ZnWO4 s intillating rystals to sear h for various modes of ββ de ay.This work improves the limits for dierent modes of 64Zn de ay into the ground stateof 64Ni, in this ase for the 0νβ+EC mode. Supersedes BELLI 08.46BELLI 09A use ZnWO4 s intillating rystals to sear h for various modes of ββ de ay.This work improves the limits for dierent modes of 64Zn de ay into the ground stateof 64Ni, in this ase for the 0νββ ECEC mode. Supersedes BELLI 08.47KIDD 09 ombine past and new data with an improved oin iden e dete tion eÆ ien ydetermination. The result agrees with ARNOLD 95. Supersedes DEBRAECKELEER 01and BARABASH 95.48BELLI 08 use ZnWO4 s intillation alorimeter to sear h for neutrinoless β+ plus ele tron apture de ay of 64Zn. The hal ife limit for the 2νββ mode is 2.1× 1020 years.49BELLI 08B use CdWO4 s intillation alorimeter to sear h for 0νββ de ay of 114Cd.50UMEHARA 08 use CaF2 s intillation alorimeter to sear h for double beta de ay of48Ca. Limit is signi antly more stringent than quoted sensitivity: 18 × 1021 years.51 First ex lusive measurement of 2ν-de ay to the rst ex ited 0+1 -state of daughter nu leus.ARNOLD 07 use the NEMO-3 tra king alorimeter to dete t all parti les emitted in de ay.Result agrees with the in lusive (0ν + 2ν) measurement of DEBRAECKELEER 01.52 Limit on 0ν-de ay to the rst ex ited 0+1 -state of daughter nu leus using NEMO-3tra king alorimeter. Supersedes DASSIE 95.53 Limit on 0ν-de ay to the rst ex ited 2+-state of daughter nu leus using NEMO-3tra king alorimeter.54KLAPDOR-KLEINGROTHAUS 06A present re-analysis of data originally published inKLAPDOR-KLEINGROTHAUS 04A. Modied pulse shape analysis leads the authors to laim improved 6σ statisti al eviden e for observation of 0ν-de ay, ompared to 4.2σin KLAPDOR-KLEINGROTHAUS 04A. Analysis of the systemati un ertainty is notpresented. This re-analysis is disputed in AGOSTINI 13A and SCHWINGENHEUER 13.55 Supersedes ARNABOLDI 04. Bolometri TeO2 dete tor array CUORICINO is used forhigh resolution sear h for 0νββ de ay. The half-life limit is derived from 3.09 kg yr130Te exposure.56NEMO-3 tra king alorimeter is used in ARNOLD 05A to pla e limit on 0ν ββ half-lifeof 82Se. Dete tor ontains 0.93 kg of enri hed 82Se. Supersedes ARNOLD 04.57ARNOLD 05A use the NEMO-3 tra king dete tor to determine the 2ν ββ half-life of82Se with high statisti s and low ba kground (389 days of data taking). SupersedesARNOLD 04.58ARNOLD 04 use the NEMO-3 tra king dete tor to determine the limit for 0νββ hal ifeof 82Se. This represents an improvement, by a fa tor of ∼ 10, when ompared withELLIOTT 92. It supersedes the limit of ARNOLD 98 for this de ay using NEMO-2.59BARABASH 04 perform an in lusive measurement of the ββ de ay of 150Nd into therst ex ited (0+1 ) state of 150Sm. Gamma radiation emitted in de ay of the ex itedstate is dete ted.60De ay into rst ex ited state of daughter nu leus.61 Supersedes ALESSANDRELLO 00. Array of TeO2 rystals in high resolution ryogeni alorimeter. Some enri hed in 128Te. Ground state to ground state de ay.62Calorimetri measurement of 2νββ ground state de ay of 116Cd using enri hed CdWO4s intillators. Agrees with EJIRI 95 and ARNOLD 96. Supersedes DANEVICH 00.63 Limit on 0νββ de ay of 116Cd using enri hed CdWO4 s intillators. SupersedesDANEVICH 00.64 Limit on 0νββ de ay of 116Cd into rst ex ited 2+ state of daughter nu leus usingenri hed CdWO4 s intillators. Supersedes DANEVICH 00.

65 Limit on 0νββ de ay of 116Cd into rst ex ited 0+ state of daughter nu leus usingenri hed CdWO4 s intillators. Supersedes DANEVICH 00.66 Limit on 0νββ de ay of 116Cd into se ond ex ited 0+ state of daughter nu leus usingenri hed CdWO4 s intillators. Supersedes DANEVICH 00.67 Limit on the 0νββ ground state de ay of 186W using enri hed CdWO4 s intillators.68 Limit on the 0νββ de ay of 186W to the rst ex ited 2+ state of the daughter nu leususing enri hed CdWO4 s intillators.69AALSETH 02B limit is based on 117 mol·yr of data using enri hed Ge dete -tors. Ba kground redu tion by means of pulse shape analysis is applied to partof the data set. Reported limit is slightly less restri tive than that in KLAPDOR-KLEINGROTHAUS 01 However, it ex ludes part of the allowed half-life range reportedin KLAPDOR-KLEINGROTHAUS 01B for the same nu lide. The analysis has been rit-i ized in KLAPDOR-KLEINGROTHAUS 04B. The riti ism was addressed and disputedin AALSETH 04.70BERNABEI 02D report a limit for the 0ν, 0+ → 0+ de ay of 134Xe, present in thesour e at 17%, by onsidering the maximum number of events for this mode ompatiblewith the tted smooth ba kground.71DANEVICH 01 pla e limit on 0νββ de ay of 160Gd using Gd2SiO5:Ce rystal s intilla-tors. The limit is more stringent than KOBAYASHI 95.72DANEVICH 01 pla e limits on 0νββ de ay of 160Gd into ex ited 2+ state of daughternu leus using Gd2SiO5:Ce rystal s intillators.73KLAPDOR-KLEINGROTHAUS 01 is a ontinuation of the work published in BAUDIS 99.Isotopi ally enri hed Ge dete tors are used in alorimetri measurement. The most strin-gent bound is derived from the data set in whi h pulse-shape analysis has been used toredu e ba kground. Exposure time is 35.5 kg y. Supersedes BAUDIS 99 as most stringentresult.74WIESER 01 reports an in lusive geo hemi al measurement of 96Zr ββ half life.Their result agrees within 2σ with ARNOLD 99 but only marginally, within 3σ, withKAWASHIMA 93.75BRUDANIN 00 determine the 2νββ hal ife of 48Ca. Their value is less a urate thanBALYSH 96.76ARNOLD 99 measure dire tly the 2νββ de ay of Zr for the rst time, using the NEMO-2tra king dete tor and an isotopi ally enri hed sour e. The lifetime is more a urate thanthe geo hemi al result of KAWASHIMA 93.77ARNOLD 98 determine the limit for 0νββ de ay to the ex ited 2+ state of 82Se usingthe NEMO-2 tra king dete tor.78DESILVA 97 result for 2νββ de ay of 150Nd is in marginal agreement with ARTEMEV 93.It has smaller errors.79BALYSH 96 measure the 2νββ de ay of 48Ca, using a passive sour e of enri hed 48Cain a TPC.80BERNATOWICZ 92 nds 128Te/130Te a tivity ratio from slope of 128Xe/132Xe vs130Xe/132Xe ratios during extra tion, and normalizes to lead-dated ages for the 130Telifetime. The authors state that their results imply that \(a) the double beta de ay of128Te has been rmly established and its half-life has been determined . . . without anyambiguity due to trapped Xe interferen es. . . (b) Theoreti al al ulations . . . underes-timate the [long half-lives of 128Te 130Te by 1 or 2 orders of magnitude, pointing toa real suppression in the 2νββ de ay rate of these isotopes. ( ) Despite [this, mostββ-models predi t a ratio of 2νββ de ay widths . . . in fair agreement with observation."Further details of the experiment are given in BERNATOWICZ 93. Our listed half-lifehas been revised downward from the published value by the authors, on the basis ofreevaluated osmi -ray 128Xe produ tion orre tions.81TURKEVICH 91 observes a tivity in old U sample. The authors ompare their resultswith theoreti al al ulations. They state \Using the phase-spa e fa tors of Boehm andVogel (BOEHM 87) leads to matrix element values for the 238U transition in the samerange as dedu ed for 130Te and 76Ge. On the other hand, the latest theoreti al estimates(STAUDT 90) give an upper limit that is 10 times lower. This large dis repan y implieseither a defe t in the al ulations or the presen e of a faster path than the standardtwo-neutrino mode in this ase." See BOEHM 87 and STAUDT 90.82Ratio of in lusive double beta half lives of 128Te and 130Te determined from mineralsmelonite (NiTe2) and altaite (PbTe) by means of mass spe tros opi measurement ofabundan e of ββ-de ay produ ts. As gas-retention-age ould not be determined theauthors use half life of 130Te (LIN 88) to infer the half life of 128Te. No estimate of thesystemati un ertainty of this method is given. The dire tly determined half life ratioagrees with BERNATOWICZ 92. However, the inferred 128Te half life disagrees withKIRSTEN 83 and BERNATOWICZ 92.

⟨mν

⟩, The Ee tive Weighted Sum of Majorana Neutrino Masses⟨mν



⟩, The Ee tive Weighted Sum of Majorana Neutrino MassesContributing to Neutrinoless Double-β De ayContributing to Neutrinoless Double-β De ayContributing to Neutrinoless Double-β De ayContributing to Neutrinoless Double-β De ay⟨mν

⟩ = ∣∣ U21 jmνj ∣∣, where the sum goes from 1 to n and where n = number ofneutrino generations, and νj is a Majorana neutrino. Note that U2e j , not ∣∣Ue j ∣∣2,o urs in the sum. The possibility of an ellations has been stressed. In the followingListings, only best or omparable limits or lifetimes for ea h isotope are reported.VALUE (eV) CL% ISOTOPE TRANSITION METHOD DOCUMENT ID• • • We do not use the following data for averages, ts, limits, et . • • •

< 0.270.65 90 130Te 0ν,g.s.→ g.s. CUORE 1 ALFONSO 15< 0.330.62 90 100Mo 0ν NEMO-3 2 ARNOLD 15< 0.190.45 90 136Xe 0ν,g.s.→ g.s. EXO-200 3 ALBERT 14B< 0.20.4 90 76Ge 0ν GERDA 4 AGOSTINI 13A< 0.120.25 90 136Xe 0ν,g.s.→ g.s. KamLAND-Zen 5 GANDO 13A< 0.30.6 90 136Xe 0ν,g.s.→ g.s. KamLAND-Zen 6 GANDO 12A< 0.892.43 90 82Se 0ν NEMO-3 7 BARABASH 11A< 7.219.5 90 96Zr 0ν NEMO-3 8 ARGYRIADES 10< 4.06.8 90 150Nd 0ν NEMO-3 9 ARGYRIADES 09

771771771771See key on page 601 LeptonParti le ListingsDouble-β De ay< 3.522 90 48Ca 0ν CaF2 s int. 10 UMEHARA 08< 9.360 90 100Mo 0+→ 0+1 NEMO-3 11 ARNOLD 07< 6500 90 100Mo 0+→ 2+ NEMO-3 12 ARNOLD 070.32±0.03 68 76Ge 0ν Enri hed HPGe 13 KLAPDOR-K... 06A< 0.21.1 90 130Te Cryog. det. 14 ARNABOLDI 05< 0.72.8 90 100Mo 0ν NEMO-3 15 ARNOLD 05A< 1.74.9 90 82Se 0ν NEMO-3 16 ARNOLD 05A< 0.371.9 90 130Te Cryog. det. 17 ARNABOLDI 04< 0.81.2 90 100Mo 0ν NEMO-3 18 ARNOLD 04< 1.53.1 90 82Se 0ν NEMO-3 18 ARNOLD 040.10.9 99.776Ge Enri hed HP Ge 19 KLAPDOR-K... 04A< 7.244.7 90 48Ca CaF2 s int. 20 OGAWA 04< 1.12.6 90 130Te Cryog. det. 21 ARNABOLDI 03< 1.51.7 90 116Cd 0ν 116CdWO4 s int. 22 DANEVICH 03< 0.331.35 90 Enri hed HPGe 23 AALSETH 02B<2.9 90 136Xe 0ν Liquid Xe S int. 24 BERNABEI 02D0.39+0.17

−0.28 76Ge 0ν Enri hed HPGe 25 KLAPDOR-K... 02D< 2.14.8 90 100Mo 0ν ELEGANT V 26 EJIRI 01< 0.35 90 76Ge Enri hed HPGe 27 KLAPDOR-K... 01<23 90 96Zr NEMO-2 28 ARNOLD 99< 1.11.5 128Te Geo hem 29 BERNATOW... 92<5 68 82Se TPC 30 ELLIOTT 92<8.3 76 48Ca 0ν CaF2 s int. YOU 911ALFONSO 15 report a range of mass limits using the ombined data of the CUORICINOand CUORE-0 experiments. The reported mass range re e ts the variability of the nu learmatrix element al ulations.2ARNOLD 15 use the NEMO-3 tra king alorimeter with 34.3 kg yr exposure to determinethe neutrino mass limit based on the 0νββ-half life of 100Mo. The spread range re e tsdierent nu lear matrix elements. Supersedes ARNOLD 14 and BARABASH 11A.3ALBERT 14B is based on 100 kg yr of exposure of the EXO-200 tra king alorimeter.The mass range re e ts the nu lear matrix element al ulations. Supersedes AUGER 12.4AGOSTINI 13A is based on 21.6 kg yr of data olle ted by the GERDA dete tor. Thereported range re e ts dierent nu lear matrix elements. This result is in tension withthe eviden e for 0νββ-de ay reported in KLAPDOR-KLEINGROTHAUS 06A and earlierreferen es to that work.5GANDO 13A limit is based on a ombination of KamLAND-Zen and EXO-200(AUGER 12) data. The reported range re e ts dierent nu lear matrix elements. Su-persedes GANDO 12A.6GANDO 12A limit is based on the KamLAND-Zen data. The reported range re e tsdierent nu lear matrix elements. Superseded by GANDO 13A.7BARABASH 11A limit is based on NEMO-3 data for 82Se. The reported range re e tsdierent nu lear matrix elements. Supersedes ARNOLD 05A and ARNOLD 04.8ARGYRIADES 10 use 96Zr and the NEMO-3 tra king dete tor to obtain the reportedmass limit. The range re e ts the u tuation of the nu lear matrix elements onsidered.9ARGYRIADES 09 limit is based on data taken with the NEMO-3 dete tor and 150Nd.A range of nu lear matrix elements that in lude the ee t of nu lear deformation havebeen used.10 Limit was obtained using CaF2 s intillation alorimeter to sear h for double beta de ayof 48Ca. Reported range of limits re e ts spread of QRPA and SM matrix element al ulations used. Supersedes OGAWA 04.11ARNOLD 07 use NEMO-3 half life limit for 0ν-de ay of 100Mo to the rst ex ited 0+1 -state of daughter nu leus to obtain neutrino mass limit. The spread re e ts the hoi eof two dierent nu lear matrix elements. This limit is not ompetitive when omparedto the de ay to the ground state.12ARNOLD 07 use NEMO-3 half life limit for 0ν-de ay of 100Mo to the rst ex ited 2+-state of daughter nu leus to obtain neutrino mass limit. This limit is not ompetitivewhen ompared to the de ay to the ground state.13Re-analysis of data originally published in KLAPDOR-KLEINGROTHAUS 04A. Modiedpulse shape analysis leads the authors to laim 6σ statisti al eviden e for observation of0ν-de ay. Authors use matrix element of STAUDT 90. Un ertainty of nu lear matrixelement is not re e ted in stated error. Supersedes KLAPDOR-KLEINGROTHAUS 04A.14 Supersedes ARNABOLDI 04. Reported range of limits due to use of dierent nu learmatrix element al ulations.15Mass limits reported in ARNOLD 05A are derived from 100Mo data, obtained by theNEMO-3 ollaboration. The range re e ts the spread of matrix element al ulations onsidered in this work. Supersedes ARNOLD 04.16Neutrino mass limits based on 82Se data utilizing the NEMO-3 dete tor. The rangereported in ARNOLD 05A re e ts the spread of matrix element al ulations onsideredin this work. Supersedes ARNOLD 04.17 Supersedes ARNABOLDI 03. Reported range of limits due to use of dierent nu learmatrix element al ulations.18ARNOLD 04 limit is based on the nu lear matrix elements of SIMKOVIC 99, STOICA 01and CIVITARESE 03.19 Supersedes KLAPDOR-KLEINGROTHAUS 02D. Event ex ess at ββ-de ay energy is usedto derive Majorana neutrino mass using the nu lear matrix elements of STAUDT 90.The mass range shown is based on the authors evaluation of the un ertainties of theSTAUDT 90 matrix element al ulation. If this un ertainty is negle ted, and only statis-ti al errors are onsidered, the range in ⟨m⟩ be omes (0.20.6) eV at the 3 σ level.20Calorimetri CaF2 s intillator. Range of limits re e ts authors' estimate of the un er-tainty of the nu lear matrix elements. Repla es YOU 91 as the most stringest limit basedon 48Ca.21 Supersedes ALESSANDRELLO 00. Cryogeni alorimeter sear h. Reported a rangere e ting un ertainty in nu lear matrix element al ulations.

22 Limit for ⟨mν⟩ is based on the nu lear matrix elements of STAUDT 90 and ARNOLD 96.Supersedes DANEVICH 00.23AALSETH 02B reported range of limits on ⟨mν

⟩ re e ts the spread of theoreti al nu- lear matrix elements. Ex ludes part of allowed mass range reported in KLAPDOR-KLEINGROTHAUS 01B.24BERNABEI 02D limit is based on the matrix elements of SIMKOVIC 02. The range ofneutrino masses based on a variety of matrix elements is 1.12.9 eV.25KLAPDOR-KLEINGROTHAUS 02D is a detailed des ription of the analysis of the data olle ted by the Heidelberg-Mos ow experiment, previously presented in KLAPDOR-KLEINGROTHAUS 01B. Matrix elements in STAUDT 90 have been used. Seethe footnote in the pre eding table for further details. See also KLAPDOR-KLEINGROTHAUS 02B.26The range of the reported ⟨mν⟩ values re e ts the spread of the nu lear matrix elements.On axis value assuming ⟨

λ⟩=⟨

η⟩=0.27KLAPDOR-KLEINGROTHAUS 01 uses the al ulation by STAUDT 90. Using severalother models in the literature ould worsen the limit up to 1.2 eV. This is the moststringent experimental bound on mν . It supersedes BAUDIS 99B.28ARNOLD 99 limit based on the nu lear matrix elements of STAUDT 90.29BERNATOWICZ 92 nds these majorana neutrino mass limits assuming that the mea-sured geo hemi al de ay width is a limit on the 0ν de ay width. The range is the rangefound using matrix elements from HAXTON 84, TOMODA 87, and SUHONEN 91.Further details of the experiment are given in BERNATOWICZ 93.30ELLIOTT 92 uses the matrix elements of HAXTON 84.Limits on Lepton-Number Violating (V+A) Current AdmixtureLimits on Lepton-Number Violating (V+A) Current AdmixtureLimits on Lepton-Number Violating (V+A) Current AdmixtureLimits on Lepton-Number Violating (V+A) Current AdmixtureFor reasons given in the dis ussion at the beginning of this se tion, we list only resultsfrom 1989 and later. ⟨

λ⟩ = λ

∑UejVej and ⟨η⟩ = η

∑UejVej , where the sum isover the number of neutrino generations. This sum vanishes for massless or unmixedneutrinos. In the following Listings, only best or omparable limits or lifetimes for ea hisotope are reported.⟨λ

⟩ (10−6) CL% ⟨η⟩ (10−8) CL% ISOTOPE METHOD DOCUMENT ID


< 0.91.3 90 < 0.50.8 90 100Mo NEMO-3 1 ARNOLD 14<120 90 100Mo 0+→ 2+ 2 ARNOLD 070.692+0.058

−0.056 68 0.305+0.026−0.025 68 76Ge Enri hed HPGe 3 KLAPDOR-K... 06A

< 2.5 90 100Mo 0ν, NEMO-3 4 ARNOLD 05A< 3.8 90 82Se 0ν, NEMO-3 5 ARNOLD 05A< 1.52.0 90 100Mo 0ν, NEMO-3 6 ARNOLD 04< 3.23.8 90 82Se 0ν, NEMO-3 7 ARNOLD 04< 1.62.4 90 < 0.95.3 90 130Te Cryog. det. 8 ARNABOLDI 03< 2.2 90 <2.5 90 116Cd 116CdWO4 s int. 9 DANEVICH 03< 3.24.7 90 < 2.42.7 90 100Mo ELEGANT V 10 EJIRI 01< 1.1 90 <0.64 90 76Ge Enri hed HPGe 11 GUENTHER 97< 4.4 90 <2.3 90 136Xe TPC 12 VUILLEUMIER 93

<5.3 128Te Geo hem 13 BERNATOW... 921ARNOLD 14 is based on 34.7 kg yr of exposure of the NEMO-3 tra king alorimeter.The reported range limit on ⟨λ⟩ and ⟨

η⟩ re e ts the nu lear matrix element un ertaintyin 100Mo.2ARNOLD 07 use NEMO-3 half life limit for 0ν-de ay of 100Mo to the rst ex ited 2+-state of daughter nu leus to limit the right-right handed admixture of weak urrents ⟨

λ⟩.This limit is not ompetitive when ompared to the de ay to the ground state.3Re-analysis of data originally published in KLAPDOR-KLEINGROTHAUS 04A. Modiedpulse shape analysis leads the authors to laim 6σ statisti al eviden e for observationof 0ν-de ay. Authors use matrix element of MUTO 89 to determine ⟨

λ⟩ and ⟨

η⟩.Un ertainty of nu lear matrix element is not re e ted in stated errors.4ARNOLD 05A derive limit for ⟨

λ⟩ based on 100Mo data olle ted with NEMO-3 dete tor.No limit for ⟨

η⟩ is given. Supersedes ARNOLD 04.5ARNOLD 05A derive limit for ⟨

λ⟩ based on 82Se data olle ted with NEMO-3 dete tor.No limit for ⟨

η⟩ is given. Supersedes ARNOLD 04.6ARNOLD 04 use the matrix elements of SUHONEN 94 to obtain a limit for ⟨

λ⟩, no limitfor ⟨

η⟩ is given. This limit is more stringent than the limit in EJIRI 01 for the samenu leus.7ARNOLD 04 use the matrix elements of TOMODA 91 and SUHONEN 91 to obtain alimit for ⟨

λ⟩, no limit for ⟨

η⟩ is given.8 Supersedes ALESSANDRELLO 00. Cryogeni alorimeter sear h. Reported a rangere e ting un ertainty in nu lear matrix element al ulations.9 Limits for ⟨

λ⟩ and ⟨

η⟩ are based on nu lear matrix elements of STAUDT 90. SupersedesDANEVICH 00.10The range of the reported ⟨

λ⟩ and ⟨

η⟩ values re e ts the spread of the nu lear matrixelements. On axis value assuming ⟨mν⟩=0 and ⟨

λ⟩=⟨

η⟩=0, respe tively.11GUENTHER 97 limits use the matrix elements of STAUDT 90. Supersedes BALYSH 95and BALYSH 92.12VUILLEUMIER 93 uses the matrix elements of MUTO 89. Based on a half-life limit2.6× 1023 y at 90%CL.13BERNATOWICZ 92 takes the measured geo hemi al de ay width as a limit on the 0νwidth, and uses the SUHONEN 91 oeÆ ients to obtain the least restri tive limit on η.Further details of the experiment are given in BERNATOWICZ 93.

772772772772LeptonParti le ListingsDouble-β De ay, NeutrinoMixingDouble-β De ay REFERENCESDouble-β De ay REFERENCESDouble-β De ay REFERENCESDouble-β De ay REFERENCESASAKURA 16 NP A946 171 K. Asakura et al. (KamLAND-Zen Collab.)AGOSTINI 15A EPJ C75 416 M. Agostini et al. (GERDA Collab.)ALFONSO 15 PRL 115 102502 K. Alfonso et al. (CUORE Collab.)ARNOLD 15 PR D92 072011 R. Arnold et al. (NEMO-3 Collab.)ALBERT 14 PR C89 015502 J. Albert et al. (EXO-200 Collab.)ALBERT 14B NAT 510 229 J.B. Albert et al. (EXO-200 Collab.)ARNOLD 14 PR D89 111101 R. Arnold et al. (NEMO-3 Collab.)KIDD 14 PR C90 055501 M.F. Kidd et al.AGOSTINI 13A PRL 111 122503 M. Agostini et al. (GERDA Collab.)BELLI 13A PR C87 034607 P. Belli et al. (DAMA-INR Collab.)GANDO 13A PRL 110 062502 A. Gando et al. (KamLAND-Zen Collab.)GAVRILYAK 13 PR C87 035501 Yu.M. Gavrilyuk et al.SCHWINGEN... 13 ANP 525 269 B. S hwingenheuer (MPIH)ANDREOTTI 12 PR C85 045503 E. Andreotti et al. (CUORICINO Collab.)AUGER 12 PRL 109 032505 M. Auger et al. (EXO-200 Collab.)BELLI 12A PR C85 044610 P. Belli et al.GANDO 12A PR C85 045504 A. Gando et al. (KamLAND-Zen Collab.)ACKERMAN 11 PRL 107 212501 N. A kerman et al. (EXO Collab.)ARNOLD 11 PRL 107 062504 R. Arnold et al. (NEMO-3 Collab.)BARABASH 11 PR C83 045503 A.S. Barabash et al.BARABASH 11A PAN 74 312 A.S. Barabash et al. (NEMO-3 Collab.)Translated from YAF 74 330.BELLI 11D JP G38 115107 P. Belli et al. (DAMA-INR Collab.)RUKHADZE 11 NP A852 197 N.I. Rukhadze et al. (TGV-2 Collab.)ARGYRIADES 10 NP A847 168 J. Argyriades et al. (NEMO-3 Collab.)BELLI 10 NP A846 143 P. Belli et al. (DAMA-INR Collab.)ARGYRIADES 09 PR C80 032501 J. Argyriades et al. (NEMO-3 Collab.)BELLI 09A NP A826 256 P. Belli et al. (DAMA-INR Collab.)KIDD 09 NP A821 251 M. Kidd et al.ARNABOLDI 08 PR C78 035502 C. Arnaboldi et al.BELLI 08 PL B658 193 P. Belli et al. (DAMA-INR Collab.)BELLI 08B EPJ A36 167 P. Belli et al.UMEHARA 08 PR C78 058501 S. Umehara et al.ARNOLD 07 NP A781 209 R. Arnold et al. (NEMO-3 Collab.)KLAPDOR-K... 06A MPL A21 1547 H.V. Klapdor-Kleingrothaus, I.V. KrivosheinaARNABOLDI 05 PRL 95 142501 C. Arnaboldi et al. (CUORICINO Collab.)ARNOLD 05A PRL 95 182302 R. Arnold et al. (NEMO-3 Collab.)AALSETH 04 PR D70 078302 C.E. Aalseth et al.ARNABOLDI 04 PL B584 260 C. Arnaboldi et al.ARNOLD 04 JETPL 80 377 R. Arnold et al. (NEMO-3 Collab.)Translated from ZETFP 80 429.BARABASH 04 JETPL 79 10 A.S. Barabash et al.KLAPDOR-K... 04A PL B586 198 H.V. Klapdor-Kleingrothaus et al.KLAPDOR-K... 04B PR D70 078301 H.V. Klapdor-Kleingrothaus, A. Dietz, I.V. KrivosheinaOGAWA 04 NP A730 215 I. Ogawa et al.ARNABOLDI 03 PL B557 167 C. Arnaboldi et al.CIVITARESE 03 NP A729 867 O. Civitarese, J. SuhonenDANEVICH 03 PR C68 035501 F.A. Danevi h et al.AALSETH 02B PR D65 092007 C.E. Aalseth et al. (IGEX Collab.)BERNABEI 02D PL B546 23 R. Bernabei et al. (DAMA Collab.)KLAPDOR-K... 02B PPNL 110 57 H.V. Klapdor-Kleingrothaus, A. Dietz, I.V. KrivosheinaKLAPDOR-K... 02D FP 32 1181 H.V. Klapdor-Kleingrothaus, A. Dietz, I.V. KrivosheinaSIMKOVIC 02 hep-ph/0204278 F. Simkovi , P. Domin, A. FaesslerDANEVICH 01 NP A694 375 F.A. Danevi h et al.DEBRAECKEL...01 PRL 86 3510 L. De Brae keleer et al.EJIRI 01 PR C63 065501 H. Ejiri et al.KLAPDOR-K... 01 EPJ A12 147 H.V. Klapdor-Kleingrothaus et al.KLAPDOR-K... 01B MPL A16 2409 H.V. Klapdor-Kleingrothaus et al.STOICA 01 NP A694 269 S. Stoi a, H.V. Klapdor-KleingrothousWIESER 01 PR C64 024308 M.E. Wieser, J.R. De LaeterALESSAND... 00 PL B486 13 A. Alessandrello et al.BRUDANIN 00 PL B495 63 V.B. Brudanin et al. (TGV Collab.)DANEVICH 00 PR C62 045501 F.A. Danevi h et al.ARNOLD 99 NP A658 299 R. Arnold et al. (NEMO Collab.)BAUDIS 99 PR D59 022001 L. Baudis et al. (Heidelberg-Mos ow Collab.)BAUDIS 99B PRL 83 41 L. Baudis et al. (Heidelberg-Mos ow Collab.)SIMKOVIC 99 PR C60 055502 F. Simkovi et al.ARNOLD 98 NP A636 209 R. Arnold et al. (NEMO-2 Collab.)DESILVA 97 PR C56 2451 A. de Silva et al. (UCI)GUENTHER 97 PR D55 54 M. Gunther et al. (Heidelberg-Mos ow Collab.)ARNOLD 96 ZPHY C72 239 R. Arnold et al. (BCEN, CAEN, JINR+)BALYSH 96 PRL 77 5186 A. Balysh et al. (KIAE, UCI, CIT)ARNOLD 95 JETPL 61 170 R.G. Arnold et al. (NEMO Collab.)Translated from ZETFP 61 168.BALYSH 95 PL B356 450 A. Balysh et al. (Heidelberg-Mos ow Collab.)BARABASH 95 PL B345 408 A.S. Barabash et al. (ITEP, SCUC, PNL+)DASSIE 95 PR D51 2090 D. Dassie et al. (NEMO Collab.)EJIRI 95 JPSJ 64 339 H. Ejiri et al. (OSAK, KIEV)KOBAYASHI 95 NP A586 457 M. Kobayashi, M. Kobayashi (KEK, SAGA)SUHONEN 94 PR C49 3055 J. Suhonen, O. CivitareseARTEMEV 93 JETPL 58 262 V.A. Artemiev et al. (ITEP, INRM)Translated from ZETFP 58 256.BERNATOW... 93 PR C47 806 T. Bernatowi z et al. (WUSL, TATA)KAWASHIMA 93 PR C47 R2452 A. Kawashima, K. Takahashi, A. Masuda (TOKYC+)VUILLEUMIER 93 PR D48 1009 J.C. Vuilleumier et al. (NEUC, CIT, VILL)BALYSH 92 PL B283 32 A. Balysh et al. (MPIH, KIAE, SASSO)BERNATOW... 92 PRL 69 2341 T. Bernatowi z et al. (WUSL, TATA)ELLIOTT 92 PR C46 1535 S.R. Elliott et al. (UCI)SUHONEN 91 NP A535 509 J. Suhonen, S.B. Khadkikar, A. Faessler (JYV+)TOMODA 91 RPP 54 53 T. TomodaTURKEVICH 91 PRL 67 3211 A. Turkevi h, T.E. E onomou, G.A. Cowan (CHIC+)YOU 91 PL B265 53 K. You et al. (BHEP, CAST+)STAUDT 90 EPL 13 31 A. Staudt, K. Muto, H.V. Klapdor-KleingrothausMUTO 89 ZPHY A334 187 K. Muto, E. Bender, H.V. Klapdor (TINT, MPIH)LIN 88 NP A481 477 W.J. Lin et al.LIN 88B NP A481 484 W.J. Lin et al.BOEHM 87 Massive Neutrinos F. Bohm, P. Vogel (CIT)Cambridge Univ. Press, CambridgeTOMODA 87 PL B199 475 T. Tomoda, A. Faessler (TUBIN)HAXTON 84 PPNP 12 409 W.C. Haxton, G.J. StevensonKIRSTEN 83 PRL 50 474 T. Kirsten, H. Ri hter, E. Jessberger (MPIH)Neutrino MixingWith the exception of a few possible anomalies such as

LSND, current neutrino data can be described within the

framework of a 3×3 mixing matrix between the flavor eigen-

states νe, νµ, and ντ and the mass eigenstates ν1, ν2, and

ν3. (See Eq. (14.6) of the review “Neutrino Mass, Mixing, and

Oscillations” by K. Nakamura and S.T. Petcov.) The Listings

are divided into the following sections:

(A) Neutrino fluxes and event ratios: shows measurements

which correspond to various oscillation tests for Accelerator, Re-

actor, Atmospheric, and Solar neutrino experiments. Typically

ratios involve a measurement in a realm sensitive to oscillations

compared to one for which no oscillation effect is expected.

(B) Three neutrino mixing parameters: shows measure-

ments of sin2(2θ12), sin2(2θ23), ∆m221, ∆m2

32, and sin2(2θ13)

which are all interpretations of data based on the three neu-

trino mixing scheme described in the review “Neutrino Mass,

Mixing, and Oscillations.” by K. Nakamura and S.T. Petcov.

Many parameters have been calculated in the two-neutrino

approximation.

(C) Other neutrino mixing results: shows measurements

and limits for the probability of oscillation for experiments

which might be relevant to the LSND oscillation claim. In-

cluded are experiments which are sensitive to νµ → νe, νµ → νe,

sterile neutrinos, and CPT tests.(A) Neutrino uxes and event ratios(A) Neutrino uxes and event ratios(A) Neutrino uxes and event ratios(A) Neutrino uxes and event ratiosEvents (observed/expe ted) from a elerator νµ experiments.Events (observed/expe ted) from a elerator νµ experiments.Events (observed/expe ted) from a elerator νµ experiments.Events (observed/expe ted) from a elerator νµ experiments.Some neutrino os illation experiments ompare the ux in two or more dete tors. Thisis usually quoted as the ratio of the event rate in the far dete tor to the expe ted ratebased on an extrapolation from the near dete tor in the absen e of os illations.VALUE DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •1.01±0.10 1 ABE 14B T2K νe rate in T2K near dete t.0.71±0.08 2 AHN 06A K2K K2K to Super-K0.64±0.05 3 MICHAEL 06 MINS All harged urrent events0.71+0.08

−0.09 4 ALIU 05 K2K KEK to Super-K0.70+0.10−0.11 5 AHN 03 K2K KEK to Super-K1The rate of νe from µ de ay was measured to be 0.68 ± 0.30 ompared to the predi ted ux. From K de ay 1.10 ± 0.14 ompared to the predi ted ux.2Based on the observation of 112 events when 158.1+9.2

−8.6 were expe ted without os- illations. In luding not only the number of events but also the shape of the energydistribution, the eviden e for os illation is at the level of about 4.3 σ. SupersedesALIU 05.3This ratio is based on the observation of 215 events ompared to an expe tation of336 ± 14 without os illations. See also ADAMSON 08.4This ratio is based on the observation of 107 events at the far dete tor 250 km awayfrom KEK, and an expe tation of 151+12−10.5This ratio is based on the observation of 56 events with an expe tation of 80.1+6.2

−5.4.Events (observed/expe ted) from rea tor νe experiments.Events (observed/expe ted) from rea tor νe experiments.Events (observed/expe ted) from rea tor νe experiments.Events (observed/expe ted) from rea tor νe experiments.The quoted values are the ratios of the measured rea tor νe event rate at the quoteddistan es, and the rate expe ted without os illations. The expe ted rate is based onthe experimental data for the most signi ant rea tor fuels (235U, 239Pu, 241Pu)and on al ulations for 238U.A re ent re-evaluation of the spe tral onversion of ele tron to νe in MUELLER 11results in an upward shift of the rea tor νe spe trum by 3% and, thus, might requirerevisions to the ratios listed in this table.VALUE DOCUMENT ID TECN COMMENT0.944±0.007±0.0030.944±0.007±0.0030.944±0.007±0.0030.944±0.007±0.003 1 AN 13 DAYA DayaBay, LIng Ao/Ao II rea tors• • • We do not use the following data for averages, ts, limits, et . • • •0.944±0.016±0.040 2 ABE 12 DCHZ Chooz rea tors0.920±0.009±0.014 3 AHN 12 RENO Yonggwang rea tors0.940±0.011±0.004 4 AN 12 DAYA DayaBay, LIng Ao/Ao II rea tors1.08 ±0.21 ±0.16 5 DENIZ 10 TEXO Kuo-Sheng rea tor, 28 m0.658±0.044±0.047 6 ARAKI 05 KLND Japanese rea t. ∼ 180 km0.611±0.085±0.041 7 EGUCHI 03 KLND Japanese rea t. ∼ 180 km1.01 ±0.024±0.053 8 BOEHM 01 Palo Verde rea t. 0.750.89 km1.01 ±0.028±0.027 9 APOLLONIO 99 CHOZ Chooz rea tors 1 km

773773773773See key on page 601 LeptonParti le ListingsNeutrinoMixing0.987±0.006±0.037 10 GREENWOOD 96 Savannah River, 18.2 m0.988±0.004±0.05 ACHKAR 95 CNTR Bugey rea tor, 15 m0.994±0.010±0.05 ACHKAR 95 CNTR Bugey rea tor, 40 m0.915±0.132±0.05 ACHKAR 95 CNTR Bugey rea tor, 95 m0.987±0.014±0.027 11 DECLAIS 94 CNTR Bugey rea tor, 15 m0.985±0.018±0.034 KUVSHINN... 91 CNTR Rovno rea tor1.05 ±0.02 ±0.05 VUILLEUMIER 82 Gosgen rea tor0.955±0.035±0.110 12 KWON 81 νe p → e+ n0.89 ±0.15 12 BOEHM 80 νe p → e+ n1AN 13 use six identi al dete tors, with three pla ed near the rea tor ores ( ux-weightedbaselines of 470 and 576 m) and the remaining three at the far hall (at the ux averageddistan e of 1648 m from all six rea tor ores) to determine the mixing angle θ13 using theνe observed intera tion rate ratios. This rate-only analysis ex ludes the no-os illationhypothesis at 7.7 standard deviations. The value of m231 = 2.32 × 10−3 eV2 wasassumed in the analysis. This is an improved result (2.5 times in rease in statisti s) ompared to AN 12.2ABE 12 determine the νe intera tion rate in a single dete tor, lo ated 1050 m from the ores of two rea tors. The rate normalization is xed by the results of the Bugey4 rea torexperiment, thus avoiding any dependen e on possible very short baseline os illations.3AHN 12 use two identi al dete tors, pla ed at ux weighted distan es of 408.56 m and1433.99m from six rea tor ores, to determine the νe intera tion rate ratio.4AN 12 use six identi al dete tors with three pla ed near the rea tor ores ( ux-weightedbaselines of 470 m and 576 m) and the remaining three at the far hall (at the uxaveraged distan e of 1648 m from all six rea tor ores) to determine the νe intera tionrate ratios. Superseded by AN 13.5DENIZ 10 observe rea tor νe e s attering with re oil kineti energies 38 MeV usingCsI(Tl) dete tors. The observed rate is onsistent with the Standard Model predi tion,leading to a onstraint on sin2θW = 0.251 ± 0.031(stat)±0.024(sys).6Updated result of KamLAND, in luding the data used in EGUCHI 03. Note that thesurvival probabilities for dierent periods are not dire tly omparable be ause the ee tivebaseline varies with power output of the rea tor sour es involved, and there were largevariations in the rea tor power produ tion in Japan in 2003.7 EGUCHI 03 observe rea tor neutrino disappearan e at ∼ 180 km baseline to variousJapanese nu lear power rea tors.8BOEHM 01 sear h for neutrino os illations at 0.75 and 0.89 km distan e from the PaloVerde rea tors.9APOLLONIO 99, APOLLONIO 98 sear h for neutrino os illations at 1.1 km xed dis-tan e from Chooz rea tors. They use νe p → e+ n in Gd-loaded s intillator target.APOLLONIO 99 supersedes APOLLONIO 98. See also APOLLONIO 03 for detaileddes ription.10GREENWOOD 96 sear h for neutrino os illations at 18 m and 24 m from the rea tor atSavannah River.11DECLAIS 94 result based on integral measurement of neutrons only. Result is ra-tio of measured ross se tion to that expe ted in standard V-A theory. Repla ed byACHKAR 95.12KWON 81 represents an analysis of a larger set of data from the same experiment asBOEHM 80. Atmospheri neutrinosAtmospheri neutrinosAtmospheri neutrinosAtmospheri neutrinosNeutrinos and antineutrinos produ ed in the atmosphere indu e µ-like ande-like events in underground dete tors. The ratio of the numbers of thetwo kinds of events is dened as µ/e. It has the advantage that systemati ee ts, su h as ux un ertainty, tend to an el, for both experimental andtheoreti al values of the ratio. The \ratio of the ratios" of experimentalto theoreti al µ/e, R(µ/e), or that of experimental to theoreti al µ/total,R(µ/total) with total = µ+e, is reported below. If the a tual value isnot unity, the value obtained in a given experiment may depend on theexperimental onditions. In addition, the measured \up-down asymmetry"for µ (Nup(µ)/Ndown(µ)) or e (Nup(e)/Ndown(e)) is reported. Theexpe ted \up-down asymmetry" is nearly unity if there is no neutrinoos illation.R(µ/e) = (Measured Ratio µ/e) / (Expe ted Ratio µ/e)R(µ/e) = (Measured Ratio µ/e) / (Expe ted Ratio µ/e)R(µ/e) = (Measured Ratio µ/e) / (Expe ted Ratio µ/e)R(µ/e) = (Measured Ratio µ/e) / (Expe ted Ratio µ/e)VALUE DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, ts, limits, et . • • •0.658±0.016±0.035 1 ASHIE 05 SKAM sub-GeV0.702+0.032−0.030±0.101 2 ASHIE 05 SKAM multi-GeV0.69 ±0.10 ±0.06 3 SANCHEZ 03 SOU2 Calorimeter raw data4 FUKUDA 96B KAMI Water Cherenkov1.00 ±0.15 ±0.08 5 DAUM 95 FREJ Calorimeter0.60 +0.06−0.05 ±0.05 6 FUKUDA 94 KAMI sub-GeV0.57 +0.08−0.07 ±0.07 7 FUKUDA 94 KAMI multi-Gev8 BECKER-SZ... 92B IMB Water Cherenkov1ASHIE 05 results are based on an exposure of 92 kton yr during the omplete Super-Kamiokande I running period. The analyzed data sample onsists of fully- ontainedsingle-ring e-like events with 0.1 GeV/ < pe and µ-like events 0.2 GeV/ < pµ,both having a visible energy < 1.33 GeV. These riteria mat h the denition used byFUKUDA 94.2ASHIE 05 results are based on an exposure of 92 kton yr during the omplete Super-Kamiokande I running period. The analyzed data sample onsists of fully- ontainedsingle-ring events with visible energy > 1.33 GeV and partially- ontained events. Allpartially- ontained events are lassied as µ-like.

3 SANCHEZ 03 result is based on an exposure of 5.9 kton yr, and updates ALLISON 99result. The analyzed data sample onsists of fully- ontained e- avor and µ- avor eventshaving lepton momentum > 0.3 GeV/ .4 FUKUDA 96B studied neutron ba kground in the atmospheri neutrino sample observedin the Kamiokande dete tor. No eviden e for the ba kground ontamination was found.5DAUM 95 results are based on an exposure of 2.0 kton yr whi h in ludes the data usedby BERGER 90B. This ratio is for the ontained and semi ontained events. DAUM 95also report R(µ/e) = 0.99 ± 0.13 ± 0.08 for the total neutrino indu ed data samplewhi h in ludes upward going stopping muons and horizontal muons in addition to the ontained and semi ontained events.6 FUKUDA 94 result is based on an exposure of 7.7 kton yr and updates the HIRATA 92result. The analyzed data sample onsists of fully- ontained e-like events with 0.1 <pe < 1.33 GeV/ and fully- ontained µ-like events with 0.2 < pµ < 1.5 GeV/ .7 FUKUDA 94 analyzed the data sample onsisting of fully ontained events with visibleenergy > 1.33 GeV and partially ontained µ-like events.8BECKER-SZENDY 92B reports the fra tion of nonshowering events (mostly muons fromatmospheri neutrinos) as 0.36± 0.02± 0.02, as ompared with expe ted fra tion 0.51±0.01 ± 0.05. After utting the energy range to the Kamiokande limits, BEIER 92 ndsR(µ/e) very lose to the Kamiokande value.R(νµ) = (Measured Flux of νµ) / (Expe ted Flux of νµ)R(νµ) = (Measured Flux of νµ) / (Expe ted Flux of νµ)R(νµ) = (Measured Flux of νµ) / (Expe ted Flux of νµ)R(νµ) = (Measured Flux of νµ) / (Expe ted Flux of νµ)VALUE DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.84±0.12 1 ADAMSON 06 MINS MINOS atmospheri 0.72±0.026±0.13 2 AMBROSIO 01 MCRO upward through-going0.57±0.05 ±0.15 3 AMBROSIO 00 MCRO upgoing partially ontained0.71±0.05 ±0.19 4 AMBROSIO 00 MCRO downgoing partially ontained+ upgoing stopping0.74±0.036±0.046 5 AMBROSIO 98 MCRO Streamer tubes6 CASPER 91 IMB Water Cherenkov7 AGLIETTA 89 NUSX0.95±0.22 8 BOLIEV 81 Baksan0.62±0.17 CROUCH 78 Case Western/UCI1ADAMSON 06 uses a measurement of 107 total neutrinos ompared to an expe ted rateof 127 ± 13 without os illations.2AMBROSIO 01 result is based on the upward through-going muon tra ks with Eµ > 1GeV. The data ame from three dierent dete tor ongurations, but the statisti s islargely dominated by the full dete tor run, from May 1994 to De ember 2000. The totallive time, normalized to the full dete tor onguration, is 6.17 years. The rst error isthe statisti al error, the se ond is the systemati error, dominated by the theoreti al errorin the predi ted ux.3AMBROSIO 00 result is based on the upgoing partially ontained event sample. It amefrom 4.1 live years of data taking with the full dete tor, from April 1994 to February1999. The average energy of atmospheri muon neutrinos orresponding to this sampleis 4 GeV. The rst error is statisti al, the se ond is the systemati error, dominated bythe 25% theoreti al error in the rate (20% in the ux and 15% in the ross se tion, addedin quadrature). Within statisti s, the observed de it is uniform over the zenith angle.4AMBROSIO 00 result is based on the ombined samples of downgoing partially ontainedevents and upgoing stopping events. These two subsamples ould not be distinguisheddue to the la k of timing information. The result ame from 4.1 live years of datataking with the full dete tor, from April 1994 to February 1999. The average energyof atmospheri muon neutrinos orresponding to this sample is 4 GeV. The rst error isstatisti al, the se ond is the systemati error, dominated by the 25% theoreti al error inthe rate (20% in the ux and 15% in the ross se tion, added in quadrature). Withinstatisti s, the observed de it is uniform over the zenith angle.5AMBROSIO 98 result is for all nadir angles and updates AHLEN 95 result. The lower uto on the muon energy is 1 GeV. In addition to the statisti al and systemati errors,there is a Monte Carlo ux error (theoreti al error) of ±0.13. With a neutrino os il-lation hypothesis, the t either to the ux or zenith distribution independently yieldssin22θ=1.0 and (m2) ∼ a few times 10−3 eV2. However, the t to the observedzenith distribution gives a maximum probability for χ2 of only 5% for the best os illationhypothesis.6CASPER 91 orrelates showering/nonshowering signature of single-ring events with par-ent atmospheri -neutrino avor. They nd nonshowering (≈ νµ indu ed) fra tion is0.41 ± 0.03 ± 0.02, as ompared with expe ted 0.51 ± 0.05 (syst).7AGLIETTA 89 nds no eviden e for any anomaly in the neutrino ux. They de-ne ρ = (measured number of νe 's)/(measured number of νµ's). They report

ρ(measured)=ρ(expe ted) = 0.96+0.32−0.28.8 From this data BOLIEV 81 obtain the limit (m2) ≤ 6 × 10−3 eV2 for maximalmixing, νµ 6→ νµ type os illation.R(µ/total) = (Measured Ratio µ/total) / (Expe ted Ratio µ/total)R(µ/total) = (Measured Ratio µ/total) / (Expe ted Ratio µ/total)R(µ/total) = (Measured Ratio µ/total) / (Expe ted Ratio µ/total)R(µ/total) = (Measured Ratio µ/total) / (Expe ted Ratio µ/total)VALUE DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, ts, limits, et . • • •1.1+0.07−0.12±0.11 1 CLARK 97 IMB multi-GeV1CLARK 97 obtained this result by an analysis of fully ontained and partially ontainedevents in the IMB water-Cherenkov dete tor with visible energy > 0.95 GeV.Nup(µ)/Ndown(µ)Nup(µ)/Ndown(µ)Nup(µ)/Ndown(µ)Nup(µ)/Ndown(µ)VALUE DOCUMENT ID TECN COMMENT


774774774774LeptonParti le ListingsNeutrinoMixing0.71 ±0.06 1 ADAMSON 12B MINS ontained-vertex muons0.551+0.035−0.033±0.004 2 ASHIE 05 SKAM multi-GeV1ADAMSON 12B reports the atmospheri neutrino results obtained with MINOS far de-te tor in 2,553 live days (an exposure of 37.9 kton·yr). This result is obtained with asample of high resolution ontained-vertex muons. The quoted error is statisti al only.2ASHIE 05 results are based on an exposure of 92 kton yr during the omplete Super-Kamiokande I running period. The analyzed data sample onsists of fully- ontainedsingle-ring µ-like events with visible energy > 1.33 GeV and partially- ontained events.All partially- ontained events are lassied as µ-like. Upward-going events are thosewith −1 < os(zenith angle) < −0.2 and downward-going events are those with 0.2< os(zenith angle) <1. The µ-like up-down ratio for the multi-GeV data deviates from 1(the expe tation for no atmospheri νµ os illations) by more than 12 standard deviations.Nup(e)/Ndown(e)Nup(e)/Ndown(e)Nup(e)/Ndown(e)Nup(e)/Ndown(e)VALUE DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, ts, limits, et . • • •0.961+0.086−0.079±0.016 1 ASHIE 05 SKAM multi-GeV1ASHIE 05 results are based on an exposure of 92 kton yr during the omplete Super-Kamiokande I running period. The analyzed data sample onsists of fully- ontainedsingle-ring e-like events with visible energy > 1.33 GeV. Upward-going events are thosewith −1 < os(zenith angle) < −0.2 and downward-going events are those with 0.2

< os(zenith angle) < 1. The e-like up-down ratio for the multi-GeV data is onsistentwith 1 (the expe tation for no atmospheri νe os illations).R(up/down; µ) = (Measured up/down; µ) / (Expe ted up/down; µ)R(up/down; µ) = (Measured up/down; µ) / (Expe ted up/down; µ)R(up/down; µ) = (Measured up/down; µ) / (Expe ted up/down; µ)R(up/down; µ) = (Measured up/down; µ) / (Expe ted up/down; µ)VALUE DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.62±0.05±0.02 1 ADAMSON 12B MINS ontained-vertex muons0.62+0.19

−0.14±0.02 2 ADAMSON 06 MINS atmospheri ν with far dete tor1ADAMSON 12B reports the atmospheri neutrino results obtained with MINOS far de-te tor in 2,553 live days (an exposure of 37.9 kton·yr). This result is obtained with asample of high resolution ontained-vertex muons. The expe ted ratio is al ulated withno neutrino os illation.2ADAMSON 06 result is obtained with the MINOS far dete tor with an exposure of 4.54kton yr. The expe ted ratio is al ulated with no neutrino os illation.N(µ+)/N(µ−)N(µ+)/N(µ−)N(µ+)/N(µ−)N(µ+)/N(µ−)VALUE DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.46+0.05

−0.04 1,2 ADAMSON 12B MINS ontained-vertex muons0.63+0.09−0.08 1,3 ADAMSON 12B MINS ν-indu ed ro k-muons1ADAMSON 12B reports the atmospheri neutrino results obtained with MINOS fardete tor in 2,553 live days (an exposure of 37.9 kton·yr). The muon harge ratioN(µ+)/N(µ−) represents the νµ/νµ ratio.2This result is obtained with a harge-separated sample of high resolution ontained-vertexmuons. The quoted error is statisti al only.3This result is obtained with a harge-separated sample of high resolution neutrino-indu edro k-muons. The quoted error is statisti al only.R(µ+/µ−) = (Measured N(µ+)/N(µ−)) / (Expe ted N(µ+)/N(µ−))R(µ+/µ−) = (Measured N(µ+)/N(µ−)) / (Expe ted N(µ+)/N(µ−))R(µ+/µ−) = (Measured N(µ+)/N(µ−)) / (Expe ted N(µ+)/N(µ−))R(µ+/µ−) = (Measured N(µ+)/N(µ−)) / (Expe ted N(µ+)/N(µ−))VALUE DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, ts, limits, et . • • •0.93±0.09±0.09 1,2 ADAMSON 12B MINS ontained-vertex muons1.29+0.19−0.17±0.16 1,3 ADAMSON 12B MINS ν-indu ed ro k-muons1.03±0.08±0.08 1,4 ADAMSON 12B MINS ontained1.39+0.35−0.46+0.08

−0.14 5 ADAMSON 07 MINS Upward and horizontal µ withfar dete tor0.96+0.38−0.27±0.15 6 ADAMSON 06 MINS atmospheri ν with far dete tor1ADAMSON 12B reports the atmospheri neutrino results obtained with MINOS fardete tor in 2,553 live days (an exposure of 37.9 kton·yr). The muon harge ratioN(µ+)/N(µ−) represents the νµ/νµ ratio. As far as the same os illation parametersare used for νs and νs, the expe ted νµ/νµ ratio is almost entirely independent of anyinput os illations.2This result is obtained with a harge-separated sample of high resolution ontained-vertexmuons.3This result is obtained with a harge-separated sample of high resolution neutrino-indu edro k-muons.4The harge-separated samples of high resolution ontained-vertex muons and neutrino-indu ed ro k-muons are ombined to obtain this result whi h is onsistent with unity.5ADAMSON 07 result is obtained with the MINOS far dete tor in 854.24 live days, basedon neutrino-indu ed upward-going and horizontal muons. This result is onsistent withCPT onservation.6ADAMSON 06 result is obtained with the MINOS far dete tor with an exposure of 4.54kton yr, based on ontained events. The expe ted ratio is al ulated by assuming thesame os illation parameters for neutrinos and antineutrinos.

Solar neutrinosSolar neutrinosSolar neutrinosSolar neutrinosSolar neutrinos are produ ed by thermonu lear fusion rea tions in theSun. Radio hemi al experiments measure parti ular ombinations of uxesfrom various neutrino-produ ing rea tions, whereas water-Cherenkov ex-periments mainly measure a ux of neutrinos from de ay of 8B. Solarneutrino uxes are omposed of all a tive neutrino spe ies, νe , νµ, andντ . In addition, some other me hanisms may ause antineutrino ompo-nents in solar neutrino uxes. Ea h measurement method is sensitive toa parti ular omponent or a ombination of omponents of solar neutrino uxes. For details, see Se tion 13.4 of Reviews, Tables, and Plots.

νe Capture Rates from Radio hemi al Experimentsνe Capture Rates from Radio hemi al Experimentsνe Capture Rates from Radio hemi al Experimentsνe Capture Rates from Radio hemi al Experiments1 SNU (Solar Neutrino Unit) = 10−36 aptures per atom per se ond.VALUE (SNU) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •73.4 +6.1

−6.0 +3.7−4.1 1 KAETHER 10 GALX reanalysis67.6 ±4.0 ±3.2 2 KAETHER 10 GNO+GALX reanalysis ombined65.4 +3.1

−3.0 +2.6−2.8 3 ABDURASHI... 09 SAGE 71Ga → 71Ge62.9 +5.5

−5.3 ±2.5 4 ALTMANN 05 GNO 71Ga → 71Ge69.3 ±4.1 ±3.6 5 ALTMANN 05 GNO GNO + GALX ombined77.5 ±6.2 +4.3−4.7 6 HAMPEL 99 GALX 71Ga → 71Ge2.56±0.16±0.16 7 CLEVELAND 98 HOME 37Cl → 37Ar1KAETHER 10 reports the reanalysis results of a omplete GALLEX data (GALLEXI+II+III+IV, reported in HAMPEL 99) based on the event sele tion with a new pulseshape analysis, whi h provides a better ba kground redu tion than the rise time analysisadopted in HAMPEL 99.2Combined result of GALLEX I+II+III+IV reanalysis and GNO I+II+III (ALTMANN 05).3ABDURASHITOV 09 reports a ombined analysis of 168 extra tions of the SAGE solarneutrino experiment during the period January 1990 through De ember 2007, and up-dates the ABDURASHITOV 02 result. The data are onsistent with the assumption thatthe solar neutrino produ tion rate is onstant in time. Note that a ∼ 15% systemati un ertainty in the overall normalization may be added to the ABDURASHITOV 09 result,be ause alibration experiments for gallium solar neutrino measurements using intense51Cr (twi e by GALLEX and on e by SAGE) and 37Ar (by SAGE) result in an averageratio of 0.87 ± 0.05 of the observed to al ulated rates.4ALTMANN 05 reports the omplete result from the GNO solar neutrino experiment(GNO I+II+III), whi h is the su essor proje t of GALLEX. Experimental te hnique ofGNO is essentially the same as that of GALLEX. The run data over the period 20 May1998 through 9 April 2003.5Combined result of GALLEX I+II+III+IV (HAMPEL 99) and GNO I+II+III.6HAMPEL 99 report the ombined result for GALLEX I+II+III+IV (65 runs in total),whi h update the HAMPEL 96 result. The GALLEX IV result (12 runs) is 118.4 ±17.8 ± 6.6 SNU. (HAMPEL 99 dis uss the onsisten y of partial results with the mean.)The GALLEX experimental program has been ompleted with these runs. The total rundata over the period 14 May 1991 through 23 January 1997. A total of 300 71Ge eventswere observed. Note that a ∼ 15% systemati un ertainty in the overall normalizationmay be added to the HAMPEL 99 result, be ause alibration experiments for galliumsolar neutrino measurements using intense 51Cr (twi e by GALLEX and on e by SAGE)and 37Ar (by SAGE) result in an average ratio of 0.87±0.05 of the observed to al ulatedrates.7CLEVELAND 98 is a detailed report of the 37Cl experiment at the Homestake Mine.The average solar neutrino-indu ed 37Ar produ tion rate from 108 runs between 1970and 1994 updates the DAVIS 89 result.

φES (8B)φES (8B)φES (8B)φES (8B)8B solar-neutrino ux measured via ν e elasti s attering. This pro ess is sensitive toall a tive neutrino avors, but with redu ed sensitivity to νµ, ντ due to the ross-se tion dieren e, σ(ν µ,τ e) ∼ 0.16σ(νe e). If the 8B solar-neutrino ux involvesnonele tron avor a tive neutrinos, their ontribution to the ux is ∼ 0.16 times ofνe .VALUE (106 m−2s−1) DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, ts, limits, et . • • •2.32±0.04±0.05 1 ABE 11 SKAM SK-III average ux2.41±0.05+0.16−0.15 2 ABE 11 SKAM SK-II average ux2.38±0.02±0.08 3 ABE 11 SKAM SK-I average ux2.77±0.26±0.32 4 ABE 11B KLND average ux2.4 ±0.4 ±0.1 5 BELLINI 10A BORX average ux1.77+0.24

−0.21+0.09−0.10 6 AHARMIM 08 SNO Phase III2.38±0.05+0.16−0.15 7 CRAVENS 08 SKAM average ux2.35±0.02±0.08 8 HOSAKA 06 SKAM average ux2.35±0.22±0.15 9 AHARMIM 05A SNO Salty D2O; 8B shape not on-strained2.34±0.23+0.15−0.14 9 AHARMIM 05A SNO Salty D2O; 8B shape onstrained2.39+0.24

−0.23±0.12 10 AHMAD 02 SNO average ux

775775775775See key on page 601 LeptonParti le ListingsNeutrinoMixing2.39±0.34+0.16−0.14 11 AHMAD 01 SNO average ux2.80±0.19±0.33 12 FUKUDA 96 KAMI average ux2.70±0.27 12 FUKUDA 96 KAMI day ux2.87+0.27

−0.26 12 FUKUDA 96 KAMI night ux1ABE 11 reports the Super-Kamiokande-III results for 548 live days from August 4, 2006to August 18, 2008. The analysis threshold is 5.0 MeV, but the event sample in the5.06.5 MeV total ele tron range has a total live time of 298 days.2ABE 11 re al ulated the Super-Kamiokande-II results using 8B spe trum of WIN-TER 06A.3ABE 11 re al ulated the Super-Kamiokande-I results using 8B spe trum of WINTER 06A.4ABE 11B use a 123 kton·day exposure of the KamLAND liquid s intillation dete torto measure the 8B solar neutrino ux. They utilize ν − e elasti s attering above are onstru ted-energy threshold of 5.5 MeV, orresponding to 5 MeV ele tron re oil en-ergy. 299 ele tron re oil andidate events are reported, of whi h 157 ± 23.6 are assignedto ba kground.5BELLINI 10A reports the Borexino result with 3 MeV energy threshold for s atteredele trons. The data orrespond to 345.3 live days with a target mass of 100 t, betweenJuly 15, 2007 and August 23, 2009.6AHARMIM 08 reports the results from SNO Phase III measurement using an array of3He proportional ounters to measure the rate of NC intera tions in heavy water, overthe period between November 27, 2004 and November 28, 2006, orresponding to 385.17live days. A simultaneous t was made for the number of NC events dete ted by theproportional ounters and the numbers of NC, CC, and ES events dete ted by the PMTs,where the spe tral distributions of the ES and CC events were not onstrained to the 8Bshape.7CRAVENS 08 reports the Super-Kamiokande-II results for 791 live days from De ember2002 to O tober 2005. The photo athode overage of the dete tor is 19% (redu ed from40% of that of Super-Kamiokande-I due to an a ident in 2001). The analysis thresholdfor the average ux is 7 MeV.8HOSAKA 06 reports the nal results for 1496 live days with Super-Kamiokande-I betweenMay 31, 1996 and July 15, 2001, and repla e FUKUDA 02 results. The analysis thresholdis 5 MeV ex ept for the rst 280 live days (6.5 MeV).9AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) inheavy water over the period between July 26, 2001 and August 28, 2003, orrespondingto 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statisti allyseparated. In one method, the 8B energy spe trum was not onstrained. In the othermethod, the onstraint of an undistorted 8B energy spe trum was added for omparisonwith AHMAD 02 results.10AHMAD 02 reports the 8B solar-neutrino ux measured via ν e elasti s attering abovethe kineti energy threshold of 5 MeV. The data orrespond to 306.4 live days with SNObetween November 2, 1999 and May 28, 2001, and updates AHMAD 01 results.11AHMAD 01 reports the 8B solar-neutrino ux measured via ν e elasti s attering abovethe kineti energy threshold of 6.75 MeV. The data orrespond to 241 live days withSNO between November 2, 1999 and January 15, 2001.12 FUKUDA 96 results are for a total of 2079 live days with Kamiokande II and III fromJanuary 1987 through February 1995, overing the entire solar y le 22, with thresholdEe > 9.3MeV (rst 449 days), > 7.5 MeV (middle 794 days), and > 7.0MeV (last 836days). These results update the HIRATA 90 result for the average 8B solar-neutrino uxand HIRATA 91 result for the day-night variation in the 8B solar-neutrino ux. The totaldata sample was also analyzed for short-term variations: within experimental errors, nostrong orrelation of the solar-neutrino ux with the sunspot numbers was found.φCC (8B)φCC (8B)φCC (8B)φCC (8B)8B solar-neutrino ux measured with harged- urrent rea tion whi h is sensitive ex- lusively to νe .VALUE (106 m−2s−1) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •1.67+0.05

−0.04+0.07−0.08 1 AHARMIM 08 SNO Phase III1.68±0.06+0.08−0.09 2 AHARMIM 05A SNO Salty D2O; 8B shapenot onst.1.72±0.05±0.11 2 AHARMIM 05A SNO Salty D2O; 8B shape onstrained1.76+0.06

−0.05±0.09 3 AHMAD 02 SNO average ux1.75 ± 0.07+0.12−0.11 ± 0.05 4 AHMAD 01 SNO average ux1AHARMIM 08 reports the results from SNO Phase III measurement using an array of3He proportional ounters to measure the rate of NC intera tions in heavy water, overthe period between November 27, 2004 and November 28, 2006, orresponding to 385.17live days. A simultaneous t was made for the number of NC events dete ted by theproportional ounters and the numbers of NC, CC, and ES events dete ted by the PMTs,where the spe tral distributions of the ES and CC events were not onstrained to the 8Bshape.2AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) inheavy water over the period between July 26, 2001 and August 28, 2003, orrespondingto 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statisti allyseparated. In one method, the 8B energy spe trum was not onstrained. In the othermethod, the onstraint of an undistorted 8B energy spe trum was added for omparisonwith AHMAD 02 results.3AHMAD 02 reports the SNO result of the 8B solar-neutrino ux measured with harged- urrent rea tion on deuterium, νe d → ppe−, above the kineti energy threshold of5 MeV. The data orrespond to 306.4 live days with SNO between November 2, 1999and May 28, 2001, and updates AHMAD 01 results. The omplete des ription of theSNO Phase I data set is given in AHARMIM 07.

4AHMAD 01 reports the rst SNO result of the 8B solar-neutrino ux measured with the harged- urrent rea tion on deuterium, νe d → ppe− , above the kineti energy thresh-old of 6.75 MeV. The data orrespond to 241 live days with SNO between November 2,1999 and January 15, 2001.φNC (8B)φNC (8B)φNC (8B)φNC (8B)8B solar neutrino ux measured with neutral- urrent rea tion, whi h is equally sensitiveto νe , νµ, and ντ .VALUE (106 m−2s−1) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •5.25 ±0.16 +0.11

−0.13 1 AHARMIM 13 SNO All three phases ombined5.140+0.160−0.158+0.132

−0.117 2 AHARMIM 10 SNO Phase I+II, low threshold5.54 +0.33−0.31 +0.36

−0.34 3 AHARMIM 08 SNO Phase III, prop. ounter + PMT4.94 ±0.21 +0.38−0.34 4 AHARMIM 05A SNO Salty D2O; 8B shape not onst.4.81 ±0.19 +0.28−0.27 4 AHARMIM 05A SNO Salty D2O; 8B shape onstrained5.09 +0.44

−0.43 +0.46−0.43 5 AHMAD 02 SNO average ux; 8B shape onst.6.42 ±1.57 +0.55−0.58 5 AHMAD 02 SNO average ux; 8B shape not onst.1AHARMIM 13 obtained this result from a ombined analysis of the data from all threephases, SNO-I, II, and III. The measurement of the 8B ux mostly omes from the NCsignal, however, CC ontribution is in luded in the t.2AHARMIM 10 reports this result from a joint analysis of SNO Phase I+II data with the"ee tive ele tron kineti energy" threshold of 3.5 MeV. This result is obtained with a"binned-histogram un onstrained t" where binned probability distribution fun tions ofthe neutrino signal observables were used without any model onstraints on the shapeof the neutrino spe trum.3AHARMIM 08 reports the results from SNO Phase III measurement using an array of3He proportional ounters to measure the rate of NC intera tions in heavy water, overthe period between November 27, 2004 and November 28, 2006, orresponding to 385.17live days. A simultaneous t was made for the number of NC events dete ted by theproportional ounters and the numbers of NC, CC, and ES events dete ted by the PMTs,where the spe tral distributions of the ES and CC events were not onstrained to the 8Bshape.4AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) inheavy water over the period between July 26, 2001 and August 28, 2003, orrespondingto 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statisti allyseparated. In one method, the 8B energy spe trum was not onstrained. In the othermethod, the onstraint of an undistorted 8B energy spe trum was added for omparisonwith AHMAD 02 results.5AHMAD 02 reports the rst SNO result of the 8B solar-neutrino ux measured withthe neutral- urrent rea tion on deuterium, νℓ d → npνℓ, above the neutral- urrentrea tion threshold of 2.2 MeV. The data orrespond to 306.4 live days with SNO betweenNovember 2, 1999 and May 28, 2001. The omplete des ription of the SNO Phase Idata set is given in AHARMIM 07.

φνµ+ντ(8B)φνµ+ντ(8B)φνµ+ντ(8B)φνµ+ντ(8B)Nonele tron- avor a tive neutrino omponent (νµ and ντ ) in the 8B solar-neutrino ux.VALUE (106 m−2s−1) DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, ts, limits, et . • • •3.26±0.25+0.40−0.35 1 AHARMIM 05A SNO From φNC , φCC , and φES ;8B shape not onst.3.09±0.22+0.30−0.27 1 AHARMIM 05A SNO From φNC , φCC , and φES ;8B shape onstrained3.41±0.45+0.48−0.45 2 AHMAD 02 SNO From φNC , φCC , and φES3.69±1.13 3 AHMAD 01 Derived from SNO+SuperKam,water Cherenkov1AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) inheavy water over the period between July 26, 2001 and August 28, 2003, orrespondingto 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statisti allyseparated. In one method, the 8B energy spe trum was not onstrained. In the othermethod, the onstraint of an undistorted 8B energy spe trum was added for omparisonwith AHMAD 02 results.2AHMAD 02 dedu ed the nonele tron- avor a tive neutrino omponent (νµ and ντ )in the 8B solar-neutrino ux, by ombining the harged- urrent result, the ν e elasti -s attering result and the neutral- urrent result. The omplete des ription of the SNOPhase I data set is given in AHARMIM 07.3AHMAD 01 dedu ed the nonele tron- avor a tive neutrino omponent (νµ and ντ ) inthe 8B solar-neutrino ux, by ombining the SNO harged- urrent result (AHMAD 01)and the Super-Kamiokande ν e elasti -s attering result (FUKUDA 01).Total Flux of A tive 8B Solar NeutrinosTotal Flux of A tive 8B Solar NeutrinosTotal Flux of A tive 8B Solar NeutrinosTotal Flux of A tive 8B Solar NeutrinosTotal ux of a tive neutrinos (νe , νµ, and ντ ).VALUE (106 m−2s−1) DOCUMENT ID TECN COMMENT


776776776776Lepton Parti le ListingsNeutrino Mixing5.25 ±0.16 +0.11−0.13 1 AHARMIM 13 SNO All three phases ombined5.046+0.159

−0.152+0.107−0.123 2 AHARMIM 10 SNO From φNC in Phase I+II, lowthreshold5.54 +0.33

−0.31 +0.36−0.34 3 AHARMIM 08 SNO φNC in Phase III4.94 ±0.21 +0.38−0.34 4 AHARMIM 05A SNO From φNC ; 8B shape not onst.4.81 ±0.19 +0.28−0.27 4 AHARMIM 05A SNO From φNC ; 8B shape onstrained5.09 +0.44

−0.43 +0.46−0.43 5 AHMAD 02 SNO Dire t measurement from φNC5.44 ±0.99 6 AHMAD 01 Derived from SNO+SuperKam,water Cherenkov1AHARMIM 13 obtained this result from a ombined analysis of the data from all threephases, SNO-I, II, and III. The measurement of the 8B ux mostly omes from the NCsignal, however, CC ontribution is in luded in the t.2AHARMIM 10 reports this result from a joint analysis of SNO Phase I+II data withthe "ee tive ele tron kineti energy" threshold of 3.5 MeV. This result is obtainedwith the assumption of unitarity, whi h relates the NC, CC, and ES rates. The datawere t with the free parameters dire tly des ribing the total 8B neutrino ux and theenergy-dependent νe survival probability.3AHARMIM 08 reports the results from SNO Phase III measurement using an array of3He proportional ounters to measure the rate of NC intera tions in heavy water, overthe period between November 27, 2004 and November 28, 2006, orresponding to 385.17live days. A simultaneous t was made for the number of NC events dete ted by theproportional ounters and the numbers of NC, CC, and ES events dete ted by the PMTs,where the spe tral distributions of the ES and CC events were not onstrained to the 8Bshape.4AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) inheavy water over the period between July 26, 2001 and August 28, 2003, orrespondingto 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statisti allyseparated. In one method, the 8B energy spe trum was not onstrained. In the othermethod, the onstraint of an undistorted 8B energy spe trum was added for omparisonwith AHMAD 02 results.5AHMAD 02 determined the total ux of a tive 8B solar neutrinos by dire tly measuringthe neutral- urrent rea tion, νℓ d → npνℓ, whi h is equally sensitive to νe , νµ, and ντ .The omplete des ription of the SNO Phase I data set is given in AHARMIM 07.6AHMAD 01 dedu ed the total ux of a tive 8B solar neutrinos by ombining the SNO harged- urrent result (AHMAD 01) and the Super-Kamiokande ν e elasti -s atteringresult (FUKUDA 01).Day-Night Asymmetry (8B)Day-Night Asymmetry (8B)Day-Night Asymmetry (8B)Day-Night Asymmetry (8B)A = (φnight − φday) / φaverageVALUE DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, ts, limits, et . • • •0.032±0.011±0.005 1 RENSHAW 14 SKAM Based on φES0.063±0.042±0.037 2 CRAVENS 08 SKAM Based on φES0.021±0.020+0.012−0.013 3 HOSAKA 06 SKAM Based on φES0.017±0.016+0.012−0.013 4 HOSAKA 06 SKAM Fitted in the LMA region

−0.056±0.074±0.053 5 AHARMIM 05A SNO From salty SNO φCC−0.037±0.063±0.032 5 AHARMIM 05A SNO From salty SNO φCC ; onst.of no φNC asymmetry0.14 ±0.063+0.015

−0.014 6 AHMAD 02B SNO Derived from SNO φCC0.07 ±0.049+0.013−0.012 7 AHMAD 02B SNO Const. of no φNC asymmetry1RENSHAW 14 obtains this result by using the "amplitude t" introdu ed in SMY 04.The data from the Super-Kamiokande(SK)-I, -II, -III, and 1306 live days of the SK-IVmeasurements are used. The analysis threshold is re oil-ele tron kineti energy of 4.5MeV for SK-III, and SK-IV ex ept for 250 live days in SK-III (6.0 MeV). The analysisthreshold for SK-I and SK-II is the same as in the previous reports. (Note that in theprevious SK solar-neutrino results, the analysis threshold is quoted as re oil-ele trontotal energy.) This day-night asymmetry result is onsistent with neutrino os illationsfor 4 × 10−5 eV2 < m221 < 7 × 10−5 eV2 and large mixing values of θ12 at the68% CL.2CRAVENS 08 reports the Super-Kamiokande-II results for 791 live days from De ember2002 to O tober 2005. The photo athode overage of the dete tor is 19% (redu ed from40% of that of Super-Kamiokande-I due to an a ident in 2001). The analysis thresholdfor the day and night uxes is 7.5 MeV ex ept for the rst 159 live days (8.0 MeV).3HOSAKA 06 reports the nal results for 1496 live days with Super-Kamiokande-I betweenMay 31, 1996 and July 15, 2001, and repla e FUKUDA 02 results. The analysis thresholdis 5 MeV ex ept for the rst 280 live days (6.5 MeV).4This result with redu ed statisti al un ertainty is obtained by assuming two-neutrinoos illations within the LMA (large mixing angle) region and by tting the time variation ofthe solar neutrino ux measured via νe elasti s attering to the variations expe ted fromneutrino os illations. For details, see SMY 04. There is an additional small systemati error of ±0.0004 oming from un ertainty of os illation parameters.5AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) inheavy water over the period between July 26, 2001 and August 28, 2003, with 176.5days of the live time re orded during the day and 214.9 days during the night. Thisresult is obtained with the spe tral distribution of the CC events not onstrained to the8B shape.6AHMAD 02B results are based on the harged- urrent intera tions re orded betweenNovember 2, 1999 and May 28, 2001, with the day and night live times of 128.5 and177.9 days, respe tively. The omplete des ription of the SNO Phase I data set is givenin AHARMIM 07.

7AHMAD 02B results are derived from the harged- urrent intera tions, neutral- urrentintera tions, and ν e elasti s attering, with the total ux of a tive neutrinos onstrainedto have no asymmetry. The data were re orded between November 2, 1999 and May28, 2001, with the day and night live times of 128.5 and 177.9 days, respe tively. The omplete des ription of the SNO Phase I data set is given in AHARMIM 07.φES (7Be)φES (7Be)φES (7Be)φES (7Be)7Be solar-neutrino ux measured via νe elasti s attering. This pro ess is sensitiveto all a tive neutrino avors, but with redu ed sensitivity to νµ, ντ due to the ross-se tion dieren e, σ(ν µ,τ e) ∼ 0.2 σ(νe e). If the 7Be solar-neutrino ux involvesnonele tron avor a tive neutrinos, their ontribution to the ux is ∼ 0.2 times thatof νe .VALUE (109 m−2 s−1) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •3.26±0.52 1 GANDO 15 KLND average ux3.10±0.15 2 BELLINI 11A BORX average ux1GANDO 15 uses 165.4 kton·day exposure of the KamLAND liquid s intillator dete torto measure the 862 keV 7Be solar neutrino ux via ν − e elasti s attering2BELLINI 11A reports the 7Be solar neutrino ux measured via ν − e elasti s attering.The data orrespond to 740.7 live days between May 16, 2007 and May 8, 2010, andalso orrespond to 153.6 ton·year du ial exposure. BELLINI 11A measured the 862 keV7Be solar neutrino ux, whi h is an 89.6% bran h of the 7Be solar neutrino ux, to be(2.78 ± 0.13)× 109 m−2 s−1. Super edes ARPESELLA 08A.φES (pe p)φES (pe p)φES (pe p)φES (pe p)pe p solar-neutrino ux measured via νe elasti s attering. This pro ess is sensitiveto all a tive neutrino avors, but with redu ed sensitivity to νµ, ντ due to the rossse tion dieren e, σ(νµ,τ e) ∼ 0.2 σ(νe e). If the pe p solar-neutrino ux involvesnon-ele tron avor a tive neutrinos, their ontribution to the ux is ∼ 0.2 times thatof νe .VALUE (108 m−2s−1) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •1.0±0.2 1 BELLINI 12A BORX average ux1BELLINI 12A reports 1.44 MeV pe p solar-neutrino ux measured via νe elasti s attering.The data were olle ted between January 13, 2008 and May 9, 2010, orresponding to20,4009 ton·day du ial exposure. The listed ux value is al ulated from the observedrate of pe p solar neutrino intera tions in Borexino (3.1 ± 0.6 ± 0.3 ounts/(day·100ton)) and the orresponding rate expe ted for no neutrino avor os illations (4.47± 0.05 ounts/(day·100 ton)), using the SSM predi tion for the pe p solar neutrino ux of(1.441 ± 0.012) × 108 m−2s−1.φES (CNO)φES (CNO)φES (CNO)φES (CNO)CNO solar-neutrino ux measured via νe elasti s attering. This pro ess is sensitiveto all a tive neutrino avors, but with redu ed sensitivity to νµ, ντ due to the rossse tion dieren e, σ(νµ,τ e) ∼ 0.2 σ(νe e). If the CNO solar-neutrino ux involvesnon-ele tron avor a tive neutrinos, their ontribution to the ux is ∼ 0.2 times thatof νe .VALUE (108 m−2s−1) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<7.7 90 1 BELLINI 12A BORX MSW-LMA solution assumed1BELLINI 12A reports an upper limit of the CNO solar neutrino ux measured via νeelasti s attering. The data were olle ted between January 13, 2008 and May 9, 2010, orresponding to 20,409 ton·day du ial exposure.φES(pp)φES(pp)φES(pp)φES(pp)pp solar-neutrino ux measured via ν e elasti s attering. This pro ess is sensitiveto all a tive neutrino avors, but with redu ed sensitivity to νµ, ντ due to the rossse tion dieren e, σ(νµ,τ e) ∼ 0.3 σ(νe e). If the pp solar-neutrino ux involvesnonele tron avor a tive neutrinos, their ontribution to the ux is ∼ 0.3 times of νe .VALUE (1010 m−2 s−1) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •4.4±0.5 1 BELLINI 14A BORX average ux1BELLINI 14A reports pp solar-neutrino ux measured via ν e elasti s attering. Thedata were olle ted between January 2012 and May 2013, orresponding to 408 days ofdata. The pp neutrino intera tion rate in Borexino is measured to be 144 ± 13 ± 10 ounts/(day·100 ton) by tting the measured energy spe trum of events in the 165590keV re oil ele tron kineti energy window with the expe ted signal + ba kground spe -trum. The listed ux value φES(pp) is al ulated from the observed rate and the numberof (3.307± 0.003)×1031 ele trons for 100 tons of the Borexino s intillator, and the νe eintegrated ross se tion over the pp neutrino spe trum, σ(νe e) = 11.38× 10−46 m2.φCC (pp)φCC (pp)φCC (pp)φCC (pp)pp solar-neutrino ux measured with harged- urrent rea tion whi h is sensitive ex lu-sively to νe .VALUE (1010 m−2 s−1) DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •3.38±0.47 1 ABDURASHI... 09 FIT Fit existing solar-ν data

777777777777See key on page 601 Lepton Parti le ListingsNeutrino Mixing1ABDURASHITOV 09 reports the pp solar-neutrino ux derived from the Ga solar neu-trino apture rate by subtra ting ontributions from 8B, 7Be, pe p and CNO solar neu-trino uxes determined by other solar neutrino experiments as well as neutrino os illationparameters determined from available world neutrino os illation data.φES (hep)φES (hep)φES (hep)φES (hep)hep solar-neutrino ux measured via ν e elasti s attering. This pro ess is sensitiveto all a tive neutrino avors, but with redu ed sensitivity to νµ, ντ due to the ross-se tion dieren e, σ(ν µ,τ e) ∼ 0.16σ(νe e). If the hep solar-neutrino ux involvesnonele tron avor a tive neutrinos, their ontribution to the ux is ∼ 0.16 times of

νe .VALUE (103 m−2s−1) CL% DOCUMENT ID TECN• • • We do not use the following data for averages, ts, limits, et . • • •

<73 90 1 HOSAKA 06 SKAM1HOSAKA 06 result is obtained from the re oil ele tron energy window of 1821 MeV,and updates FUKUDA 01 result.φνe (8B)φνe (8B)φνe (8B)φνe (8B)Sear hes are made for ele tron antineutrino ux from the Sun. Flux limits listed hereare derived relative to the BS05(OP) Standard Solar Model 8B solar neutrino ux(5.69× 106 m−2 s−1), with an assumption that solar νe s follow an unos illated 8Bneutrino spe trum.VALUE (%) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<0.013 90 BELLINI 11 BORX Eνe > 1.8 MeV<1.9 90 1 BALATA 06 CNTR 1.8< Eνe < 20.0 MeV<0.72 90 AHARMIM 04 SNO 4.0< Eνe < 14.8 MeV<0.022 90 EGUCHI 04 KLND 8.3< Eνe < 14.8 MeV<0.7 90 GANDO 03 SKAM 8.0< Eνe < 20.0 MeV<1.7 90 AGLIETTA 96 LSD 7< Eνe < 17 MeV1BALATA 06 obtained this result from the sear h for νe intera tions with Counting TestFa ility (the prototype of the Borexino dete tor).(B) Three-neutrino mixing parameters(B) Three-neutrino mixing parameters(B) Three-neutrino mixing parameters(B) Three-neutrino mixing parametersINTRODUCTION TO THREE-NEUTRINO MIXINGPARAMETERS LISTINGS

Updated November 2015 by M. Goodman (ANL).

Introduction and Notation: With the exception of possible

short-baseline anomalies (such as LSND), current accelerator,

reactor, solar and atmospheric neutrino data can be described

within the framework of a 3 × 3 mixing matrix between the

flavor eigenstates νe, νµ and ντ and mass eigenstates ν1, ν2 and

ν3. (See equation 14.6 of the review “Neutrino Mass, Mixing

and Oscillations” by K. Nakamura and S.T. Petcov.) Whether

or not this is the ultimately correct framework, it is currently

widely used to parametrize neutrino mixing data and to plan

new experiments.

The mass differences are called ∆m221 ≡ m2

2 − m21 and

∆m232 ≡ m2

3 − m22. In these listings, we assume

∆m232 ∼ ∆m2

31 (1)

even though the experimental error is comparable to the dif-

ference ∆m231 − ∆m2

32 = ∆m221. The measurements made by

νµ disappearance at accelerators and by νe disappearance at

reactors are slightly different mixtures of ∆m232 and ∆m2

31. The

angles are labeled θ12, θ23 and θ13. The CP violating phase is

called δ. The familiar two neutrino form for oscillations is

P (νa → νb; a 6= b) = sin2(2θ) sin2(∆m2L/4E). (2)

Despite the fact that the mixing angles have been measured

to be much larger than in the quark sector, the two neutrino

form is often a very good approximation and is used in many

situations.

The angles appear in the equations below in many forms.

They most often appear as sin2(2θ). The listings currently now

use sin2(θ) because this distinguishes whether θ23 is larger or

smaller than 45.

Accelerator neutrino experiments: Ignoring ∆m221, CP vi-

olation, and matter effects, the equations for the probability of

appearance in an accelerator oscillation experiment are:

P (νµ → ντ ) = sin2(2θ23) cos4(θ13) sin2(∆m232L/4E) (3)

P (νµ → νe) = sin2(2θ13) sin2(θ23) sin2(∆m232L/4E) (4)

P (νe → νµ) = sin2(2θ13) sin2(θ23) sin2(∆m232L/4E) (5)

P (νe → ντ ) = sin2(2θ13) cos2(θ23) sin2(∆m232L/4E) . (6)

Current and future long-baseline accelerator experiments

are studying non-zero θ13 through P (νµ → νe). Including the

CP terms and low mass scale, the equation for neutrino oscilla-

tion in vacuum is:

P (νµ → νe) = P1 + P2 + P3 + P4

P1 = sin2(θ23) sin2(2θ13) sin2(∆m232L/4E)

P2 = cos2(θ23) sin2(2θ13) sin2(∆m221L/4E)

P3 = −/+ J sin(δ) sin(∆m232L/4E)

P4 = J cos(δ) cos(∆m232L/4E) (7)

where

J = cos(θ13) sin(2θ12) sin(2θ13) sin(2θ23)×sin(∆m2

32L/4E) sin(∆m221L/4E) (8)

and the sign in P3 is negative for neutrinos and positive for anti-

neutrinos respectively. For most new long-baseline accelerator

experiments, P2 can safely be neglected but the other three

terms can all be large. Also, depending on the distance and the

mass hierarchy, matter effects will need to be included.

Reactor neutrino experiments: Nuclear reactors are prolific

sources of νe with an energy near 4 MeV. The oscillation

probability can be expressed

P (νe → νe) = 1 − cos4(θ13) sin2(2θ12) sin2(∆m221L/4E)

− cos2(θ12) sin2(2θ13) sin2(∆m231L/4E)

− sin2(θ12) sin2(2θ13) sin2(∆m232L/4E) (9)

not using the approximation in Eq. (1). For short distances

(L<5 km) we can ignore the second term on the right and can

reimpose approximation Eq. (1). This takes the familiar two

neutrino form with θ13 and ∆m232:

P (νe → νe) = 1 − sin2(2θ13) sin2(∆m232L/4E). (10)

Solar and Atmospheric neutrino experiments: Solar neu-

trino experiments are sensitive to νe disappearance and have

778778778778Lepton Parti le ListingsNeutrino Mixingallowed the measurement of θ12 and ∆m2

21. They are also

sensitive to θ13. We identify ∆m2⊙ = ∆m2

21 and θ⊙ = θ12.

Atmospheric neutrino experiments are primarily sensitive

to νµ disappearance through νµ → ντ oscillations, and have

allowed the measurement of θ23 and ∆m232. We identify ∆m2

A =

∆m232 and θA = θ23. Despite the large νe component of the

atmospheric neutrino flux, it is difficult to measure ∆m221

effects. This is because of a cancellation between νµ → νe and

νe → νµ together with the fact that the ratio of νµ and νe

atmospheric fluxes, which arise from sequential π and µ decay,

is near 2.

Oscillation Parameter Listings: In Section (B) we encode

the three mixing angles θ12, θ23, θ13 and two mass squared differ-

ences ∆m221 and ∆m2

32. Our knowledge of θ12 and ∆m221 comes

from the KamLAND reactor neutrino experiment together with

solar neutrino experiments. Our knowledge of θ23 and ∆m232

comes from atmospheric, reactor and long-baseline accelerator

neutrino experiments. For the earlier experiments, we identified

the large mass splitting as ∆m232. Now that σ(∆m2

32) ≈ ∆m221,

some experiments report separate values for the two hierarchies.

Results on θ13 come from reactor antineutrino disappearance

experiments. There are also results from long-baseline acceler-

ator experiments looking for νe appearance. The interpretation

of both kinds of results depends on ∆m232, and the accelerator

results also depend on the mass hierarchy, θ23 and the CP

violating phase δ.

Accelerator and atmospheric experiments are beginning to

have some sensitivity to the CP violation phase δ through

Eq. (7). Note that P3 depends on the sign of ∆m232 so the

sensitivity depends on the mass hierarchy. For non-maximal

θ23 mixing, it also depends on the octant of θ23, i.e. whether

θ23 > π/4 or θ23 < π/4.sin2(θ12)sin2(θ12)sin2(θ12)sin2(θ12)VALUE DOCUMENT ID TECN COMMENT0.304+0.014−0.0130.304+0.014−0.0130.304+0.014−0.0130.304+0.014−0.013 1 GANDO 13 FIT KamLAND + global solar +SBL + a elerator: 3ν

• • • We do not use the following data for averages, ts, limits, et . • • •0.323±0.016 2 FORERO 14 FIT 3ν0.304+0.013−0.012 3 GONZALEZ-G...14 FIT Either mass ordering; global t0.299+0.014−0.014 4,5 AHARMIM 13 FIT global solar: 2ν0.307+0.016−0.013 5,6 AHARMIM 13 FIT global solar: 3ν0.304+0.022−0.018 5,7 AHARMIM 13 FIT KamLAND + global solar: 3ν0.304+0.014−0.013 8 GANDO 13 FIT KamLAND + global solar: 3ν0.325+0.039−0.039 9 GANDO 13 FIT KamLAND: 3ν0.30 +0.02−0.01 10 ABE 11 FIT KamLAND + global solar: 2ν0.30 +0.02−0.01 11 ABE 11 FIT global solar: 2ν0.31 +0.03−0.02 12 ABE 11 FIT KamLAND + global solar: 3ν0.31 +0.03−0.03 13 ABE 11 FIT global solar: 3ν0.314+0.015−0.012 14 BELLINI 11A FIT KamLAND + global solar: 2ν0.319+0.017−0.015 15 BELLINI 11A FIT global solar: 2ν0.311+0.016−0.016 16 GANDO 11 FIT KamLAND + solar: 3ν0.304+0.046−0.042 17 GANDO 11 FIT KamLAND: 3ν0.314+0.018−0.014 18,19 AHARMIM 10 FIT KamLAND + global solar: 2ν

0.314+0.017−0.020 18,20 AHARMIM 10 FIT global solar: 2ν0.319+0.019−0.016 18,21 AHARMIM 10 FIT KamLAND + global solar: 3ν0.319+0.023−0.024 18,22 AHARMIM 10 FIT global solar: 3ν0.36 +0.05−0.04 23 ABE 08A FIT KamLAND0.32 ±0.03 24 ABE 08A FIT KamLAND + global t0.32 ±0.02 25 AHARMIM 08 FIT KamLAND + global solar0.31 +0.04−0.04 26 HOSAKA 06 FIT KamLAND + global solar0.31 +0.04−0.03 27 HOSAKA 06 FIT SKAM+SNO+KamLAND0.31 +0.03−0.04 28 HOSAKA 06 FIT SKAM+SNO0.31 +0.02−0.03 29 AHARMIM 05A FIT KamLAND + global solar0.250.39 30 AHARMIM 05A FIT global solar0.29 ±0.03 31 ARAKI 05 FIT KamLAND + global solar0.29 +0.03−0.02 32 AHMED 04A FIT KamLAND + global solar0.230.37 33 AHMED 04A FIT global solar0.31 +0.04−0.04 34 SMY 04 FIT KamLAND + global solar0.29 +0.04−0.04 35 SMY 04 FIT global solar0.32 +0.06−0.05 36 SMY 04 FIT SKAM + SNO0.190.33 37 AHMAD 02B FIT global solar0.190.39 38 FUKUDA 02 FIT global solar1GANDO 13 obtained this result by a three-neutrino os illation analysis using KamLAND,global solar neutrino, short-baseline (SBL) rea tor, and a elerator data, assuming CPTinvarian e. Supersedes GANDO 11.2 FORERO 14 performs a global t to neutrino os illations using solar, rea tor, long-baseline a elerator, and atmospheri neutrino data.3GONZALEZ-GARCIA 14 result omes from a frequentist global t. The orrespond-ing Bayesian global t to the same data results are reported in BERGSTROM 15 as0.304+0.013

−0.012 for normal and 0.305+0.012−0.013 for inverted mass ordering.4AHARMIM 13 obtained this result by a two-neutrino os illation analysis using globalsolar neutrino data.5AHARMIM 13 global solar neutrino data in lude SNO's all-phases- ombined analysisresults on the total a tive 8B neutrino ux and energy-dependent νe survival probabilityparameters, measurements of Cl (CLEVELAND 98), Ga (ABDURASHITOV 09 whi h ontains ombined analysis with GNO (ALTMANN 05 and Ph.D. thesis of F. Kaether)),and 7Be (BELLINI 11A) rates, and 8B solar-neutrino re oil ele tron measurements of SK-I (HOSAKA 06) zenith, SK-II (CRAVENS 08) and SK-III (ABE 11) day/night spe tra,and Borexino (BELLINI 10A) spe tra.6AHARMIM 13 obtained this result by a three-neutrino os illation analysis with the valueof m232 xed to 2.45 × 10−3 eV2, using global solar neutrino data.7AHARMIM 13 obtained this result by a three-neutrino os illation analysis with thevalue of m232 xed to 2.45 × 10−3 eV2, using global solar neutrino and KamLAND(GANDO 11) data. CPT invarian e is assumed.8GANDO 13 obtained this result by a three-neutrino os illation analysis using KamLANDand global solar neutrino data, assuming CPT invarian e. Supersedes GANDO 11.9GANDO 13 obtained this result by a three-neutrino os illation analysis using KamLANDdata. Supersedes GANDO 11.10ABE 11 obtained this result by a two-neutrino os illation analysis using solar neu-trino data in luding Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake,GALLEX/GNO, SAGE, and KamLAND data. CPT invarian e is assumed.11ABE 11 obtained this result by a two-neutrino os illation analysis using solar neu-trino data in luding Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake,GALLEX/GNO, and SAGE data.12ABE 11 obtained this result by a three-neutrino os illation analysis with the value ofm232 xed to 2.4× 10−3 eV2, using solar neutrino data in luding Super-Kamiokande,SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, SAGE, and KamLANDdata. The normal neutrino mass ordering and CPT invarian e are assumed.13ABE 11 obtained this result by a three-neutrino os illation analysis with the value ofm232 xed to 2.4× 10−3 eV2, using solar neutrino data in luding Super-Kamiokande,SNO, Borexino (ARPESELLA 08A), Homestake, and GALLEX/GNO data. The normalneutrino mass ordering is assumed.14BELLINI 11A obtained this result by a two-neutrino os illation analysis using KamLAND,Homestake, SAGE, Gallex, GNO, Kamiokande, Super-Kamiokande, SNO, and Borexino(BELLINI 11A) data and the SSM ux predi tion in SERENELLI 11 (Astrophysi al Jour-nal 743743743743 24 (2011)) with the ex eption that the 8B ux was left free. CPT invarian e isassumed.15BELLINI 11A obtained this result by a two-neutrino os illation analysis using Home-stake, SAGE, Gallex, GNO, Kamiokande, Super-Kamiokande, SNO, and Borexino(BELLINI 11A) data and the SSM ux predi tion in SERENELLI 11 (Astrophysi al Jour-nal 743743743743 24 (2011)) with the ex eption that the 8B ux was left free.16GANDO 11 obtain this result with three-neutrino t using the KamLAND + solar data.Superseded by GANDO 13.17GANDO 11 obtain this result with three-neutrino t using the KamLAND data only.Superseded by GANDO 13.18AHARMIM 10 global solar neutrino data in lude SNO's low-energy-threshold analysissurvival probability day/night urves, SNO Phase III integral rates (AHARMIM 08), Cl(CLEVELAND 98), SAGE (ABDURASHITOV 09), Gallex/GNO (HAMPEL 99, ALT-MANN 05), Borexino (ARPESELLA 08A), SK-I zenith (HOSAKA 06), and SK-IIday/night spe tra (CRAVENS 08).

779779779779See key on page 601 Lepton Parti le ListingsNeutrino Mixing19AHARMIM 10 obtained this result by a two-neutrino os illation analysis using globalsolar neutrino data and KamLAND data (ABE 08A). CPT invarian e is assumed.20AHARMIM 10 obtained this result by a two-neutrino os illation analysis using globalsolar neutrino data.21AHARMIM 10 obtained this result by a three-neutrino os illation analysis with the valueof m231 xed to 2.3×10−3 eV2, using global solar neutrino data and KamLAND data(ABE 08A). CPT invarian e is assumed.22AHARMIM 10 obtained this result by a three-neutrino os illation analysis with the valueof m231 xed to 2.3× 10−3 eV2, using global solar neutrino data.23ABE 08A obtained this result by a rate + shape + time ombined geoneutrino andrea tor two-neutrino t for m221 and tan2θ12, using KamLAND data only. Supersededby GANDO 11.24ABE 08A obtained this result by means of a two-neutrino t using KamLAND, Homestake,SAGE, GALLEX, GNO, SK (zenith angle and E-spe trum), the SNO χ2-map, and solar ux data. CPT invarian e is assumed. Superseded by GANDO 11.25The result given by AHARMIM 08 is θ = (34.4+1.3−1.2). This result is obtained bya two-neutrino os illation analysis using solar neutrino data in luding those of Borex-ino (ARPESELLA 08A) and Super-Kamiokande-I (HOSAKA 06), and KamLAND data(ABE 08A). CPT invarian e is assumed.26HOSAKA 06 obtained this result by a two-neutrino os illation analysis using SK νe data,CC data from other solar neutrino experiments, and KamLAND data (ARAKI 05). CPTinvarian e is assumed.27HOSAKA 06 obtained this result by a two-neutrino os illation analysis using the data fromSuper-Kamiokande, SNO (AHMAD 02 and AHMAD 02B), and KamLAND (ARAKI 05)experiments. CPT invarian e is assumed.28HOSAKA 06 obtained this result by a two-neutrino os illation analysis using the Super-Kamiokande and SNO (AHMAD 02 and AHMAD 02B) solar neutrino data.29The result given by AHARMIM 05A is θ = (33.9 ± 1.6). This result is obtained bya two-neutrino os illation analysis using SNO pure deuteron and salt phase data, SK

νe data, Cl and Ga CC data, and KamLAND data (ARAKI 05). CPT invarian e isassumed. AHARMIM 05A also quotes θ = (33.9+2.4−2.2) as the error enveloping the 68%CL two-dimensional region. This translates into sin22 θ = 0.86+0.05

−0.06.30AHARMIM 05A obtained this result by a two-neutrino os illation analysis using the datafrom all solar neutrino experiments. The listed range of the parameter envelops the 95%CL two-dimensional region shown in gure 35a of AHARMIM 05A. AHARMIM 05A alsoquotes tan2θ = 0.45+0.09−0.08 as the error enveloping the 68% CL two-dimensional region.This translates into sin22 θ = 0.86+0.05

−0.07.31ARAKI 05 obtained this result by a two-neutrino os illation analysis using KamLAND andsolar neutrino data. CPT invarian e is assumed. The 1σ error shown here is translatedfrom the number provided by the KamLAND ollaboration, tan2θ = 0.40+0.07−0.05. The orresponding number quoted in ARAKI 05 is tan2θ = 0.40+0.10

−0.07 (sin22 θ = 0.82 ±0.07), whi h envelops the 68% CL two-dimensional region.32The result given by AHMED 04A is θ = (32.5+1.7−1.6). This result is obtained by a two-neutrino os illation analysis using solar neutrino and KamLAND data (EGUCHI 03). CPTinvarian e is assumed. AHMED 04A also quotes θ = (32.5+2.4

−2.3) as the error envelopingthe 68% CL two-dimensional region. This translates into sin22 θ = 0.82 ± 0.06.33AHMED 04A obtained this result by a two-neutrino os illation analysis using the datafrom all solar neutrino experiments. The listed range of the parameter envelops the 95%CL two-dimensional region shown in Fig. 5(a) of AHMED 04A. The best-t point is(m2) = 6.5× 10−5 eV2, tan2θ = 0.40 (sin22 θ = 0.82).34The result given by SMY 04 is tan2θ = 0.44 ± 0.08. This result is obtained by a two-neutrino os illation analysis using solar neutrino and KamLAND data (IANNI 03). CPTinvarian e is assumed.35 SMY 04 obtained this result by a two-neutrino os illation analysis using the data fromall solar neutrino experiments. The 1σ errors are read from Fig. 6(a) of SMY 04.36 SMY 04 obtained this result by a two-neutrino os illation analysis using the Super-Kamiokande and SNO (AHMAD 02 and AHMAD 02B) solar neutrino data. The 1σerrors are read from Fig. 6(a) of SMY 04.37AHMAD 02B obtained this result by a two-neutrino os illation analysis using the datafrom all solar neutrino experiments. The listed range of the parameter envelops the 95%CL two-dimensional region shown in Fig. 4(b) of AHMAD 02B. The best t point is(m2) = 5.0× 10−5 eV2 and tanθ = 0.34 (sin22 θ = 0.76).38 FUKUDA 02 obtained this result by a two-neutrino os illation analysis using the datafrom all solar neutrino experiments. The listed range of the parameter envelops the 95%CL two-dimensional region shown in Fig. 4 of FUKUDA 02. The best t point is (m2)= 6.9× 10−5 eV2 and tan2θ = 0.38 (sin22 θ = 0.80).m221m221m221m221VALUE (10−5 eV2) DOCUMENT ID TECN COMMENT7.53±0.187.53±0.187.53±0.187.53±0.18 1 GANDO 13 FIT KamLAND + global solar + SBL+ a elerator: 3ν• • • We do not use the following data for averages, ts, limits, et . • • •7.6 +0.19

−0.18 2 FORERO 14 FIT 3ν7.50+0.19−0.17 3 GONZALEZ-G...14 FIT Either mass ordering; global t5.13+1.29−0.96 4,5 AHARMIM 13 FIT global solar: 2ν5.13+1.49−0.98 5,6 AHARMIM 13 FIT global solar: 3ν7.46+0.20−0.19 5,7 AHARMIM 13 FIT KamLAND + global solar: 3ν

7.53+0.19−0.18 8 GANDO 13 FIT KamLAND + global solar: 3ν7.54+0.19−0.18 9 GANDO 13 FIT KamLAND: 3ν7.6 ±0.2 10 ABE 11 FIT KamLAND + global solar: 2ν6.2 +1.1−1.9 11 ABE 11 FIT global solar: 2ν7.7 ±0.3 12 ABE 11 FIT KamLAND + global solar: 3ν6.0 +2.2−2.5 13 ABE 11 FIT global solar: 3ν7.50+0.16−0.24 14 BELLINI 11A FIT KamLAND + global solar: 2ν5.2 +1.5−0.9 15 BELLINI 11A FIT global solar: 2ν7.50+0.19−0.20 16 GANDO 11 FIT KamLAND + solar: 3ν7.49±0.20 17 GANDO 11 FIT KamLAND: 3ν7.59+0.20−0.21 18,19 AHARMIM 10 FIT KamLAND + global solar: 2ν5.89+2.13−2.16 18,20 AHARMIM 10 FIT global solar: 2ν7.59±0.21 18,21 AHARMIM 10 FIT KamLAND + global solar: 3ν6.31+2.49−2.58 18,22 AHARMIM 10 FIT global solar: 3ν7.58+0.14−0.13±0.15 23 ABE 08A FIT KamLAND7.59±0.21 24 ABE 08A FIT KamLAND + global solar7.59+0.19−0.21 25 AHARMIM 08 FIT KamLAND + global solar8.0 ±0.3 26 HOSAKA 06 FIT KamLAND + global solar8.0 ±0.3 27 HOSAKA 06 FIT SKAM+SNO+KamLAND6.3 +3.7−1.5 28 HOSAKA 06 FIT SKAM+SNO512 29 HOSAKA 06 FIT SKAM day/night in the LMAregion8.0 +0.4−0.3 30 AHARMIM 05A FIT KamLAND + global solar LMA3.314.4 31 AHARMIM 05A FIT global solar7.9 +0.4−0.3 32 ARAKI 05 FIT KamLAND + global solar7.1 +1.0−0.3 33 AHMED 04A FIT KamLAND + global solar3.213.7 34 AHMED 04A FIT global solar7.1 +0.6−0.5 35 SMY 04 FIT KamLAND + global solar6.0 +1.7−1.6 36 SMY 04 FIT global solar6.0 +2.5−1.6 37 SMY 04 FIT SKAM + SNO2.812.0 38 AHMAD 02B FIT global solar3.219.1 39 FUKUDA 02 FIT global solar1GANDO 13 obtained this result by a three-neutrino os illation analysis using KamLAND,global solar neutrino, short-baseline (SBL) rea tor, and a elerator data, assuming CPTinvarian e. Supersedes GANDO 11.2 FORERO 14 performs a global t to m221 using solar, rea tor, long-baseline a elerator,and atmospheri neutrino data.3GONZALEZ-GARCIA 14 result omes from a frequentist global t. The orrespond-ing Bayesian global t to the same data results are reported in BERGSTROM 15 as(7.50+0.19

−0.17) × 10−5 eV2 for normal and (7.50+0.18−0.17) × 10−5 eV2 for inverted massordering.4AHARMIM 13 obtained this result by a two-neutrino os illation analysis using globalsolar neutrino data.5AHARMIM 13 global solar neutrino data in lude SNO's all-phases- ombined analysisresults on the total a tive 8B neutrino ux and energy-dependent νe survival probabilityparameters, measurements of Cl (CLEVELAND 98), Ga (ABDURASHITOV 09 whi h ontains ombined analysis with GNO (ALTMANN 05 and Ph.D. thesis of F. Kaether)),and 7Be (BELLINI 11A) rates, and 8B solar-neutrino re oil ele tron measurements of SK-I (HOSAKA 06) zenith, SK-II (CRAVENS 08), and SK-III (ABE 11) day/night spe tra,and Borexino (BELLINI 10A) spe tra.6AHARMIM 13 obtained this result by a three-neutrino os illation analysis with the valueof m231 xed to 2.45 × 10−3 eV2, using global solar neutrino data.7AHARMIM 13 obtained this result by a three-neutrino os illation analysis with the valueof m231 xed to 2.45 × 10−3 eV2, using global solar neutrino and KamLAND data(GANDO 11). CPT invarian e is assumed.8GANDO 13 obtained this result by a three-neutrino os illation analysis using KamLANDand global solar neutrino data, assuming CPT invarian e. Supersedes GANDO 11.9GANDO 13 obtained this result by a three-neutrino os illation analysis using KamLANDdata. Supersedes GANDO 11.10ABE 11 obtained this result by a two-neutrino os illation analysis using solar neu-trino data in luding Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake,GALLEX/GNO, SAGE, and KamLAND data. CPT invarian e is assumed.11ABE 11 obtained this result by a two-neutrino os illation analysis using solar neu-trino data in luding Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake,GALLEX/GNO, and SAGE data.12ABE 11 obtained this result by a three-neutrino os illation analysis with the value ofm232 xed to 2.4× 10−3 eV2, using solar neutrino data in luding Super-Kamiokande,SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, SAGE, and KamLANDdata. The normal neutrino mass ordering and CPT invarian e are assumed.13ABE 11 obtained this result by a three-neutrino os illation analysis with the value ofm232 xed to 2.4× 10−3 eV2, using solar neutrino data in luding Super-Kamiokande,SNO, Borexino (ARPESELLA 08A), Homestake, and GALLEX/GNO data. The normalneutrino mass ordering is assumed.

780780780780Lepton Parti le ListingsNeutrino Mixing14BELLINI 11A obtained this result by a two-neutrino os illation analysis using KamLAND,Homestake, SAGE, Gallex, GNO, Kamiokande, Super-Kamiokande, SNO, and Borexino(BELLINI 11A) data and the SSM ux predi tion in SERENELLI 11 (Astrophysi al Jour-nal 743743743743 24 (2011)) with the ex eption that the 8B ux was left free. CPT invarian e isassumed.15BELLINI 11A obtained this result by a two-neutrino os illation analysis using Home-stake, SAGE, Gallex, GNO, Kamiokande, Super-Kamiokande, SNO, and Borexino(BELLINI 11A) data and the SSM ux predi tion in SERENELLI 11 (Astrophysi al Jour-nal 743743743743 24 (2011)) with the ex eption that the 8B ux was left free.16GANDO 11 obtain this result with three-neutrino t using the KamLAND + solar data.Superseded by GANDO 13.17GANDO 11 obtain this result with three-neutrino t using the KamLAND data only.Supersedes ABE 08A.18AHARMIM 10 global solar neutrino data in lude SNO's low-energy-threshold analysissurvival probability day/night urves, SNO Phase III integral rates (AHARMIM 08), Cl(CLEVELAND 98), SAGE (ABDURASHITOV 09), Gallex/GNO (HAMPEL 99, ALT-MANN 05), Borexino (ARPESELLA 08A), SK-I zenith (HOSAKA 06), and SK-IIday/night spe tra (CRAVENS 08).19AHARMIM 10 obtained this result by a two-neutrino os illation analysis using globalsolar neutrino data and KamLAND data (ABE 08A). CPT invarian e is assumed.20AHARMIM 10 obtained this result by a two-neutrino os illation analysis using globalsolar neutrino data.21AHARMIM 10 obtained this result by a three-neutrino os illation analysis with the valueof m231 xed to 2.3×10−3 eV2, using global solar neutrino data and KamLAND data(ABE 08A). CPT invarian e is assumed.22AHARMIM 10 obtained this result by a three-neutrino os illation analysis with the valueof m231 xed to 2.3× 10−3 eV2, using global solar neutrino data.23ABE 08A obtained this result by a rate + shape + time ombined geoneutrino andrea tor two-neutrino t for m221 and tan2θ12, using KamLAND data only. Supersededby GANDO 11.24ABE 08A obtained this result by means of a two-neutrino t using KamLAND, Homestake,SAGE, GALLEX, GNO, SK (zenith angle and E-spe trum), the SNO χ2-map, and solar ux data. CPT invarian e is assumed. Superseded by GANDO 11.25AHARMIM 08 obtained this result by a two-neutrino os illation analysis using all solarneutrino data in luding those of Borexino (ARPESELLA 08A) and Super-Kamiokande-I(HOSAKA 06), and KamLAND data (ABE 08A). CPT invarian e is assumed.26HOSAKA 06 obtained this result by a two-neutrino os illation analysis using solar neutrinoand KamLAND data (ARAKI 05). CPT invarian e is assumed.27HOSAKA 06 obtained this result by a two-neutrino os illation analysis using the data fromSuper-Kamiokande, SNO (AHMAD 02 and AHMAD 02B), and KamLAND (ARAKI 05)experiments. CPT invarian e is assumed.28HOSAKA 06 obtained this result by a two-neutrino os illation analysis using the Super-Kamiokande and SNO (AHMAD 02 and AHMAD 02B) solar neutrino data.29HOSAKA 06 obtained this result from the onsisten y between the observed and expe tedday-night ux asymmetry amplitude. The listed 68% CL range is derived from the 1σboundary of the amplitude t to the data. Os illation parameters are onstrained to bein the LMA region. The mixing angle is xed at tan2θ = 0.44 be ause the t dependsonly very weekly on it.30AHARMIM 05A obtained this result by a two-neutrino os illation analysis using solarneutrino and KamLAND data (ARAKI 05). CPT invarian e is assumed. AHARMIM 05Aalso quotes (m2) = (8.0+0.6−0.4)× 10−5 eV2 as the error enveloping the 68% CL two-dimensional region.31AHARMIM 05A obtained this result by a two-neutrino os illation analysis using the datafrom all solar neutrino experiments. The listed range of the parameter envelops the95% CL two-dimensional region shown in gure 35a of AHARMIM 05A. AHARMIM 05Aalso quotes (m2) = (6.5+4.4−2.3)× 10−5 eV2 as the error enveloping the 68% CL two-dimensional region.32ARAKI 05 obtained this result by a two-neutrino os illation analysis using KamLANDand solar neutrino data. CPT invarian e is assumed. The 1σ error shown here is providedby the KamLAND ollaboration. The error quoted in ARAKI 05, (m2) = (7.9+0.6

−0.5)×10−5, envelops the 68% CL two-dimensional region.33AHMED 04A obtained this result by a two-neutrino os illation analysis using solar neu-trino and KamLAND data (EGUCHI 03). CPT invarian e is assumed. AHMED 04Aalso quotes (m2) = (7.1+1.2−0.6)× 10−5 eV2 as the error enveloping the 68% CL two-dimensional region.34AHMED 04A obtained this result by a two-neutrino os illation analysis using the datafrom all solar neutrino experiments. The listed range of the parameter envelops the 95%CL two-dimensional region shown in Fig. 5(a) of AHMED 04A. The best-t point is(m2) = 6.5× 10−5 eV2, tan2θ = 0.40 (sin22 θ = 0.82).35 SMY 04 obtained this result by a two-neutrino os illation analysis using solar neutrinoand KamLAND data (IANNI 03). CPT invarian e is assumed.36 SMY 04 obtained this result by a two-neutrino os illation analysis using the data fromall solar neutrino experiments. The 1σ errors are read from Fig. 6(a) of SMY 04.37 SMY 04 obtained this result by a two-neutrino os illation analysis using the Super-Kamiokande and SNO (AHMAD 02 and AHMAD 02B) solar neutrino data. The 1σerrors are read from Fig. 6(a) of SMY 04.38AHMAD 02B obtained this result by a two-neutrino os illation analysis using the datafrom all solar neutrino experiments. The listed range of the parameter envelops the 95%CL two-dimensional region shown in Fig. 4(b) of AHMAD 02B. The best t point is(m2) = 5.0× 10−5 eV2 and tanθ = 0.34 (sin22 θ = 0.76).39 FUKUDA 02 obtained this result by a two-neutrino os illation analysis using the datafrom all solar neutrino experiments. The listed range of the parameter envelops the 95%

CL two-dimensional region shown in Fig. 4 of FUKUDA 02. The best t point is (m2)= 6.9× 10−5 eV2 and tan2θ = 0.38 (sin22 θ = 0.80).sin2(θ23)sin2(θ23)sin2(θ23)sin2(θ23)The reported limits below orrespond to the proje tion onto the sin2(θ23) axis of the90% CL ontours in the sin2(θ23) − m232 plane presented by the authors. Unlessotherwise spe ied, the limits are 90% CL and the reported un ertainties are 68% CL.VALUE DOCUMENT ID TECN COMMENT0.50 ±0.05 OUR FIT0.50 ±0.05 OUR FIT0.50 ±0.05 OUR FIT0.50 ±0.05 OUR FIT Assuming inverted mass hierar hy0.51 ±0.05 OUR FIT0.51 ±0.05 OUR FIT0.51 ±0.05 OUR FIT0.51 ±0.05 OUR FIT Assuming normal mass hierar hy0.53 +0.09−0.12 1 AARTSEN 15A ICCB 3ν os ; normal mass ordering0.51 +0.09−0.11 1 AARTSEN 15A ICCB 3ν os ; inverted mass ordering0.514+0.055−0.056 2 ABE 14 T2K 3ν os .; normal mass ordering0.511±0.055 2 ABE 14 T2K 3ν os .; inverted mass ordering0.41 +0.23−0.06 3 ADAMSON 14 MINS 3ν os ., normal mass ordering0.41 +0.26−0.07 3 ADAMSON 14 MINS 3ν os .; inverted mass ordering

• • • We do not use the following data for averages, ts, limits, et . • • •0.567+0.032−0.128 4 FORERO 14 FIT Normal mass ordering0.573+0.025−0.043 4 FORERO 14 FIT Inverted mass ordering0.452+0.052−0.028 5 GONZALEZ-G...14 FIT Normal mass ordering; global t0.579+0.025−0.037 5 GONZALEZ-G...14 FIT Inverted mass ordering; global t0.24 to 0.76 6 AARTSEN 13B ICCB DeepCore, 2ν os illation0.514±0.082 7 ABE 13G T2K 3ν os .; normal mass ordering0.388+0.051−0.053 8 ADAMSON 13B MINS Beam + Atmospheri ; identi al ν & ν0.3 to 0.7 9 ABE 12A T2K o-axis beam0.28 to 0.72 10 ADAMSON 12 MINS ν beam0.25 to 0.75 11,12 ADAMSON 12B MINS MINOS atmospheri 0.27 to 0.73 11,13 ADAMSON 12B MINS MINOS pure atmospheri ν0.21 to 0.79 11,13 ADAMSON 12B MINS MINOS pure atmospheri ν0.15 to 0.85 14 ADRIAN-MAR...12 ANTR atmospheri ν with deep see teles ope0.39 to 0.61 15 ABE 11C SKAM Super-Kamiokande0.34 to 0.66 ADAMSON 11 MINS 2ν os .; maximal mixing0.31 +0.10−0.07 16 ADAMSON 11B MINS ν beam0.41 to 0.59 17 WENDELL 10 SKAM 3ν os . with solar terms; θ13=00.39 to 0.61 18 WENDELL 10 SKAM 3ν os .; normal mass ordering0.37 to 0.63 19 WENDELL 10 SKAM 3ν os .; inverted mass ordering0.31 to 0.69 ADAMSON 08A MINS MINOS0.05 to 0.95 20 ADAMSON 06 MINS atmospheri ν with far dete tor0.18 to 0.82 21 AHN 06A K2K KEK to Super-K0.23 to 0.77 22 MICHAEL 06 MINS MINOS0.18 to 0.82 23 ALIU 05 K2K KEK to Super-K0.18 to 0.82 24 ALLISON 05 SOU20.36 to 0.64 25 ASHIE 05 SKAM Super-Kamiokande0.28 to 0.72 26 AMBROSIO 04 MCRO MACRO0.34 to 0.66 27 ASHIE 04 SKAM L/E distribution0.08 to 0.92 28 AHN 03 K2K KEK to Super-K0.13 to 0.87 29 AMBROSIO 03 MCRO MACRO0.26 to 0.74 30 AMBROSIO 03 MCRO MACRO0.15 to 0.85 31 SANCHEZ 03 SOU2 Soudan-2 Atmospheri 0.28 to 0.72 32 AMBROSIO 01 MCRO upward µ0.29 to 0.71 33 AMBROSIO 01 MCRO upward µ0.13 to 0.87 34 FUKUDA 99C SKAM upward µ0.23 to 0.77 35 FUKUDA 99D SKAM upward µ0.08 to 0.92 36 FUKUDA 99D SKAM stop µ / through0.29 to 0.71 37 FUKUDA 98C SKAM Super-Kamiokande0.08 to 0.92 38 HATAKEYAMA98 KAMI Kamiokande0.24 to 0.76 39 HATAKEYAMA98 KAMI Kamiokande0.20 to 0.80 40 FUKUDA 94 KAMI Kamiokande1AARTSEN 15A obtains this result by a three-neutrino os illation analysis using 10100GeV muon neutrino sample from a total of 953 days of measurement with the low-energysubdete tor DeepCore of the I eCube neutrino teles ope.2ABE 14 results are based on νµ disappearan e using three-neutrino os illation t. The onden e intervals are derived from one dimensional proled likelihoods.3ADAMSON 14 uses a omplete set of a elerator and atmospheri data. The analysis ombines the νµ disappearan e and νe appearan e data using three-neutrino os illationt. The t results are obtained for normal and inverted mass ordering assumptions. Thebest t is for lower θ23 quadrant and inverted mass ordering.4 FORERO 14 performs a global t to neutrino os illations using solar, rea tor, long-baseline a elerator, and atmospheri neutrino data.5GONZALEZ-GARCIA 14 result omes from a frequentist global t. The orrespondingBayesian global t to the same data results are reported in BERGSTROM 15 as 68% CLintervals of 0.4330.496 or 0.5300.594 for normal and 0.5140.612 for inverted massordering.6AARTSEN 13B obtained this result by a two-neutrino os illation analysis using 20100GeV muon neutrino sample from a total of 318.9 days of live-time measurement withthe low-energy subdete tor DeepCore of the I eCube neutrino teles ope.

781781781781See key on page 601 LeptonParti le ListingsNeutrinoMixing7The best t value is sin2(θ23) = 0.514 ± 0.082. Superseded by ABE 14.8ADAMSON 13B obtained this result from νµ and νµ disappearan e using νµ (10.71 ×1020 POT) and νµ (3.36× 1020 POT) beams, and atmospheri (37.88kton-years) datafrom MINOS The t assumed two- avor neutrino hypothesis and identi al νµ and νµos illation parameters. Superseded by ADAMSON 14.9ABE 12A obtained this result by a two-neutrino os illation analysis. The best-t point issin2(2θ23) = 0.98.10ADAMSON 12 is a two-neutrino os illation analysis using antineutrinos. The best tvalue is sin2(2θ23) = 0.95+0.10−0.11 ± 0.01.11ADAMSON 12B obtained this result by a two-neutrino os illation analysis of the L/Edistribution using 37.9 kton·yr atmospheri neutrino data with the MINOS far dete tor.12The best t point is m2 = 0.0019 eV2 and sin22θ = 0.99. The 90% single-parameter onden e interval at the best t point is sin22θ > 0.86.13The data are separated into pure samples of νs and νs, and separate os illation parametersfor νs and νs are t to the data. The best t point is (m2, sin22θ) = (0.0022 eV2,0.99) and (m2, sin22θ) = (0.0016 eV2, 1.00). The quoted result is taken from the90% C.L. ontour in the (m2, sin22θ) plane obtained by minimizing the four parameterlog-likelihood fun tion with respe t to the other os illation parameters.14ADRIAN-MARTINEZ 12 measured the os illation parameters of atmospheri neutrinoswith the ANTARES deep sea neutrino teles ope using the data taken from 2007 to 2010(863 days of total live time).15ABE 11C obtained this result by a two-neutrino os illation analysis using the Super-Kamiokande-I+II+III atmospheri neutrino data. ABE 11C also reported results undera two-neutrino disappearan e model with separate mixing parameters between ν and ν,and obtained sin22θ > 0.93 for ν and sin22θ > 0.83 for ν at 90% C.L.16ADAMSON 11B obtained this result by a two-neutrino os illation analysis of antineutrinosin an antineutrino enhan ed beam with 1.71 × 1020 protons on target. This results is onsistent with the neutrino measurements of ADAMSON 11 at 2% C.L.17WENDELL 10 obtained this result (sin2θ23 = 0.4070.583) by a three-neutrino os illa-tion analysis using the Super-Kamiokande-I+II+III atmospheri neutrino data, assuming

θ13 = 0 but in luding the solar os illation parameters m221 and sin2θ12 in the t.18WENDELL 10 obtained this result (sin2θ23 = 0.430.61) by a three-neutrino os illationanalysis with one mass s ale dominan e (m221 = 0) using the Super-Kamiokande-I+II+III atmospheri neutrino data, and updates the HOSAKA 06A result.19WENDELL 10 obtained this result (sin2θ23 = 0.440.63) by a three-neutrino os illationanalysis with one mass s ale dominan e (m221 = 0) using the Super-Kamiokande-I+II+III atmospheri neutrino data, and updates the HOSAKA 06A result.20ADAMSON 06 obtained this result by a two-neutrino os illation analysis of the L/Edistribution using 4.54 kton yr atmospheri neutrino data with the MINOS far dete tor.21 Super edes ALIU 05.22MICHAEL 06 best t is for maximal mixing. See also ADAMSON 08.23The best t is for maximal mixing.24ALLISON 05 result is based upon atmospheri neutrino intera tions in luding upward-stopping muons, with an exposure of 5.9 kton yr. From a two- avor os illation analysisthe best-t point is m2 = 0.0017 eV2 and sin2(2θ) = 0.97.25ASHIE 05 obtained this result by a two-neutrino os illation analysis using 92 kton yratmospheri neutrino data from the omplete Super-Kamiokande I running period.26AMBROSIO 04 obtained this result, without using the absolute normalization of theneutrino ux, by ombining the angular distribution of upward through-going muon tra kswith Eµ > 1 GeV, Nlow and Nhigh, and the numbers of InDown + UpStop and InUpevents. Here, Nlow and Nhigh are the number of events with re onstru ted neutrinoenergies < 30 GeV and > 130 GeV, respe tively. InDown and InUp represent eventswith downward and upward-going tra ks starting inside the dete tor due to neutrinointera tions, while UpStop represents entering upward-going tra ks whi h stop in thedete tor. The best t is for maximal mixing.27ASHIE 04 obtained this result from the L( ight length)/E(estimated neutrino energy)distribution of νµ disappearan e probability, using the Super-Kamiokande-I 1489 live-dayatmospheri neutrino data.28There are several islands of allowed region from this K2K analysis, extending to highvalues of m2. We only in lude the one that overlaps atmospheri neutrino analyses.The best t is for maximal mixing.29AMBROSIO 03 obtained this result on the basis of the ratio R = Nlow/Nhigh, whereNlow and Nhigh are the number of upward through-going muon events with re on-stru ted neutrino energy < 30 GeV and > 130 GeV, respe tively. The data ame fromthe full dete tor run started in 1994. The method of FELDMAN 98 is used to obtainthe limits.30AMBROSIO 03 obtained this result by using the ratio R and the angular distributionof the upward through-going muons. R is given in the previous note and the angulardistribution is reported in AMBROSIO 01. The method of FELDMAN 98 is used toobtain the limits. The best t is to maximal mixing.31 SANCHEZ 03 is based on an exposure of 5.9 kton yr. The result is obtained using alikelihood analysis of the neutrino L/E distribution for a sele tion µ avor sample whilethe e- avor sample provides ux normalization. The method of FELDMAN 98 is usedto obtain the allowed region. The best t is sin2(2θ) = 0.97.32AMBROSIO 01 result is based on the angular distribution of upward through-going muontra ks with Eµ > 1 GeV. The data ame from three dierent dete tor ongurations, butthe statisti s is largely dominated by the full dete tor run, from May 1994 to De ember2000. The total live time, normalized to the full dete tor onguration is 6.17 years.The best t is obtained outside the physi al region. The method of FELDMAN 98 isused to obtain the limits. The best t is for maximal mixing.33AMBROSIO 01 result is based on the angular distribution and normalization of upwardthrough-going muon tra ks with Eµ > 1 GeV. See the previous footnote.

34 FUKUDA 99C obtained this result from a total of 537 live days of upward through-goingmuon data in Super-Kamiokande between April 1996 to January 1998. With a thresholdof Eµ > 1.6 GeV, the observed ux is (1.74 ± 0.07 ± 0.02) × 10−13 m−2s−1sr−1.The best t is sin2(2θ) = 0.95.35 FUKUDA 99D obtained this result from a simultaneous tting to zenith angle distributionsof upward-stopping and through-going muons. The ux of upward-stopping muons ofminimum energy of 1.6 GeV measured between April 1996 and January 1998 is (0.39 ±0.04 ± 0.02)×10−13 m−2s−1sr−1. This is ompared to the expe ted ux of (0.73 ±0.16 (theoreti al error)) × 10−13 m−2s−1sr−1. The best t is to maximal mixing.36 FUKUDA 99D obtained this result from the zenith dependen e of the upward-stopping/through-going ux ratio. The best t is to maximal mixing.37 FUKUDA 98C obtained this result by an analysis of 33.0 kton yr atmospheri neutrinodata. The best t is for maximal mixing.38HATAKEYAMA 98 obtained this result from a total of 2456 live days of upward-goingmuon data in Kamiokande between De ember 1985 and May 1995. With a threshold ofEµ > 1.6 GeV, the observed ux of upward through-going muons is (1.94±0.10+0.07−0.06)×10−13 m−2s−1sr−1. This is ompared to the expe ted ux of (2.46±0.54 (theoreti alerror)) × 10−13 m−2s−1sr−1. The best t is for maximal mixing.39HATAKEYAMA 98 obtained this result from a ombined analysis of Kamiokande on-tained events (FUKUDA 94) and upward going muon events. The best t is sin2(2θ) =0.95.40 FUKUDA 94 obtained the result by a ombined analysis of sub- and multi-GeV atmo-spheri neutrino events in Kamiokande. The best t is for maximal mixing.m232m232m232m232The sign of m232 is not known at this time. Only the absolute value is quoted below.Unless otherwise spe ied, the ranges below orrespond to the proje tion onto them232 axis of the 90% CL ontours in the sin2(2θ23) − m232 plane presented by theauthors. If un ertainties are reported with the value, they orrespond to one standarddeviation un ertainty.VALUE (10−3 eV2) DOCUMENT ID TECN COMMENT2.51 ±0.06 OUR FIT2.51 ±0.06 OUR FIT2.51 ±0.06 OUR FIT2.51 ±0.06 OUR FIT Assuming inverted mass hierar hy2.44 ±0.06 OUR FIT2.44 ±0.06 OUR FIT2.44 ±0.06 OUR FIT2.44 ±0.06 OUR FIT Assuming normal mass hierar hy2.72 +0.19

−0.20 1 AARTSEN 15A ICCB 3ν os ; normal mass ordering2.73 +0.18−0.21 1 AARTSEN 15A ICCB 3ν os ; inverted mass ordering2.37 ±0.11 2 AN 15 DAYA 3ν os .; normal mass ordering2.47 ±0.11 2 AN 15 DAYA 3ν os .; inverted mass ordering2.51 ±0.10 3 ABE 14 T2K 3ν os .; normal mass ordering2.56 ±0.10 3 ABE 14 T2K 3ν os .; inverted mass ordering2.37 ±0.09 4 ADAMSON 14 MINS 3ν os ., a el., atmospheri ;normal mass ordering2.41 +0.12−0.09 4 ADAMSON 14 MINS 3ν os ., a el., atmsopheri ;inverted mass ordering

• • • We do not use the following data for averages, ts, limits, et . • • •2.54 +0.19−0.20 5 AN 14 DAYA 3ν os .; normal mass ordering2.64 +0.19−0.20 5 AN 14 DAYA 3ν os .; inverted mass ordering2.48 +0.05−0.07 6 FORERO 14 FIT 3ν; normal mass ordering2.38 +0.05−0.06 6 FORERO 14 FIT 3ν; inverted mass ordering2.457±0.047 7,8 GONZALEZ-G...14 FIT Normal mass ordering; globalt2.449+0.048−0.047 7 GONZALEZ-G...14 FIT Inverted mass ordering; globalt2.3 +0.6−0.5 9 AARTSEN 13B ICCB DeepCore, 2ν os illation2.44 +0.17−0.15 10 ABE 13G T2K 3ν os .; normal mass ordering2.41 +0.09−0.10 11 ADAMSON 13B MINS 2ν os .; beam + atmospheri ;identi al ν & ν2.23.1 12 ABE 12A T2K o-axis beam2.62 +0.31−0.28 ±0.09 13 ADAMSON 12 MINS ν beam1.352.55 14,15 ADAMSON 12B MINS MINOS atmospheri 1.45.6 14,16 ADAMSON 12B MINS MINOS pure atmospheri ν0.92.5 14,16 ADAMSON 12B MINS MINOS pure atmospheri ν1.85.0 17 ADRIAN-MAR...12 ANTR atm. ν with deep see tele-s ope1.34.0 18 ABE 11C SKAM atmospheri ν2.32 +0.12−0.08 ADAMSON 11 MINS 2ν os illation; maximal mixing3.36 +0.46−0.40 19 ADAMSON 11B MINS ν beam

<3.37 20 ADAMSON 11C MINS MINOS1.92.6 21 WENDELL 10 SKAM 3ν os .; normal mass ordering1.72.7 21 WENDELL 10 SKAM 3ν os .; inverted mass ordering2.43 ±0.13 ADAMSON 08A MINS MINOS0.0750 22 ADAMSON 06 MINS atmospheri ν with far dete -tor1.94.0 23,24 AHN 06A K2K KEK to Super-K2.23.8 25 MICHAEL 06 MINS MINOS

782782782782LeptonParti le ListingsNeutrinoMixing1.93.6 23 ALIU 05 K2K KEK to Super-K0.312 26 ALLISON 05 SOU21.53.4 27 ASHIE 05 SKAM atmospheri neutrino0.68.0 28 AMBROSIO 04 MCRO MACRO1.9 to 3.0 29 ASHIE 04 SKAM L/E distribution1.53.9 30 AHN 03 K2K KEK to Super-K0.259.0 31 AMBROSIO 03 MCRO MACRO0.67.0 32 AMBROSIO 03 MCRO MACRO0.1515 33 SANCHEZ 03 SOU2 Soudan-2 Atmospheri 0.615 34 AMBROSIO 01 MCRO upward µ1.06.0 35 AMBROSIO 01 MCRO upward µ1.050 36 FUKUDA 99C SKAM upward µ1.515.0 37 FUKUDA 99D SKAM upward µ0.718 38 FUKUDA 99D SKAM stop µ / through0.56.0 39 FUKUDA 98C SKAM Super-Kamiokande0.5550 40 HATAKEYAMA98 KAMI Kamiokande423 41 HATAKEYAMA98 KAMI Kamiokande525 42 FUKUDA 94 KAMI Kamiokande1AARTSEN 15A obtains this result by a three-neutrino os illation analysis using 10100GeV muon neutrino sample from a total of 953 days of measurements with the low-energysubdete tor DeepCore of the I eCube neutrino teles ope.2AN 15 uses all eight identi al dete tors, with four pla ed near the rea tor ores and theremaining four at the far hall to determine prompt energy spe tra. The results orrespondto the exposure of 6.9×105 GWth-ton-days. They derive m2ee = (2.42± 0.11)×10−3eV2. Assuming the normal (inverted) ordering, the tted m232 = (2.37± 0.11)×10−3((2.47 ± 0.11) × 10−3) eV2. Supersedes AN 14.3ABE 14 results are based on νµ disappearan e using three-neutrino os illation t. The onden e intervals are derived from one dimensional proled likelihoods. In ABE 14 theinverted mass ordering result is reported as m213 = (2.48 ± 0.10) × 10−3 eV2 whi hwe onverted to m232 by adding PDG 14 value of m221 = (7.53 ± 0.18)×10−5 eV2.4ADAMSON 14 uses a omplete set of a elerator and atmospheri data. The analysis ombines The analysis ombines the νµ disappearan e and νe appearan e data usingthree-neutrino os illation t. The t results are obtained for normal and inverted massordering assumptions.5AN 14 uses six identi al dete tors, with three pla ed near the rea tor ores ( ux-weightedbaselines of 512 and 561 m) and the remaining three at the far hall (at the ux averageddistan e of 1579 m from all six rea tor ores) to determine prompt energy spe tra andderive m2ee = (2.59+0.19−0.20) × 10−3 eV2. Assuming the normal (inverted) ordering,the tted m232 = (2.54+0.19

−0.20) × 10−3 ((2.64+0.19−0.20) × 10−3) eV2. Superseded byAN 15.6 FORERO 14 performs a global t to m231 using solar, rea tor, long-baseline a elerator,and atmospheri neutrino data.7GONZALEZ-GARCIA 14 result omes from a frequentist global t. The orrespondingBayesian global t to the same data results are reported in BERGSTROM 15 as (2.460±0.046)×10−3 eV2 for normal and (2.445+0.047

−0.045)×10−3 eV2 for inverted mass ordering.8The value for normal mass ordering is a tually a measurement of m231 whi h diersfrom m232 by a mu h smaller value of m212.9AARTSEN 13B obtained this result by a two-neutrino os illation analysis using 20100GeV muon neutrino sample from a total of 318.9 days of live-time measurement withthe low-energy subdete tor DeepCore of the I eCube neutrino teles ope.10Based on the observation of 58 νµ events with 205 ± 17(syst) expe ted in the absen eof neutrino os illations. Superseded by ABE 14.11ADAMSON 13B obtained this result from νµ and νµ disappearan e using νµ (10.71 ×1020 POT) and νµ (3.36×1020 POT) beams, and atmospheri (37.88 kton-years) datafrom MINOS. The t assumed two- avor neutrino hypothesis and identi al νµ and νµos illation parameters.12ABE 12A obtained this result by a two-neutrino os illation analysis. The best-t point ism232 = 2.65× 10−3 eV2.13ADAMSON 12 is a two-neutrino os illation analysis using antineutrinos.14ADAMSON 12B obtained this result by a two-neutrino os illation analysis of the L/Edistribution using 37.9 kton·yr atmospheri neutrino data with the MINOS far dete tor.15The 90% single-parameter onden e interval at the best t point is m2 = 0.0019 ±0.0004 eV2.16The data are separated into pure samples of νs and νs, and separate os illation parametersfor νs and νs are t to the data. The best t point is (m2, sin22θ) = (0.0022 eV2,0.99) and (m2, sin22θ) = (0.0016 eV2, 1.00). The quoted result is taken from the90% C.L. ontour in the (m2, sin22θ) plane obtained by minimizing the four parameterlog-likelihood fun tion with respe t to the other os illation parameters.17ADRIAN-MARTINEZ 12 measured the os illation parameters of atmospheri neutrinoswith the ANTARES deep sea neutrino teles ope using the data taken from 2007 to 2010(863 days of total live time).18ABE 11C obtained this result by a two-neutrino os illation analysis with separate mixingparameters between neutrinos and antineutrinos, using the Super-Kamiokande-I+II+IIIatmospheri neutrino data. The orresponding 90% CL neutrino os illation parameterrange obtained from this analysis is m2 = 1.73.0× 10−3 eV2.19ADAMSON 11B obtained this result by a two-neutrino os illation analysis of antineutrinosin an antineutrino enhan ed beam with 1.71 × 1020 protons on target. This results is onsistent with the neutrino measurements of ADAMSON 11 at 2% C.L.20ADAMSON 11C obtains this result based on a study of antineutrinos in a neutrino beamand assumes maximal mixing in the two- avor approximation.21WENDELL 10 obtained this result by a three-neutrino os illation analysis with one masss ale dominan e (m221 = 0) using the Super-Kamiokande-I+II+III atmospheri neu-trino data, and updates the HOSAKA 06A result.

22ADAMSON 06 obtained this result by a two-neutrino os illation analysis of the L/Edistribution using 4.54 kton yr atmospheri neutrino data with the MINOS far dete tor.23The best t in the physi al region is for m2 = 2.8× 10−3 eV2.24 Super edes ALIU 05.25MICHAEL 06 best t is 2.74× 10−3 eV2. See also ADAMSON 08.26ALLISON 05 result is based on an atmospheri neutrino observation with an exposure of5.9 kton yr. From a two- avor os illation analysis the best-t point is m2 = 0.0017eV2 and sin22 θ = 0.97.27ASHIE 05 obtained this result by a two-neutrino os illation analysis using 92 kton yratmospheri neutrino data from the omplete Super-Kamiokande I running period. Thebest t is for m2 = 2.1× 10−3 eV2.28AMBROSIO 04 obtained this result, without using the absolute normalization of theneutrino ux, by ombining the angular distribution of upward through-going muon tra kswith Eµ > 1 GeV, Nlow and Nhigh, and the numbers of InDown + UpStop and InUpevents. Here, Nlow and Nhigh are the number of events with re onstru ted neutrinoenergies < 30 GeV and > 130 GeV, respe tively. InDown and InUp represent eventswith downward and upward-going tra ks starting inside the dete tor due to neutrinointera tions, while UpStop represents entering upward-going tra ks whi h stop in thedete tor. The best t is for m2 = 2.3× 10−3 eV2.29ASHIE 04 obtained this result from the L( ight length)/E(estimated neutrino energy)distribution of νµ disappearan e probability, using the Super-Kamiokande-I 1489 live-dayatmospheri neutrino data. The best t is for m2 = 2.4× 10−3 eV2.30There are several islands of allowed region from this K2K analysis, extending to highvalues of m2. We only in lude the one that overlaps atmospheri neutrino analyses.The best t is for m2 = 2.8× 10−3 eV2.31AMBROSIO 03 obtained this result on the basis of the ratio R = Nlow/Nhigh, whereNlow and Nhigh are the number of upward through-going muon events with re on-stru ted neutrino energy < 30 GeV and > 130 GeV, respe tively. The data ame fromthe full dete tor run started in 1994. The method of FELDMAN 98 is used to obtainthe limits. The best t is for m2 = 2.5× 10−3 eV2.32AMBROSIO 03 obtained this result by using the ratio R and the angular distributionof the upward through-going muons. R is given in the previous note and the angulardistribution is reported in AMBROSIO 01. The method of FELDMAN 98 is used toobtain the limits. The best t is for m2 = 2.5× 10−3 eV2.33 SANCHEZ 03 is based on an exposure of 5.9 kton yr. The result is obtained using alikelihood analysis of the neutrino L/E distribution for a sele tion µ avor sample whilethe e- avor sample provides ux normalization. The method of FELDMAN 98 is usedto obtain the allowed region. The best t is for m2 = 5.2× 10−3 eV2.34AMBROSIO 01 result is based on the angular distribution of upward through-going muontra ks with Eµ > 1 GeV. The data ame from three dierent dete tor ongurations, butthe statisti s is largely dominated by the full dete tor run, from May 1994 to De ember2000. The total live time, normalized to the full dete tor onguration is 6.17 years.The best t is obtained outside the physi al region. The method of FELDMAN 98 isused to obtain the limits.35AMBROSIO 01 result is based on the angular distribution and normalization of upwardthrough-going muon tra ks with Eµ > 1 GeV. See the previous footnote.36 FUKUDA 99C obtained this result from a total of 537 live days of upward through-goingmuon data in Super-Kamiokande between April 1996 to January 1998. With a thresholdof Eµ > 1.6 GeV, the observed ux is (1.74 ± 0.07 ± 0.02) × 10−13 m−2s−1sr−1.The best t is for m2 = 5.9× 10−3 eV2.37FUKUDA 99D obtained this result from a simultaneous tting to zenith angle distributionsof upward-stopping and through-going muons. The ux of upward-stopping muons ofminimum energy of 1.6 GeV measured between April 1996 and January 1998 is (0.39 ±0.04 ± 0.02)×10−13 m−2s−1sr−1. This is ompared to the expe ted ux of (0.73 ±0.16 (theoreti al error))×10−13 m−2s−1sr−1. The best t is for m2 = 3.9×10−3eV2.38FUKUDA 99D obtained this result from the zenith dependen e of the upward-stopping/through-going ux ratio. The best t is for m2 = 3.1× 10−3 eV2.39FUKUDA 98C obtained this result by an analysis of 33.0 kton yr atmospheri neutrinodata. The best t is for m2 = 2.2× 10−3 eV2.40HATAKEYAMA 98 obtained this result from a total of 2456 live days of upward-goingmuon data in Kamiokande between De ember 1985 and May 1995. With a threshold ofEµ > 1.6 GeV, the observed ux of upward through-going muons is (1.94±0.10+0.07−0.06)×10−13 m−2s−1sr−1. This is ompared to the expe ted ux of (2.46±0.54 (theoreti alerror)) × 10−13 m−2s−1sr−1. The best t is for m2 = 2.2× 10−3 eV2.41HATAKEYAMA 98 obtained this result from a ombined analysis of Kamiokande on-tained events (FUKUDA 94) and upward going muon events. The best t is for m2 =13 × 10−3 eV2.42FUKUDA 94 obtained the result by a ombined analysis of sub- and multi-GeV atmo-spheri neutrino events in Kamiokande. The best t is for m2 = 16× 10−3 eV2.sin2(θ13)sin2(θ13)sin2(θ13)sin2(θ13)At present time dire t measurements of sin2( θ13) are derived from the rea tor νedisappearan e at distan es orresponding to the m232 value, i.e. L ∼ 1km. Alter-natively, limits an also be obtained from the analysis of the solar neutrino data anda elerator-based νµ → νe experiments.VALUE (units 10−2) CL% DOCUMENT ID TECN COMMENT2.19± 0.12 OUR AVERAGE2.19± 0.12 OUR AVERAGE2.19± 0.12 OUR AVERAGE2.19± 0.12 OUR AVERAGE2.15± 0.13 1 AN 15 DAYA DayaBay, Ling Ao/Ao II rea tors2.3 + 0.9

− 0.8 2 ABE 14H DCHZ Chooz rea tors

783783783783See key on page 601 Lepton Parti le ListingsNeutrino Mixing2.12± 0.47 3 AN 14B DAYA DayaBay, Ling Ao/Ao II rea tors2.5 ± 0.9 ±0.9 4 ABE 13C DCHZ Chooz rea tors2.9 ± 0.3 ±0.5 5 AHN 12 RENO Yonggwang rea tors• • • We do not use the following data for averages, ts, limits, et . • • •2.6 + 1.2

− 1.1 6 ABE 14A DCHZ Chooz rea tors3.0 + 1.3− 1.0 7 ABE 14C T2K Inverted mass ordering3.6 + 1.0− 0.9 7 ABE 14C T2K Normal mass ordering2.3 ± 0.2 8 AN 14 DAYA DayaBay, Ling Ao/Ao II rea tors2.34± 0.20 9 FORERO 14 FIT Normal mass ordering2.40± 0.19 9 FORERO 14 FIT Inverted mass ordering2.18± 0.10 10 GONZALEZ-G...14 FIT Normal mass ordering; global t2.19+ 0.11− 0.10 10 GONZALEZ-G...14 FIT Inverted mass ordering; global t2.3 + 1.3− 1.0 11 ABE 13E T2K Normal mass ordering2.8 + 1.6− 1.2 11 ABE 13E T2K Inverted mass ordering1.6 + 1.3− 0.9 12 ADAMSON 13A MINS Normal mass ordering3.0 + 1.8− 1.6 12 ADAMSON 13A MINS Inverted mass ordering

<13 90 AGAFONOVA13 OPER OPERA: 3ν< 3.6 95 13 AHARMIM 13 FIT global solar: 3ν2.3 ± 0.3 ±0.1 14 AN 13 DAYA DayaBay, LIng Ao/Ao II rea tors2.2 ± 1.1 ±0.8 15 ABE 12 DCHZ Chooz rea tors2.8 ± 0.8 ±0.7 16 ABE 12B DCHZ Chooz rea tors2.4 ± 0.4 ±0.1 17 AN 12 DAYA DayaBay, Ling Ao/Ao II rea tors2.5 + 1.8

− 1.6 68 18 ABE 11 FIT KamLAND + global solar< 6.1 95 19 ABE 11 FIT Global solar1.3 to 5.6 68 20 ABE 11A T2K Normal mass ordering1.5 to 5.6 68 21 ABE 11A T2K Inverted mass ordering0.3 to 2.3 68 22 ADAMSON 11D MINS Normal mass ordering0.8 to 3.9 68 23 ADAMSON 11D MINS Inverted mass ordering8 ± 3 68 24 FOGLI 11 FIT Global neutrino data7.8 ± 6.2 68 25 GANDO 11 FIT KamLAND + solar: 3ν12.4 ±13.3 68 26 GANDO 11 FIT KamLAND: 3ν3 + 9

− 7 90 27 ADAMSON 10A MINS Normal mass ordering6 +14− 6 90 28 ADAMSON 10A MINS Inverted mass ordering8 + 8− 7 29,30 AHARMIM 10 FIT KamLAND + global solar: 3ν

< 30 9529,31 AHARMIM 10 FIT global solar: 3ν< 15 90 32 WENDELL 10 SKAM 3ν os .; normal m ordering< 33 90 32 WENDELL 10 SKAM 3ν os .; inverted m ordering11 +11

− 8 33 ADAMSON 09 MINS Normal mass ordering18 +15−11 34 ADAMSON 09 MINS Inverted mass ordering6 ± 4 35 FOGLI 08 FIT Global neutrino data8 ± 7 36 FOGLI 08 FIT Solar + KamLAND data5 ± 5 37 FOGLI 08 FIT Atmospheri +LBL+CHOOZ

< 36 90 38 YAMAMOTO06 K2K A elerator experiment< 48 90 39 AHN 04 K2K A elerator experiment< 36 90 40 BOEHM 01 Palo Verde rea t.< 45 90 41 BOEHM 00 Palo Verde rea t.< 15 90 42 APOLLONIO 99 CHOZ Rea tor Experiment1AN 15 uses all eight identi al dete tors, with four pla ed near the rea tor ores and theremaining four at the far hall to determine the mixing angle θ13 using the νe observedintera tion rates with neutron apture on Gd and energy spe tra. The result orrespondsto the exposure of 6.9× 105 GWth-ton-days. Supersedes AN 14.2ABE 14H uses 467.9 live days of one dete tor, 1050 m away from two rea tor ores ofthe Chooz nu lear power station, to determine the mixing parameter sin2(2 θ13). TheBugey4 data (DECLAIS 94) is used to onstrain the neutrino ux. The data set in ludes7.24 rea tor-o days. A rate and shape analysis is performed. Super edes ABE 14A.3AN 14B uses six identi al anti-neutrino dete tors with ux-weighted baselines of ∼ 500m and ∼ 1.6 km to six power rea tors. This rate analysis uses a 217-day data set andneutron apture on protons (not Gd) only. m231= 2.32× 10−3 eV2 is assumed.4ABE 13C uses delayed neutron apture on hydrogen instead of on Gd used previously.The physi al volume is thus three times larger. The t is based on the rate and shapeanalysis as in ABE 12B. The Bugey4 data (DECLAIS 94) is used to onstrain the neutrino ux.5AHN 12 uses two identi al dete tors, pla ed at ux weighted distan es of 408.56 m and1433.99 m from six rea tor ores, to determine the mixing angle θ13. This rate-onlyanalysis ex ludes the no-os illation hypothesis at 4.9 standard deviations. The value ofm231 = (2.32+0.12

−0.08)× 10−3 eV2 was assumed in the analysis.6ABE 14A uses 467.9 live days of one dete tor, 1050 m away from two rea tor ores ofthe Chooz nu lear power station, to determine the mixing parameter sin2(2 θ13). TheBugey4 data (DECLAIS 94) is used to onstrain the neutrino ux. The data set in ludes7.24 rea tor-o days. A "rate-modulation" analysis is performed. Super edes ABE 12B.7ABE 14C result is for νe appearan e and assumes m232 = 2.4× 10−3 eV2, sin2( θ23)= 0.5, and δ = 0.

8AN 14 uses six identi al dete tors, with three pla ed near the rea tor ores ( ux-weightedbaselines of 512 and 561 m) and the remaining three at the far hall (at the ux averageddistan e of 1579 m from all six rea tor ores) to determine the mixing angle θ13 using theνe observed intera tion rates with neutron apture on Gd and energy spe tra. SupersedesAN 13 and superseded by AN 15.9 FORERO 14 performs a global t to neutrino os illations using solar, rea tor, long-baseline a elerator, and atmospheri neutrino data.10GONZALEZ-GARCIA 14 result omes from a frequentist global t. The orrespond-ing Bayesian global t to the same data results are reported in BERGSTROM 15 as(2.18+0.10

−0.11) × 10−2 eV2 for normal and (2.19+0.12−0.10) × 10−2 eV2 for inverted massordering.11ABE 13E assumes maximal θ23 mixing and CP phase δ = 0.12ADAMSON 13A results obtained from νe appearan e, assuming δ = 0, and sin2(2 θ23)= 0.957.13AHARMIM 13 obtained this result by a three-neutrino os illation analysis with the valueof m232 xed to 2.45 × 10−3 eV2, using global solar neutrino data. AHARMIM 13global solar neutrino data in lude SNO's all-phases- ombined analysis results on thetotal a tive 8B neutrino ux and energy-dependent νe survival probability parame-ters, measurements of Cl (CLEVELAND 98), Ga (ABDURASHITOV 09 whi h ontains ombined analysis with GNO (ALTMANN 05 and Ph.D. thesis of F. Kaether)), and7Be (BELLINI 11A) rates, and 8B solar-neutrino re oil ele tron measurements of SK-I(HOSAKA 06) zenith, SK-II (CRAVENS 08) and SK-III (ABE 11) day/night spe tra,and Borexino (BELLINI 10A) spe tra. AHARMIM 13 also reported a result ombiningglobal solar and KamLAND data, whi h is sin2(2 θ13) = (9.1+2.9

−3.1) × 10−2.14AN 13 uses six identi al dete tors, with three pla ed near the rea tor ores ( ux-weightedbaselines of 498 and 555 m) and the remaining three at the far hall (at the ux averageddistan e of 1628 m from all six rea tor ores) to determine the νe intera tion rate ratios.Superseded by AN 14.15ABE 12 determines the νe intera tion rate in a single dete tor, lo ated 1050 m from the ores of two rea tors. A rate and shape analysis is performed. The rate normalization isxed by the results of the Bugey4 rea tor experiment, thus avoiding any dependen e onpossible very short baseline os illations. The value of m231 = 2.4× 10−3 eV2 is usedin the analysis. Superseded by ABE 12B.16ABE 12B determines the neutrino mixing angle θ13 using a single dete tor, lo ated1050 m from the ores of two rea tors. This result is based on a spe tral shape andrate analysis. The Bugey4 data (DECLAIS 94) is used to onstrain the neutrino ux.Superseded by ABE 14A.17AN 12 uses six identi al dete tors with three pla ed near the rea tor ores ( ux-weightedbaselines of 470 m and 576 m) and the remaining three at the far hall (at the ux averageddistan e of 1648 m from all six rea tor ores) to determine the mixing angle θ13 usingthe νe observed intera tion rate ratios. This rate-only analysis ex ludes the no-os illationhypothesis at 5.2 standard deviations. The value of m231 = (2.32+0.12−0.08)× 10−3 eV2was assumed in the analysis. Superseded by AN 13.18ABE 11 obtained this result by a three-neutrino os illation analysis with the value ofm232 xed to 2.4× 10−3 eV2, using solar neutrino data in luding Super-Kamiokande,SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, SAGE, and KamLANDdata. This result implies an upper bound of sin2θ13 < 0.059 (95% CL) or sin22θ13 <0.22 (95% CL). The normal neutrino mass ordering and CPT invarian e are assumed.19ABE 11 obtained this result by a three-neutrino os illation analysis with the value ofm232 xed to 2.4× 10−3 eV2, using solar neutrino data in luding Super-Kamiokande,SNO, Borexino (ARPESELLA 08A), Homestake, and GALLEX/GNO data. The normalneutrino mass ordering is assumed.20The quoted limit is for m232 = 2.4 × 10−3 eV2, θ23 = π/2, δ = 0, and the normalmass ordering. For other values of δ, the 68% region spans from 0.03 to 0.25, and the90% region from 0.02 to 0.32.21The quoted limit is for m232 = 2.4 × 10−3 eV2, θ23 = π/2, δ = 0, and the invertedmass ordering. For other values of δ, the 68% region spans from 0.04 to 0.30, and the90% region from 0.02 to 0.39.22The quoted limit is for m232 = 2.32× 10−3 eV2, θ23 = π/2, δ = 0, and the normalmass ordering. For other values of δ, the 68% region spans from 0.02 to 0.12, and the90% region from 0 to 0.16.23The quoted limit is for m232 = 2.32× 10−3 eV2, θ23 = π/2, δ = 0, and the invertedmass ordering. For other values of δ, the 68% region spans from 0.02 to 0.16, and the90% region from 0 to 0.21.24 FOGLI 11 obtained this result from an analysis using the atmospheri , a elerator longbaseline, CHOOZ, solar, and KamLAND data. Re ently, MUELLER 11 suggested anaverage in rease of about 3.5% in normalization of the rea tor νe uxess, and usingthese uxes, the tted result be omes 0.10 ± 0.03.25GANDO 11 report sin2θ13 = 0.020±0.016. This result was obtained with three-neutrinot using the KamLAND + solar data.26GANDO 11 report sin2θ13 = 0.032±0.037. This result was obtained with three-neutrinot using the KamLAND data only.27This result orresponds to the limit of <0.12 at 90% CL for m232 = 2.43× 10−3 eV2,

θ23 = π/2, and δ = 0. For other values of δ, the 90% CL region spans from 0 to 0.16.28This result orresponds to the limit of <0.20 at 90% CL for m232 = 2.43× 10−3 eV2,θ23 = π/2, and δ = 0. For other values of δ, the 90% CL region spans from 0 to 0.21.29AHARMIM 10 global solar neutrino data in lude SNO's low-energy-threshold analysissurvival probability day/night urves, SNO Phase III integral rates (AHARMIM 08), Cl(CLEVELAND 98), SAGE (ABDURASHITOV 09), Gallex/GNO (HAMPEL 99, ALT-MANN 05), Borexino (ARPESELLA 08A), SK-I zenith (HOSAKA 06), and SK-IIday/night spe tra (CRAVENS 08).30AHARMIM 10 obtained this result by a three-neutrino os illation analysis with the valueof m231 xed to 2.3×10−3 eV2, using global solar neutrino data and KamLAND data(ABE 08A). CPT invarian e is assumed. This result implies an upper bound of sin2θ13 <0.057 (95% CL) or sin22θ13 < 0.22 (95% CL).

784784784784LeptonParti le ListingsNeutrinoMixing31AHARMIM 10 obtained this result by a three-neutrino os illation analysis with the valueof m231 xed to 2.3× 10−3 eV2, using global solar neutrino data.32WENDELL 10 obtained this result by a three-neutrino os illation analysis with one masss ale dominan e (m221 = 0) using the Super-Kamiokande-I+II+III atmospheri neu-trino data, and updates the HOSAKA 06A result.33The quoted limit is for m232 = 2.43 × 10−3 eV2, θ23 = π/2, and δ = 0. For othervalues of δ, the 68% CL region spans from 0.02 to 0.26.34The quoted limit is for m232 = 2.43 × 10−3 eV2, θ23 = π/2, and δ = 0. For othervalues of δ, the 68% CL region spans from 0.04 to 0.34.35 FOGLI 08 obtained this result from a global analysis of all neutrino os illation data, thatis, solar + KamLAND + atmospheri + a elerator long baseline + CHOOZ.36FOGLI 08 obtained this result from an analysis using the solar and KamLAND neutrinoos illation data.37 FOGLI 08 obtained this result from an analysis using the atmospheri , a elerator longbaseline, and CHOOZ neutrino os illation data.38YAMAMOTO 06 sear hed for νµ → νe appearan e. Assumes 2 sin2(2θµe ) =sin2(2θ13). The quoted limit is for m232 = 1.9× 10−3 eV2. That value of m232 isthe one-σ low value for AHN 06A. For the AHN 06A best t value of 2.8 × 10−3 eV2,the sin2(2θ13) limit is < 0.26. Supersedes AHN 04.39AHN 04 sear hed for νµ → νe appearan e. Assuming 2 sin2(2 θµe ) = sin2(2 θ13), alimit on sin2(2 θµe ) is onverted to a limit on sin2(2 θ13).The quoted limit is for m232= 1.9 × 10−3 eV2. That value of m232 is the one-σ low value for ALIU 05. For theALIU 05 best t value of 2.8× 10−3 eV2, the sin2(2 θ13) limit is < 0.30.40The quoted limit is for m232 = 1.9× 10−3 eV2. That value of m232 is the 1-σ lowvalue for ALIU 05. For the ALIU 05 best t value of 2.8×10−3 eV2, the sin22 θ13 limitis < 0.19. In this range, the θ13 limit is larger for lower values of m232, and smallerfor higher values of m232.41The quoted limit is for m232 = 1.9× 10−3 eV2. That value of m232 is the 1-σ lowvalue for ALIU 05. For the ALIU 05 best t value of 2.8 × 10−3 eV2, the sin22 θ13limit is < 0.23.42The quoted limit is for m232 = 2.43× 10−3 eV2. That value of m232 is the entralvalue for ADAMSON 08. For the ADAMSON 08 1-σ low value of 2.30 × 10−3 eV2,the sin22 θ13 limit is < 0.16. See also APOLLONIO 03 for a detailed des ription of theexperiment. CP violating phaseCP violating phaseCP violating phaseCP violating phaseδ, CP violating phaseδ, CP violating phaseδ, CP violating phaseδ, CP violating phaseMeasurements of δ ome from atmospheri and a elarator experiments looking at νeappearan e. We en ode values between 0 and 2π, though it is equivalent to use −πto π.VALUE (π rad) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0 to 0.15, 0.83 to 2 90 ABE 15D T2K Normal mass hierar hy1.09 to 1.92 90 ABE 15D T2K Inverted mass hierar hy0.05 to 1.2 90 1 ADAMSON 14 MINS Normal mass hierar hy1.34+0.64

−0.38 FORERO 14 FIT Normal mass hierar hy1.48+0.34−0.32 FORERO 14 FIT Inverted mass hierar hy1.70+0.22−0.39 2 GONZALEZ-G...14 FIT Normal mass hierar hy;global t1.41+0.35−0.34 2 GONZALEZ-G...14 FIT Inverted mass hierar hy;global t0 to 1.5 or 1.9 to 2 90 3 ADAMSON 13A MINS Normal mass hierar hy1Based on three- avor formalism and θ23 > π/4. Likelihood as a fun tion of δ is alsoshown for the other three ombinations of hierar hy and θ23 quadrant; all values of δare allowed at 90% C.L.2GONZALEZ-GARCIA 14 result omes from a frequentist global t. The orrespondingBayesian global t to the same data results are reported in BERGSTROM 15 as 68% CLintervals of 1.241.94 for normal and 1.151.77 for inverted mass ordering.3Based on νe appearan e in MINOS and the al ulated sin2(2θ23) = 0.957, θ23 > π/4,and normal mass hierar hy. Likelihood as a fun tion of δ is also shown for the other three ombinations of hierar hy and θ23 quadrant; all values of δ are allowed at 90% C.L.(C) Other neutrino mixing results(C) Other neutrino mixing results(C) Other neutrino mixing results(C) Other neutrino mixing resultsThe LSND ollaboration reported in AGUILAR 01 a signal whi h is on-sistent with νµ → νe os illations. In a three neutrino framework, thiswould be a measurement of θ12 and m221. This does not appear to be onsistent with most of the other neutrino data. The MiniBooNE exper-iment, reported in AGUILAR-AREVALO 07, does a two-neutrino analysiswhi h, assuming CP onservation, rules out AGUILAR 01. However, theMiniBooNE antineutrino data reported in AGUILAR-AREVALO 13A are onsistent with the signal reported in AGUILAR 01. The following list-ings in lude results whi h might be relevant towards understanding theseobservations. They in lude sear hes for νµ → νe , νµ → νe , sterileneutrino os illations, and CPT violation.

(m2) for sin2(2θ) = 1 (νµ → νe )(m2) for sin2(2θ) = 1 (νµ → νe )(m2) for sin2(2θ) = 1 (νµ → νe )(m2) for sin2(2θ) = 1 (νµ → νe )VALUE (eV2) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.015 to 0.050 90 1 AGUILAR-AR...13A MBOO MiniBooNE<0.34 90 2 MAHN 12 MBOO MiniBooNE/S iBooNE<0.034 90 AGUILAR-AR...07 MBOO MiniBooNE<0.0008 90 AHN 04 K2K Water Cherenkov<0.4 90 ASTIER 03 NOMD CERN SPS<2.4 90 AVVAKUMOV 02 NTEV NUTEV FNAL3 AGUILAR 01 LSND νµ → νe os .prob.0.03 to 0.3 95 4 ATHANASSO...98 LSND νµ → νe<2.3 90 5 LOVERRE 96 CHARM/CDHS<0.9 90 VILAIN 94C CHM2 CERN SPS<0.09 90 ANGELINI 86 HLBC BEBC CERN PS1Based on νµ → νe appearan e of 162.0 ± 47.8 events; marginally ompatible with twoneutrino os illations. The best t value is m2 = 3.14 eV2.2MAHN 12 is a ombined spe tral t of MiniBooNE and S iBooNE neutrino data withthe range of m2 up to 25 eV2. The best limit is 0.04 at 7 eV2.3AGUILAR 01 is the nal analysis of the LSND full data set. Sear h is made for the

νµ → νe os illations using νµ from π+ de ay in ight by observing beam-on ele tronevents from νe C → e−X . Present analysis results in 8.1 ± 12.2 ± 1.7 ex ess eventsin the 60<Ee < 200 MeV energy range, orresponding to os illation probability of0.10 ± 0.16 ± 0.04%. This is onsistent, though less signi ant, with the previous resultof ATHANASSOPOULOS 98, whi h it supersedes. The present analysis uses sele tion riteria developed for the de ay at rest region, and is less ee tive in removing theba kground above 60 MeV than ATHANASSOPOULOS 98.4ATHANASSOPOULOS 98 is a sear h for the νµ → νe os illations using νµ from π+de ay in ight. The 40 observed beam-on ele tron events are onsistent with νe C →e−X; the expe ted ba kground is 21.9±2.1. Authors interpret this ex ess as eviden e foran os illation signal orresponding to os illations with probability (0.26± 0.10± 0.05)%.Although the signi an e is only 2.3 σ, this measurement is an important and onsistent ross he k of ATHANASSOPOULOS 96 who reported eviden e for νµ → νe os illationsfrom µ+ de ay at rest. See also ATHANASSOPOULOS 98B.5 LOVERRE 96 uses the harged- urrent to neutral- urrent ratio from the ombinedCHARM (ALLABY 86) and CDHS (ABRAMOWICZ 86) data from 1986.sin2(2θ) for \Large" (m2) (νµ → νe )sin2(2θ) for \Large" (m2) (νµ → νe )sin2(2θ) for \Large" (m2) (νµ → νe )sin2(2θ) for \Large" (m2) (νµ → νe )VALUE (units 10−3) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

< 7.2 90 AGAFONOVA 13 OPER (m2) > 0.1 eV20.8 to 3 90 1 AGUILAR-AR...13A MBOO MiniBooNE< 11 90 2 ANTONELLO 13 ICAR νµ → νe< 6.8 90 3 ANTONELLO 13A ICAR νµ → νe<100 90 4 MAHN 12 MBOO MiniBooNE/S iBooNE< 1.8 90 5 AGUILAR-AR...07 MBOO MiniBooNE<110 90 6 AHN 04 K2K Water Cherenkov< 1.4 90 ASTIER 03 NOMD CERN SPS< 1.6 90 AVVAKUMOV 02 NTEV NUTEV FNAL7 AGUILAR 01 LSND νµ → νe os .prob.0.5 to 30 95 8 ATHANASSO...98 LSND νµ → νe< 3.0 90 9 LOVERRE 96 CHARM/CDHS< 9.4 90 VILAIN 94C CHM2 CERN SPS< 5.6 90 10 VILAIN 94C CHM2 CERN SPS1Based on νµ → νe appearan e of 162.0 ± 47.8 events; marginally ompatible with twoneutrino os illations. The best t value is sin22θ = 0.002.2ANTONELLO 13 use the ICARUS T600 dete tor at LNGS and ∼ 20 GeV beam of νµfrom CERN 730 km away to sear h for an ex ess of νe events. Two events are foundwith 3.7 ± 0.6 expe ted from onventional sour es. This result ex ludes some parts ofthe parameter spa e expe ted by LSND. Superseded by ANTONELLO 13A.3Based on four events with a ba kground of 6.4 ± 0.9 from onventional sour es with anaverage energy of 20 GeV and 730 km from the sour e of νµ.4MAHN 12 is a ombined t of MiniBooNE and S iBooNE neutrino data.5The limit is sin22θ < 0.9×10−3 at m2 = 2 eV2. That value of m2 orresponds tothe smallest mixing angle onsistent with the reported signal from LSND in AGUILAR 01.6The limit be omes sin22θ < 0.15 at m2 = 2.8× 10−3 eV2, the bets-t value of the

νµ disappearan e analysis in K2K.7AGUILAR 01 is the nal analysis of the LSND full data set of the sear h for the νµ →νe os illations. See footnote in pre eding table for further details.8ATHANASSOPOULOS 98 report (0.26 ± 0.10 ± 0.05)% for the os illation probability;the value of sin22θ for large m2 is dedu ed from this probability. See footnote inpre eding table for further details, and see the paper for a plot showing allowed regions.If ee t is due to os illation, it is most likely to be intermediate sin22θ and m2. Seealso ATHANASSOPOULOS 98B.9 LOVERRE 96 uses the harged- urrent to neutral- urrent ratio from the ombinedCHARM (ALLABY 86) and CDHS (ABRAMOWICZ 86) data from 1986.10VILAIN 94C limit derived by ombining the νµ and νµ data assuming CP onservation.

785785785785See key on page 601 Lepton Parti le ListingsNeutrino Mixing(m2) for sin2(2θ) = 1 (νµ → νe )(m2) for sin2(2θ) = 1 (νµ → νe )(m2) for sin2(2θ) = 1 (νµ → νe )(m2) for sin2(2θ) = 1 (νµ → νe )VALUE (eV2) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.023 to 0.060 90 1 AGUILAR-AR...13A MBOO MiniBooNE<0.16 90 2 CHENG 12 MBOO MiniBooNE/S iBooNE0.030.09 90 3 AGUILAR-AR...10 MBOO Eν > 475 MeV0.030.07 90 4 AGUILAR-AR...10 MBOO Eν > 200 MeV<0.06 90 AGUILAR-AR...09B MBOO MiniBooNE<0.055 90 5 ARMBRUSTER02 KAR2 Liquid S i. alor.<2.6 90 AVVAKUMOV 02 NTEV NUTEV FNAL0.030.05 6 AGUILAR 01 LSND LAMPF0.050.08 90 7 ATHANASSO...96 LSND LAMPF0.0480.090 80 8 ATHANASSO...95<0.07 90 9 HILL 95<0.9 90 VILAIN 94C CHM2 CERN SPS<0.14 90 10 FREEDMAN 93 CNTR LAMPF1Based on νµ → νe appearan e of 78.4 ± 28.5 events. The best t values are m2 =0.043 eV2 and sin22θ = 0.88.2CHENG 12 is a ombined t of MiniBooNE and S iBooNE antineutrino data.3This value is for a two neutrino os illation analysis for ex ess antineutrino events withEν > 475 MeV. The best t is at 0.07. The allowed region is onsistent with LSNDreported by AGUILAR 01. Super edes AGUILAR-AREVALO 09B.4This value is for a two neutrino os illation analysis for ex ess antineutrino events withEν > 200 MeV with subtra tion of the expe ted 12 events low energy ex ess seen in theneutrino omponent of the beam. The best t value is 0.007 for (m2) = 4.4 eV2.5ARMBRUSTER 02 is the nal analysis of the KARMEN 2 data for 17.7 m distan e fromthe ISIS stopped pion and muon neutrino sour e. It is a sear h for νe , dete ted by theinverse β-de ay rea tion on protons and 12C. 15 andidate events are observed, and15.8 ± 0.5 ba kground events are expe ted, hen e no os illation signal is dete ted. Theresults ex lude large regions of the parameter area favored by the LSND experiment.6AGUILAR 01 is the nal analysis of the LSND full data set. It is a sear h for νe 30 m fromLAMPF beam stop. Neutrinos originate mainly for π+ de ay at rest. νe are dete tedthrough νe p → e+ n (20<Ee+ < 60 MeV) in delayed oin iden e with np → d γ.Authors observe 87.9 ± 22.4 ± 6.0 total ex ess events. The observation is attributedto νµ → νe os illations with the os illation probability of 0.264 ± 0.067 ± 0.045%, onsistent with the previously published result. Taking into a ount all onstraints,the most favored allowed region of os illation parameters is a band of (m2) from0.22.0 eV2. Supersedes ATHANASSOPOULOS 95, ATHANASSOPOULOS 96, andATHANASSOPOULOS 98.7ATHANASSOPOULOS 96 is a sear h for νe 30 m from LAMPF beam stop. Neutrinosoriginate mainly from π+ de ay at rest. νe ould ome from either νµ → νe or

νe → νe ; our entry assumes the rst interpretation. They are dete ted through νe p →e+ n (20 MeV <Ee+ <60 MeV) in delayed oin iden e with np → d γ. Authorsobserve 51 ± 20 ± 8 total ex ess events over an estimated ba kground 12.5 ± 2.9.ATHANASSOPOULOS 96B is a shorter version of this paper.8ATHANASSOPOULOS 95 error orresponds to the 1.6σ band in the plot. The ex-pe ted ba kground is 2.7 ± 0.4 events. Corresponds to an os illation probability of(0.34+0.20−0.18 ± 0.07)%. For a dierent interpretation, see HILL 95. Repla ed byATHANASSOPOULOS 96.9HILL 95 is a report by one member of the LSND Collaboration, reporting a dierent on- lusion from the analysis of the data of this experiment (see ATHANASSOPOULOS 95).Contrary to the rest of the LSND Collaboration, Hill nds no eviden e for the neutrinoos illation νµ → νe and obtains only upper limits.10 FREEDMAN 93 is a sear h at LAMPF for νe generated from any of the three neutrinotypes νµ, νµ, and νe whi h ome from the beam stop. The νe 's would be dete ted bythe rea tion νe p → e+ n. FREEDMAN 93 repla es DURKIN 88.sin2(2θ) for \Large" (m2) (νµ → νe )sin2(2θ) for \Large" (m2) (νµ → νe )sin2(2θ) for \Large" (m2) (νµ → νe )sin2(2θ) for \Large" (m2) (νµ → νe )VALUE (units 10−3) CL% DOCUMENT ID TECN COMMENT


<640 90 1 ANTONELLO 13A ICAR νe appearan e<150 90 2 CHENG 12 MBOO MiniBooNE/S iBooNE0.49.0 99 3 AGUILAR-AR...10 MBOO Eν > 475 MeV0.49.0 99 4 AGUILAR-AR...10 MBOO Eν > 200 MeV< 3.3 90 5 AGUILAR-AR...09B MBOO MiniBooNE< 1.7 90 6 ARMBRUSTER02 KAR2 Liquid S i. alor.< 1.1 90 AVVAKUMOV 02 NTEV NUTEV FNAL5.3±1.3±9.0 7 AGUILAR 01 LSND LAMPF6.2±2.4±1.0 8 ATHANASSO...96 LSND LAMPF312 80 9 ATHANASSO...95< 6 90 10 HILL 951ANTONELLO 13A obtained the limit by assuming νµ → νe os illation from the ∼ 2%of νµ evnets ontamination in the CNGS beam.2CHENG 12 is a ombined t of MiniBooNE and S iBooNE antineutrino data.3This value is for a two neutrino os illation analysis for ex ess antineutrino events withEν > 475 MeV. At 90% CL there is no solution at high (m2). The best t is atmaximal mixing. The allowed region is onsistent with LSND reported by AGUILAR 01.Super edes AGUILAR-AREVALO 09B.4This value is for a two neutrino os illation analysis for ex ess antineutrino events withEν > 200 MeV with subtra tion of the expe ted 12 events low energy ex ess seen in the

neutrino omponent of the beam. At 90% CL there is no solution at high (m2). Thebest t value is 0.007 for (m2) = 4.4 eV2.5This result is in on lusive with respe t to small amplitude mixing suggested by LSND.6ARMBRUSTER 02 is the nal analysis of the KARMEN 2 data. See footnote in thepre eding table for further details, and the paper for the ex lusion plot.7AGUILAR 01 is the nal analysis of the LSND full data set. The dedu ed os illation prob-ability is 0.264± 0.067± 0.045%; the value of sin22θ for large (m2) is twi e this proba-bility (although these values are ex luded by other onstraints). See footnote in pre edingtable for further details, and the paper for a plot showing allowed regions. SupersedesATHANASSOPOULOS 95, ATHANASSOPOULOS 96, and ATHANASSOPOULOS 98.8ATHANASSOPOULOS 96 reports (0.31 ± 0.12 ± 0.05)% for the os illation probability;the value of sin22θ for large (m2) should be twi e this probability. See footnote inpre eding table for further details, and see the paper for a plot showing allowed regions.9ATHANASSOPOULOS 95 error orresponds to the 1.6σ band in the plot. The ex-pe ted ba kground is 2.7 ± 0.4 events. Corresponds to an os illation probability of(0.34+0.20−0.18 ± 0.07)%. For a dierent interpretation, see HILL 95. Repla ed byATHANASSOPOULOS 96.10HILL 95 is a report by one member of the LSND Collaboration, reporting a dierent on- lusion from the analysis of the data of this experiment (see ATHANASSOPOULOS 95).Contrary to the rest of the LSND Collaboration, Hill nds no eviden e for the neutrinoos illation νµ → νe and obtains only upper limits.(m2) for sin2(2θ) = 1 (νµ (νµ ) → νe (νe ))(m2) for sin2(2θ) = 1 (νµ (νµ ) → νe (νe ))(m2) for sin2(2θ) = 1 (νµ (νµ ) → νe (νe ))(m2) for sin2(2θ) = 1 (νµ (νµ ) → νe (νe ))VALUE (eV2) CL% DOCUMENT ID TECN COMMENT

<0.075<0.075<0.075<0.075 90 BORODOV... 92 CNTR BNL E776• • • We do not use the following data for averages, ts, limits, et . • • •

<1.6 90 1 ROMOSAN 97 CCFR FNAL1ROMOSAN 97 uses wideband beam with a 0.5 km de ay region.sin2(2θ) for \Large" (m2) (νµ (νµ ) → νe (νe ))sin2(2θ) for \Large" (m2) (νµ (νµ ) → νe (νe ))sin2(2θ) for \Large" (m2) (νµ (νµ ) → νe (νe ))sin2(2θ) for \Large" (m2) (νµ (νµ ) → νe (νe ))VALUE (units 10−3) CL% DOCUMENT ID TECN COMMENT<1.8<1.8<1.8<1.8 90 1 ROMOSAN 97 CCFR FNAL• • • We do not use the following data for averages, ts, limits, et . • • •

<3.8 90 2 MCFARLAND 95 CCFR FNAL<3 90 BORODOV... 92 CNTR BNL E7761ROMOSAN 97 uses wideband beam with a 0.5 km de ay region.2MCFARLAND 95 state that \This result is the most stringent to date for 250<(m2) <450 eV2 and also ex ludes at 90%CL mu h of the high (m2) region favored bythe re ent LSND observation." See ATHANASSOPOULOS 95 and ATHANASSOPOU-LOS 96.(m2) for sin2(2θ) = 1 (νe 6→ νe)(m2) for sin2(2θ) = 1 (νe 6→ νe)(m2) for sin2(2θ) = 1 (νe 6→ νe)(m2) for sin2(2θ) = 1 (νe 6→ νe)VALUE (eV2) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<0.01 90 1 ACHKAR 95 CNTR Bugey rea tor1ACHKAR 95 bound is for L=15, 40, and 95 m.sin2(2θ) for \Large" (m2) (νe 6→ νe )sin2(2θ) for \Large" (m2) (νe 6→ νe )sin2(2θ) for \Large" (m2) (νe 6→ νe )sin2(2θ) for \Large" (m2) (νe 6→ νe )VALUE CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<0.02 90 1 ACHKAR 95 CNTR For (m2) = 0.6 eV21ACHKAR 95 bound is from data for L=15, 40, and 95 m distan e from the Bugey rea tor.Sterile neutrino limits from atmospheri neutrino studiesSterile neutrino limits from atmospheri neutrino studiesSterile neutrino limits from atmospheri neutrino studiesSterile neutrino limits from atmospheri neutrino studies(m2) for sin2(2θ) = 1 (νµ → νs )(m2) for sin2(2θ) = 1 (νµ → νs )(m2) for sin2(2θ) = 1 (νµ → νs )(m2) for sin2(2θ) = 1 (νµ → νs )νs means ντ or any sterile (nonintera ting) ν.VALUE (10−5 eV2) CL% DOCUMENT ID TECN COMMENT


<3000 (or <550) 90 1 OYAMA 89 KAMI Water Cherenkov< 4.2 or > 54. 90 BIONTA 88 IMB Flux has νµ, νµ, νe , and νe1OYAMA 89 gives a range of limits, depending on assumptions in their analysis. Theyargue that the region (m2) = (1001000) × 10−5 eV2 is not ruled out by any datafor large mixing.Sear h for νµ → νsSear h for νµ → νsSear h for νµ → νsSear h for νµ → νsVALUE DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •1 AMBROSIO 01 MCRO matter ee ts2 FUKUDA 00 SKAM neutral urrents + matter ef-fe ts

786786786786Lepton Parti le ListingsNeutrino Mixing1AMBROSIO 01 tested the pure 2- avor νµ → νs hypothesis using matter ee ts whi h hange the shape of the zenith-angle distribution of upward through-going muons. Withmaximum mixing and (m2) around 0.0024 eV2, the νµ → νs os illation is disfavoredwith 99% onden e level with respe t to the νµ → ντ hypothesis.2 FUKUDA 00 tested the pure 2- avor νµ → νs hypothesis using three omplementaryatmospheri -neutrino data samples. With this hypothesis, zenith-angle distributions areexpe ted to show hara teristi behavior due to neutral urrents and matter ee ts.In the (m2) and sin22θ region preferred by the Super-Kamiokande data, the νµ →νs hypothesis is reje ted at the 99% onden e level, while the νµ → ντ hypothesis onsistently ts all of the data sample.CPT testsCPT testsCPT testsCPT tests

⟨m221 −m221⟩⟨m221 −m221⟩⟨m221 −m221⟩⟨m221 −m221⟩VALUE (10−4 eV2) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<1.1 99.7 1 DEGOUVEA 05 FIT solar vs. rea tor1DEGOUVEA 05 obtained this bound at the 3σ CL from the KamLAND (ARAKI 05) andsolar neutrino data.⟨m232 −m232⟩⟨m232 −m232⟩⟨m232 −m232⟩⟨m232 −m232⟩VALUE (10−3 eV2) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •0.6+2.4

−0.8 90 1 ADAMSON 12B MINS MINOS atmospheri 1The quoted result is the single-parameter 90% C.L. interval determined from the 90% C.L. ontour in the (m2, m2) plane, whi h is obtained by minimizing the four parameterlog-likelihood fun tion with respe t to the other os illation parameters.REFERENCES FOR Neutrino MixingREFERENCES FOR Neutrino MixingREFERENCES FOR Neutrino MixingREFERENCES FOR Neutrino MixingAARTSEN 15A PR D91 072004 M.G. Aartsen (I eCube Collab.)ABE 15D PR D91 072010 K. Abe et al. (T2K Collab.)AN 15 PRL 115 111802 F.P. An et al. (Daya Bay Collab.)BERGSTROM 15 JHEP 1509 200 J. Bergstrom et al. (BARC, STON, MADU+)GANDO 15 PR C92 055808 A. Gando et al. (KamLAND Collab.)ABE 14 PRL 112 181801 K. Abe et al. (T2K Collab.)Also PR D91 072010 K. Abe et al. (T2K Collab.)ABE 14A PL B735 51 Y. Abe et al. (Double Chooz Collab.)ABE 14B PR D89 092003 K. Abe et al. (T2K Collab.)ABE 14C PRL 112 061802 K. Abe et al. (T2K Collab.)ABE 14H JHEP 1410 086 Y. Abe et al. (Double Chooz Collab.)Also JHEP 1502 074 (errat.) Y. Abe et al. (Double Chooz Collab.)ADAMSON 14 PRL 112 191801 P. Adamson et al. (MINOS Collab.)AN 14 PRL 112 061801 F.P. An et al. (Daya Bay Collab.)AN 14B PR D90 071101 F.P. An et al. (Daya Bay Collab.)BELLINI 14A NAT 512 383 G. Bellini et al. (Borexino Collab.)FORERO 14 PR D90 093006 D. V. Forero, M. Tortola, J. W. F. ValleGONZALEZ-G... 14 JHEP 1411 052 M.C. Gonzalez-Gar ia, M. Maltoni, T. S hwetzPDG 14 CPC 38 070001 K. Olive et al. (PDG Collab.)RENSHAW 14 PRL 112 091805 A. Renshaw et al. (Super-Kamiokande Collab.)AARTSEN 13B PRL 111 081801 M.G. Aartsen et al. (I eCube Collab.)ABE 13C PL B723 66 Y. Abe et al. (Double Chooz Collab.)ABE 13E PR D88 032002 K. Abe et al. (T2K Collab.)ABE 13G PRL 111 211803 K. Abe et al. (T2K Collab.)ADAMSON 13A PRL 110 171801 P. Adamson et al. (MINOS Collab.)ADAMSON 13B PRL 110 251801 P. Adamson et al. (MINOS Collab.)AGAFONOVA 13 JHEP 1307 004 N. Agafonova et al. (OPERA Collab.)AGUILAR-AR... 13A PRL 110 161801 A.A. Aguilar-Arevalo et al. (MiniBooNE Collab.)AHARMIM 13 PR C88 025501 B. Aharmim et al. (SNO Collab.)AN 13 CPC 37 011001 F.P. An et al. (Daya Bay Collab.)Also CPC 37 011001 (errat.) F.P. An et al. (Daya Bay Collab.)ANTONELLO 13 EPJ C73 2345 M. Antonello et al. (ICARUS Collab.)ANTONELLO 13A EPJ C73 2599 M. Antonello et al. (ICARUS Collab.)GANDO 13 PR D88 033001 A. Gando et al. (KamLAND Collab.)ABE 12 PRL 108 131801 Y. Abe et al. (Double Chooz Collab.)ABE 12A PR D85 031103 K. Abe et al. (T2K Collab.)ABE 12B PR D86 052008 Y. Abe et al. (Double Chooz Collab.)ADAMSON 12 PRL 108 191801 P. Adamson et al. (MINOS Collab.)ADAMSON 12B PR D86 052007 P. Adamson et al. (MINOS Collab.)ADRIAN-MAR...12 PL B714 224 S. Adrian-Martinez et al. (ANTARES Collab.)AHN 12 PRL 108 191802 J.K. Ahn et al. (RENO Collab.)AN 12 PRL 108 171803 F.P. An et al. (Daya Bay Collab.)Also CPC 37 011001 (errat.) F.P. An et al. (Daya Bay Collab.)BELLINI 12A PRL 108 051302 G. Bellini et al. (Borexino Collab.)CHENG 12 PR D86 052009 G. Cheng et al. (MiniBooNE/S iBooNE Collab.)MAHN 12 PR D85 032007 K.B.M. Mahn et al. (MiniBooNE/S iBooNE Collab.)ABE 11 PR D83 052010 K. Abe et al. (Super-Kamiokande Collab.)ABE 11A PRL 107 041801 K. Abe et al. (T2K Collab.)ABE 11B PR C84 035804 S. Abe et al. (KamLAND Collab.)ABE 11C PRL 107 241801 K. Abe et al. (Super-Kamiokande Collab.)ADAMSON 11 PRL 106 181801 P. Adamson et al. (MINOS Collab.)ADAMSON 11B PRL 107 021801 P. Adamson et al. (MINOS Collab.)ADAMSON 11C PR D84 071103 P. Adamson et al. (MINOS Collab.)ADAMSON 11D PRL 107 181802 P. Adamson et al. (MINOS Collab.)BELLINI 11 PL B696 191 G. Bellini et al. (Borexino Collab.)BELLINI 11A PRL 107 141302 G. Bellini et al. (Borexino Collab.)FOGLI 11 PR D84 053007 G.L. Fogli et al.GANDO 11 PR D83 052002 A. Gando et al. (KamLAND Collab.)MUELLER 11 PR C83 054615 Th.A Mueller et al.SERENELLI 11 APJ 743 24 A.M. Serenelli, W.C. Haxton, C. Pena-GarayADAMSON 10A PR D82 051102 P. Adamson et al. (MINOS Collab.)AGUILAR-AR... 10 PRL 105 181801 A.A. Aguillar-Arevalo et al. (MiniBooNE Collab.)AHARMIM 10 PR C81 055504 B. Aharmim et al. (SNO Collab.)BELLINI 10A PR D82 033006 G. Bellini et al. (Borexino Collab.)DENIZ 10 PR D81 072001 M. Deniz et al. (TEXONO Collab.)KAETHER 10 PL B685 47 F. Kaether et al.WENDELL 10 PR D81 092004 R. Wendell et al. (Super-Kamiokande Collab.)

ABDURASHI... 09 PR C80 015807 J.N. Abdurashitov et al. (SAGE Collab.)ADAMSON 09 PRL 103 261802 P. Adamson et al. (MINOS Collab.)AGUILAR-AR... 09B PRL 103 111801 A.A. Aguilar-arevalo et al. (MiniBooNE Collab.)ABE 08A PRL 100 221803 S. Abe et al. (KamLAND Collab.)Also PRL 101 119904E S. Abe et al. (KamLAND Collab.)ADAMSON 08 PR D77 072002 P. Adamson et al. (MINOS Collab.)ADAMSON 08A PRL 101 131802 P. Adamson et al. (MINOS Collab.)AHARMIM 08 PRL 101 111301 B. Aharmim et al. (SNO Collab.)Also PR C87 015502 B. Aharmim et al. (SNO Collab.)ARPESELLA 08A PRL 101 091302 C. Arpesella et al. (Borexino Collab.)CRAVENS 08 PR D78 032002 J.P. Cravens et al. (Super-Kamiokande Collab.)FOGLI 08 PRL 101 141801 G.L. Fogli, et alADAMSON 07 PR D75 092003 P. Adamson et al. (MINOS Collab.)AGUILAR-AR... 07 PRL 98 231801 A.A. Aguilar-Arevalo et al. (MiniBooNE Collab.)AHARMIM 07 PR C75 045502 B. Aharmim et al. (SNO Collab.)ADAMSON 06 PR D73 072002 P. Adamson et al. (MINOS Collab.)AHN 06A PR D74 072003 M.H. Ahn et al. (K2K Collab.)BALATA 06 EPJ C47 21 M. Balata et al. (Borexino Collab.)HOSAKA 06 PR D73 112001 J. Hosaka et al. (Super-Kamiokande Collab.)HOSAKA 06A PR D74 032002 J. Hosaka et al. (Super-Kamiokande Collab.)MICHAEL 06 PRL 97 191801 D. Mi hael et al. (MINOS Collab.)WINTER 06A PR C73 025503 W.T. Winter et al.YAMAMOTO 06 PRL 96 181801 S. Yamamoto et al. (K2K Collab.)AHARMIM 05A PR C72 055502 B. Aharmim et al. (SNO Collab.)ALIU 05 PRL 94 081802 E. Aliu et al. (K2K Collab.)ALLISON 05 PR D72 052005 W.W.M. Allison et al. (SOUDAN-2 Collab.)ALTMANN 05 PL B616 174 M. Altmann et al. (GNO Collab.)ARAKI 05 PRL 94 081801 T. Araki et al. (KamLAND Collab.)ASHIE 05 PR D71 112005 Y. Ashie et al. (Super-Kamiokande Collab.)DEGOUVEA 05 PR D71 093002 A. de Gouvea, C. Pena-GarayAHARMIM 04 PR D70 093014 B. Aharmim et al. (SNO Collab.)AHMED 04A PRL 92 181301 S.N. Ahmed et al. (SNO Collab.)AHN 04 PRL 93 051801 M.H. Ahn et al. (K2K Collab.)AMBROSIO 04 EPJ C36 323 M. Ambrosio et al. (MACRO Collab.)ASHIE 04 PRL 93 101801 Y. Ashie et al. (Super-Kamiokande Collab.)EGUCHI 04 PRL 92 071301 K. Egu hi et al. (KamLAND Collab.)SMY 04 PR D69 011104 M.B. Smy et al. (Super-Kamiokande Collab.)AHN 03 PRL 90 041801 M.H. Ahn et al. (K2K Collab.)AMBROSIO 03 PL B566 35 M. Ambrosio et al. (MACRO Collab.)APOLLONIO 03 EPJ C27 331 M. Apollonio et al. (CHOOZ Collab.)ASTIER 03 PL B570 19 P. Astier et al. (NOMAD Collab.)EGUCHI 03 PRL 90 021802 K. Egu hi et al. (KamLAND Collab.)GANDO 03 PRL 90 171302 Y. Gando et al. (Super-Kamiokande Collab.)IANNI 03 JP G29 2107 A. Ianni (INFN Gran Sasso)SANCHEZ 03 PR D68 113004 M. San hez et al. (Soudan 2 Collab.)ABDURASHI... 02 JETP 95 181 J.N. Abdurashitov et al. (SAGE Collab.)Translated from ZETF 122 211.AHMAD 02 PRL 89 011301 Q.R. Ahmad et al. (SNO Collab.)AHMAD 02B PRL 89 011302 Q.R. Ahmad et al. (SNO Collab.)ARMBRUSTER 02 PR D65 112001 B. Armbruster et al. (KARMEN 2 Collab.)AVVAKUMOV 02 PRL 89 011804 S. Avvakumov et al. (NuTeV Collab.)FUKUDA 02 PL B539 179 S. Fukuda et al. (Super-Kamiokande Collab.)AGUILAR 01 PR D64 112007 A. Aguilar et al. (LSND Collab.)AHMAD 01 PRL 87 071301 Q.R. Ahmad et al. (SNO Collab.)AMBROSIO 01 PL B517 59 M. Ambrosio et al. (MACRO Collab.)BOEHM 01 PR D64 112001 F. Boehm et al.FUKUDA 01 PRL 86 5651 S. Fukuda et al. (Super-Kamiokande Collab.)AMBROSIO 00 PL B478 5 M. Ambrosio et al. (MACRO Collab.)BOEHM 00 PRL 84 3764 F. Boehm et al.FUKUDA 00 PRL 85 3999 S. Fukuda et al. (Super-Kamiokande Collab.)ALLISON 99 PL B449 137 W.W.M. Allison et al. (Soudan 2 Collab.)APOLLONIO 99 PL B466 415 M. Apollonio et al. (CHOOZ Collab.)Also PL B472 434 (errat.) M. Apollonio et al. (CHOOZ Collab.)FUKUDA 99C PRL 82 2644 Y. Fukuda et al. (Super-Kamiokande Collab.)FUKUDA 99D PL B467 185 Y. Fukuda et al. (Super-Kamiokande Collab.)HAMPEL 99 PL B447 127 W. Hampel et al. (GALLEX Collab.)AMBROSIO 98 PL B434 451 M. Ambrosio et al. (MACRO Collab.)APOLLONIO 98 PL B420 397 M. Apollonio et al. (CHOOZ Collab.)ATHANASSO... 98 PRL 81 1774 C. Athanassopoulos et al. (LSND Collab.)ATHANASSO... 98B PR C58 2489 C. Athanassopoulos et al. (LSND Collab.)CLEVELAND 98 APJ 496 505 B.T. Cleveland et al. (Homestake Collab.)FELDMAN 98 PR D57 3873 G.J. Feldman, R.D. CousinsFUKUDA 98C PRL 81 1562 Y. Fukuda et al. (Super-Kamiokande Collab.)HATAKEYAMA 98 PRL 81 2016 S. Hatakeyama et al. (Kamiokande Collab.)CLARK 97 PRL 79 345 R. Clark et al. (IMB Collab.)ROMOSAN 97 PRL 78 2912 A. Romosan et al. (CCFR Collab.)AGLIETTA 96 JETPL 63 791 M. Aglietta et al. (LSD Collab.)Translated from ZETFP 63 753.ATHANASSO... 96 PR C54 2685 C. Athanassopoulos et al. (LSND Collab.)ATHANASSO... 96B PRL 77 3082 C. Athanassopoulos et al. (LSND Collab.)FUKUDA 96 PRL 77 1683 Y. Fukuda et al. (Kamiokande Collab.)FUKUDA 96B PL B388 397 Y. Fukuda et al. (Kamiokande Collab.)GREENWOOD 96 PR D53 6054 Z.D. Greenwood et al. (UCI, SVR, SCUC)HAMPEL 96 PL B388 384 W. Hampel et al. (GALLEX Collab.)LOVERRE 96 PL B370 156 P.F. LoverreACHKAR 95 NP B434 503 B. A hkar et al. (SING, SACLD, CPPM, CDEF+)AHLEN 95 PL B357 481 S.P. Ahlen et al. (MACRO Collab.)ATHANASSO... 95 PRL 75 2650 C. Athanassopoulos et al. (LSND Collab.)DAUM 95 ZPHY C66 417 K. Daum et al. (FREJUS Collab.)HILL 95 PRL 75 2654 J.E. Hill (PENN)MCFARLAND 95 PRL 75 3993 K.S. M Farland et al. (CCFR Collab.)DECLAIS 94 PL B338 383 Y. De lais et al.FUKUDA 94 PL B335 237 Y. Fukuda et al. (Kamiokande Collab.)VILAIN 94C ZPHY C64 539 P. Vilain et al. (CHARM II Collab.)FREEDMAN 93 PR D47 811 S.J. Freedman et al. (LAMPF E645 Collab.)BECKER-SZ... 92B PR D46 3720 R.A. Be ker-Szendy et al. (IMB Collab.)BEIER 92 PL B283 446 E.W. Beier et al. (KAM2 Collab.)Also PTRSL A346 63 E.W. Beier, E.D. Frank (PENN)BORODOV... 92 PRL 68 274 L. Borodovsky et al. (COLU, JHU, ILL)HIRATA 92 PL B280 146 K.S. Hirata et al. (Kamiokande II Collab.)CASPER 91 PRL 66 2561 D. Casper et al. (IMB Collab.)HIRATA 91 PRL 66 9 K.S. Hirata et al. (Kamiokande II Collab.)KUVSHINN... 91 JETPL 54 253 A.A. Kuvshinnikov et al. (KIAE)BERGER 90B PL B245 305 C. Berger et al. (FREJUS Collab.)HIRATA 90 PRL 65 1297 K.S. Hirata et al. (Kamiokande II Collab.)AGLIETTA 89 EPL 8 611 M. Aglietta et al. (FREJUS Collab.)DAVIS 89 ARNPS 39 467 R. Davis, A.K. Mann, L. Wolfenstein (BNL, PENN+)OYAMA 89 PR D39 1481 Y. Oyama et al. (Kamiokande II Collab.)BIONTA 88 PR D38 768 R.M. Bionta et al. (IMB Collab.)DURKIN 88 PRL 61 1811 L.S. Durkin et al. (OSU, ANL, CIT+)ABRAMOWICZ 86 PRL 57 298 H. Abramowi z et al. (CDHS Collab.)ALLABY 86 PL B177 446 J.V. Allaby et al. (CHARM Collab.)ANGELINI 86 PL B179 307 C. Angelini et al. (PISA, ATHU, PADO+)VUILLEUMIER 82 PL 114B 298 J.L. Vuilleumier et al. (CIT, SIN, MUNI)BOLIEV 81 SJNP 34 787 M.M. Boliev et al. (INRM)Translated from YAF 34 1418.KWON 81 PR D24 1097 H. Kwon et al. (CIT, ISNG, MUNI)BOEHM 80 PL 97B 310 F. Boehm et al. (ILLG, CIT, ISNG, MUNI)CROUCH 78 PR D18 2239 M.F. Crou h et al. (CASE, UCI, WITW)

787787787787See key on page 601 Lepton Parti le ListingsHeavy Neutral Leptons, Sear hes forHeavy Neutral Leptons, Sear hes for(A) Heavy Neutral Leptons(A) Heavy Neutral Leptons(A) Heavy Neutral Leptons(A) Heavy Neutral LeptonsStable Neutral Heavy Lepton MASS LIMITSStable Neutral Heavy Lepton MASS LIMITSStable Neutral Heavy Lepton MASS LIMITSStable Neutral Heavy Lepton MASS LIMITSNote that LEP results in ombination with REUSSER 91 ex lude a fourthstable neutrino with m< 2400 GeV.VALUE (GeV) CL% DOCUMENT ID TECN COMMENT>45.0>45.0>45.0>45.0 95 ABREU 92B DLPH Dira >39.5>39.5>39.5>39.5 95 ABREU 92B DLPH Majorana>44.1 95 ALEXANDER 91F OPAL Dira >37.2 95 ALEXANDER 91F OPAL Majorananone 3100 90 SATO 91 KAM2 Kamiokande II>42.8 95 1 ADEVA 90S L3 Dira >34.8 95 1 ADEVA 90S L3 Majorana>42.7 95 DECAMP 90F ALEP Dira 1ADEVA 90S limits for the heavy neutrino apply if the mixing with the harged leptonssatises ∣∣U1 j ∣∣2 + ∣∣U2 j ∣∣2 + ∣∣U3 j ∣∣2 > 6.2×10−8 atmL0 = 20 GeV and > 5.1×10−10for mL0 = 40 GeV.Heavy Neutral Lepton MASS LIMITSHeavy Neutral Lepton MASS LIMITSHeavy Neutral Lepton MASS LIMITSHeavy Neutral Lepton MASS LIMITSLimits apply only to heavy lepton type given in omment at right of dataListings.See the \Quark and Lepton Compositeness, Sear hes for" Listings forlimits on radiatively de aying ex ited neutral leptons, i.e. ν∗ → ν γ.VALUE (GeV) CL% DOCUMENT ID TECN COMMENT>101.3>101.3>101.3>101.3 95 ACHARD 01B L3 Dira oupling to e>101.5>101.5>101.5>101.5 95 ACHARD 01B L3 Dira oupling to µ

> 90.3> 90.3> 90.3> 90.3 95 ACHARD 01B L3 Dira oupling to τ

> 89.5> 89.5> 89.5> 89.5 95 ACHARD 01B L3 Majorana oupling to e> 90.7> 90.7> 90.7> 90.7 95 ACHARD 01B L3 Majorana oupling to µ

> 80.5> 80.5> 80.5> 80.5 95 ACHARD 01B L3 Majorana oupling to τ


> 76.0 95 ABBIENDI 00I OPAL Majorana, oupling to e> 88.0 95 ABBIENDI 00I OPAL Dira , oupling to e> 76.0 95 ABBIENDI 00I OPAL Majorana, oupling to µ

> 88.1 95 ABBIENDI 00I OPAL Dira , oupling to µ

> 53.8 95 ABBIENDI 00I OPAL Majorana, oupling to τ

> 71.1 95 ABBIENDI 00I OPAL Dira , oupling to τ

> 76.5 95 ABREU 99O DLPH Dira oupling to e> 79.5 95 ABREU 99O DLPH Dira oupling to µ

> 60.5 95 ABREU 99O DLPH Dira oupling to τ

> 63 95 2,3 BUSKULIC 96S ALEP Dira > 54.3 95 2,4 BUSKULIC 96S ALEP Majorana2BUSKULIC 96S requires the de ay length of the heavy lepton to be < 1 m, limiting thesquare of the mixing angle ∣∣Uℓ j ∣∣2 to 10−10.3BUSKULIC 96S limit for mixing with τ . Mass is > 63.6 GeV for mixing with e or µ.4BUSKULIC 96S limit for mixing with τ . Mass is > 55.2 GeV for mixing with e or µ.Astrophysi al Limits on Neutrino MASS for mν > 1 GeVAstrophysi al Limits on Neutrino MASS for mν > 1 GeVAstrophysi al Limits on Neutrino MASS for mν > 1 GeVAstrophysi al Limits on Neutrino MASS for mν > 1 GeVVALUE (GeV) CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •none 60115 5 FARGION 95 ASTR Dira none 9.22000 6 GARCIA 95 COSM Nu leosynthesisnone 264700 6 BECK 94 COSM Dira none 6 hundreds 7,8 MORI 92B KAM2 Dira neutrinonone 24 hundreds 7,8 MORI 92B KAM2 Majorana neutrinonone 102400 90 9 REUSSER 91 CNTR HPGe sear hnone 3100 90 SATO 91 KAM2 Kamiokande II10 ENQVIST 89 COSMnone 121400 6 CALDWELL 88 COSM Dira νnone 416 90 6,7 OLIVE 88 COSM Dira νnone 435 90 OLIVE 88 COSM Majorana ν

>4.2 to 4.7 SREDNICKI 88 COSM Dira ν

>5.3 to 7.4 SREDNICKI 88 COSM Majorana νnone 201000 95 6 AHLEN 87 COSM Dira ν

>4.1 GRIEST 87 COSM Dira ν5FARGION 95 bound is sensitive to assumed ν on entration in the Galaxy. See alsoKONOPLICH 94.6These results assume that neutrinos make up dark matter in the gala ti halo.7 Limits based on annihilations in the sun and are due to an absen e of high energyneutrinos dete ted in underground experiments.

8MORI 92B results assume that neutrinos make up dark matter in the gala ti halo. Limitsbased on annihilations in earth are also given.9REUSSER 91 uses existing ββ dete tor (see FISHER 89) to sear h for CDM Dira neutrinos.10ENQVIST 89 argue that there is no osmologi al upper bound on heavy neutrinos.(B) Other Bounds from Nu lear and Parti le De ays(B) Other Bounds from Nu lear and Parti le De ays(B) Other Bounds from Nu lear and Parti le De ays(B) Other Bounds from Nu lear and Parti le De aysLimits on ∣∣Ue x ∣∣2 as Fun tion of mνxLimits on ∣∣Ue x ∣∣2 as Fun tion of mνxLimits on ∣∣Ue x ∣∣2 as Fun tion of mνxLimits on ∣∣Ue x ∣∣2 as Fun tion of mνxPeak and kink sear h testsPeak and kink sear h testsPeak and kink sear h testsPeak and kink sear h testsLimits on ∣∣Ue x ∣∣2 as fun tion of mνjVALUE CL% DOCUMENT ID TECN COMMENT<1 × 10−7<1 × 10−7<1 × 10−7<1 × 10−7 90 11 BRITTON 92B CNTR 50 MeV < mνx < 130MeV• • • We do not use the following data for averages, ts, limits, et . • • •

<5 × 10−6 90 DELEENER-... 91 mνx=20 MeV<5 × 10−7 90 DELEENER-... 91 mνx=40 MeV<3 × 10−7 90 DELEENER-... 91 mνx=60 MeV<1 × 10−6 90 DELEENER-... 91 mνx=80 MeV<1 × 10−6 90 DELEENER-... 91 mνx=100 MeV<5 × 10−7 90 AZUELOS 86 CNTR mνx=60 MeV<2 × 10−7 90 AZUELOS 86 CNTR mνx=80 MeV<3 × 10−7 90 AZUELOS 86 CNTR mνx=100 MeV<1 × 10−6 90 AZUELOS 86 CNTR mνx=120 MeV<2 × 10−7 90 AZUELOS 86 CNTR mνx=130 MeV<1 × 10−4 90 12 BRYMAN 83B CNTR mνx=5 MeV<1.5× 10−6 90 BRYMAN 83B CNTR mνx=53 MeV<1 × 10−5 90 BRYMAN 83B CNTR mνx=70 MeV<1 × 10−4 90 BRYMAN 83B CNTR mνx=130 MeV<1 × 10−4 68 13 SHROCK 81 THEO mνx=10 MeV<5 × 10−6 68 13 SHROCK 81 THEO mνx=60 MeV<1 × 10−5 68 14 SHROCK 80 THEO mνx=80 MeV<3 × 10−6 68 14 SHROCK 80 THEO mνx=160 MeV11BRITTON 92B is from a sear h for additional peaks in the e+ spe trum from π+ →e+ νe de ay at TRIUMF. See also BRITTON 92.12BRYMAN 83B obtain upper limits from both dire t peak sear h and analysis of B(π →e ν)/B(π → µν). Latter limits are not listed, ex ept for this entry (i.e. | we list themost stringent limits for given mass).13Analysis of (π+ → e+ νe )/(π+ → µ+ νµ) and (K+ → e+ νe )/(K+ → µ+ νµ)de ay ratios.14Analysis of (K+ → e+ νe ) spe trum.Kink sear h in nu lear β de ayKink sear h in nu lear β de ayKink sear h in nu lear β de ayKink sear h in nu lear β de ayHigh-sensitivity follow-up experiments show that indi ations for a neutrino with mass17 keV (Simpson, Hime, and others) were not valid. A ordingly, we no longer listthe experiments by these authors and some others whi h made positive laims of17 keV neutrino emission. Complete listings are given in the 1994 edition (Physi alReview D50D50D50D50 1173 (1994)) and in the 1998 edition (The European Physi al JournalC3C3C3C3 1 (1998)). We list below only the best limits on ∣∣Uex

∣∣2 for ea h mνx . SeeWIETFELDT 96 for a omprehensive review.VALUE(units 10−3) CL% mνj(keV) ISOTOPE METHOD DOCUMENT ID


< 420 90 7003500 38mK Trap 15 TRINCZEK 03< 9116 95 10.1 187Re ryog. 16 GALEAZZI 01< 1 95 1090 35S Mag spe t 17 HOLZSCHUH 00< 4 95 1417 241Pu Ele trostati spe 18 DRAGOUN 99< 1 95 430 63Ni Mag spe t 19 HOLZSCHUH 99< 1040 90 370640 37Ar EC ion re oil 20 HINDI 98< 10 95 1 3H SPEC 21 HIDDEMANN 95< 6 95 2 3H SPEC 21 HIDDEMANN 95< 2 95 3 3H SPEC 21 HIDDEMANN 95< 0.7 99 16.316.6 3H Prop hamber 22 KALBFLEISCH 93< 2 95 1340 35S Si(Li) 23 MORTARA 93< 0.73 95 17 63Ni Mag spe t OHSHIMA 93< 1.0 95 1024 63Ni Mag spe t KAWAKAMI 92< 0.92.5 90 12006800 20F beta spe trum 24 DEUTSCH 90< 8 90 80 35S Mag spe t 25 APALIKOV 85< 1.5 90 60 35S Mag spe t APALIKOV 85< 3.0 90 550 Mag spe t MARKEY 85< 0.62 90 48 35S Si(Li) OHI 85< 0.90 90 30 35S Si(Li) OHI 85< 4 90 140 64Cu Mag spe t 26 SCHRECK... 83< 8 90 440 64Cu Mag spe t 26 SCHRECK... 83<100 90 0.13000 THEO 27 SHROCK 80< 0.1 68 80 THEO 28 SHROCK 80

788788788788LeptonParti le ListingsHeavyNeutral Leptons, Sear hes for15TRINCZEK 03 is a sear h for admixture of heavy neutrino to νe , in ontrast to νe usedin many other sear hes. Full kinemati re onstru tion of the neutrino momentum by useof a magneto opti al trap.16GALEAZZI 01 use an ryogeni mi ro alorimeter to sear h for mass 501000 eV neutrinoadmixtures using the 187Re beta spe trum with 2.4 keV endpoint. They derive limitsfor the admixture of heavy neutrinos, ranging from 9 × 10−3 for mass 1 keV to 0.116for mass 100 eV. This is a signi ant improvement with respe t to HIDDEMANN 95,espe ially for masses below ∼ 500 MeV, where the limit is about a fa tor of ∼ 2 higher.17HOLZSCHUH 00 use an iron-free β spe trometer to measure the 35Sβ de ay spe trum.An analysis of the spe trum in the energy range 56173 keV is used to derive limits forthe admixture of heavy neutrinos. This extends the range of neutrino masses exploredin HOLZSCHUH 99.18DRAGOUN 99 analyze the β de ay spe trum of 241Pu in the energy range 0.29.2keV to derive limits for the admixture of heavy neutrinos. It is not ompetitive withHOLZSCHUH 99.19HOLZSCHUH 99 use an iron-free β spe trometer to measure the 63Niβ de ay spe trum.An analysis of the spe trum in the energy rage 3367.8 keV is used to derive limits forthe admixture of heavy neutrinos.20HINDI 98 obtain a limit on heavy neutrino admixture from EC de ay of 37Ar by measuringthe time-of- ight distribution of the re oiling ions in oin iden e with x-rays or Augerele trons. The authors report upper limit for ∣∣Uex ∣∣2 of ≈ 3% for mνx=500 keV, 1% formνx=550 keV, 2% for mνx=600 keV, and 4% for mx=650 keV. Their reported limitsfor mνx ≤ 450 keV are inferior to the limits of SCHRECKENBACH 83.21 In the beta spe trum from tritium β de ay nonvanishing or mixed mν1 state in the massregion 0.014 keV. For mνx <1 keV, their upper limit on ∣∣Uex ∣∣2 be omes less22KALBFLEISCH 93 extends the 17 keV neutrino sear h of BAHRAN 92, using an im-proved proportional hamber to whi h a small amount of 3H is added. Systemati s aresigni antly redu ed, allowing for an improved upper limit. The authors give a 99% on-den e limit on ∣∣Ue x ∣∣2 as a fun tion of mνx in the range from 13.5 keV to 17.5 keV.See also the related papers BAHRAN 93, BAHRAN 93B, and BAHRAN 95 on theoreti alaspe ts of beta spe tra and tting methods for heavy neutrinos.23MORTARA 93 limit is from study using a high-resolution solid-state dete tor with asuper ondu ting solenoid. The authors note that \The sensitivity to neutrino mass isveried by measurement with a mixed sour e of 35S and 14C, whi h arti ially produ esa distortion in the beta spe trum similar to that expe ted from the massive neutrino."24DEUTSCH 90 sear h for emission of heavy νe in super-allowed beta de ay of 20F byspe tral analysis of the ele trons.25This limit was taken from the gure 3 of APALIKOV 85; the text gives a more restri tivelimit of 1.7× 10−3 at CL = 90%.26SCHRECKENBACH 83 is a ombined measurement of the β+ and β− spe trum.27 SHROCK 80 was a retroa tive analysis of data on several superallowed β de ays to sear hfor kinks in the Kurie plot.28Appli ation of test to sear h for kinks in β de ay Kurie plots.Sear hes for De ays of Massive νSear hes for De ays of Massive νSear hes for De ays of Massive νSear hes for De ays of Massive νLimits on ∣∣Ue x ∣∣2 as fun tion of mνxVALUE CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<1.6× 10−4 90 29 BACK 03A CNTR mνx = 4 MeV<4.5× 10−5 90 29 BACK 03A CNTR mνx = 7 MeV<3.8× 10−5 90 29 BACK 03A CNTR mνx = 10 MeV<1.5× 10−3 95 ACHARD 01 L3 mνx=80 GeV<2 × 10−2 95 ACHARD 01 L3 mνx=175 GeV<0.3 95 ACHARD 01 L3 mνx=200 GeV<4 × 10−3 95 ACCIARRI 99K L3 mνx=80 GeV<5 × 10−2 95 ACCIARRI 99K L3 mνx= 175 GeV<2 × 10−5 95 30 ABREU 97I DLPH mνx=6 GeV<3 × 10−5 95 30 ABREU 97I DLPH mνx=50 GeV<1.8× 10−3 90 31 HAGNER 95 MWPC mνh = 1.5 MeV<2.5× 10−4 90 31 HAGNER 95 MWPC mνh = 4 MeV<4.2× 10−3 90 31 HAGNER 95 MWPC mνh = 9 MeV<1 × 10−5 90 32 BARANOV 93 mνx=100 MeV<1 × 10−6 90 32 BARANOV 93 mνx= 200 MeV<3 × 10−7 90 32 BARANOV 93 mνx= 300 MeV<2 × 10−7 90 32 BARANOV 93 mνx=400 MeV<6.2× 10−8 95 ADEVA 90S L3 mνx=20 GeV<5.1× 10−10 95 ADEVA 90S L3 mνx=40 GeVall values ruled out 95 33 BURCHAT 90 MRK2 mνx < 19.6 GeV<1 × 10−10 95 33 BURCHAT 90 MRK2 mνx= 22 GeV<1 × 10−11 95 33 BURCHAT 90 MRK2 mνx= 41 GeVall values ruled out 95 DECAMP 90F ALEP mνx= 25.042.7 GeV<1 × 10−13 95 DECAMP 90F ALEP mνx= 42.745.7 GeV<5 × 10−3 90 AKERLOF 88 HRS mνx=1.8 GeV<2 × 10−5 90 AKERLOF 88 HRS mνx=4 GeV<3 × 10−6 90 AKERLOF 88 HRS mνx=6 GeV<1.2× 10−7 90 BERNARDI 88 CNTR mνx=100 MeV

<1 × 10−8 90 BERNARDI 88 CNTR mνx=200 MeV<2.4× 10−9 90 BERNARDI 88 CNTR mνx=300 MeV<2.1× 10−9 90 BERNARDI 88 CNTR mνx=400 MeV<2 × 10−2 68 34 OBERAUER 87 mνx=1.5 MeV<8 × 10−4 68 34 OBERAUER 87 mνx=4.0 MeV<8 × 10−3 90 BADIER 86 CNTR mνx=400 MeV<8 × 10−5 90 BADIER 86 CNTR mνx=1.7 GeV<8 × 10−8 90 BERNARDI 86 CNTR mνx=100 MeV<4 × 10−8 90 BERNARDI 86 CNTR mνx=200 MeV<6 × 10−9 90 BERNARDI 86 CNTR mνx=400 MeV<3 × 10−5 90 DORENBOS... 86 CNTR mνx=150 MeV<1 × 10−6 90 DORENBOS... 86 CNTR mνx=500 MeV<1 × 10−7 90 DORENBOS... 86 CNTR mνx=1.6 GeV<7 × 10−7 90 35 COOPER-... 85 HLBC mνx=0.4 GeV<8 × 10−8 90 35 COOPER-... 85 HLBC mνx=1.5 GeV<1 × 10−2 90 36 BERGSMA 83B CNTR mνx=10 MeV<1 × 10−5 90 36 BERGSMA 83B CNTR mνx=110 MeV<6 × 10−7 90 36 BERGSMA 83B CNTR mνx=410 MeV<1 × 10−5 90 GRONAU 83 mνx=160 MeV<1 × 10−6 90 GRONAU 83 mνx=480 MeV29BACK 03A sear hed for heavy neutrinos emitted from 8B de ay in the Sun using thede ay νh → νe e+ e− in the Counting Test Fa ility (the prototype of the Borexinodete tor) and obtained limits on heavy neutrino admixture for the νh mass range 1.112MeV.30ABREU 97I long-lived νx analysis. Short-lived analysis extends limit to lower masseswith de reasing sensitivity ex ept at 3.5 GeV, where the limit is the same as at 6 GeV.31HAGNER 95 obtain limits on heavy neutrino admixture from the de ay νh → νe e+ e−at a nu lear rea tor for the νh mass range 29 MeV.32BARANOV 93 is a sear h for neutrino de ays into e+ e− νe using a beam dump experi-ment at the 70 GeV Serpukhov proton syn hrotron. The limits are not as good as thosea hieved earlier by BERGSMA 83 and BERNARDI 86, BERNARDI 88.33BURCHAT 90 in ludes the analyses reported in JUNG 90, ABRAMS 89C, andWENDT 87.34OBERAUER 87 bounds from sear h for ν → ν′ e e de ay mode using rea tor(anti)neutrinos.35COOPER-SARKAR 85 also give limits based on model-dependent assumptions for ντ ux. We do not list these. Note that for this bound to be nontrivial, x is not equalto 3, i.e. νx annot be the dominant mass eigenstate in ντ sin e mν3 <70 MeV(ALBRECHT 85I). Also, of ourse, x is not equal to 1 or 2, so a fourth generation wouldbe required for this bound to be nontrivial.36BERGSMA 83B also quote limits on ∣∣Ue3∣∣2 where the index 3 refers to the mass eigen-state dominantly oupled to the τ . Those limits were based on assumptions about theDs mass and Ds → τ ντ bran hing ratio whi h are no longer valid. See COOPER-SARKAR 85.Limits on Coupling of µ to νx as Fun tion of mνxLimits on Coupling of µ to νx as Fun tion of mνxLimits on Coupling of µ to νx as Fun tion of mνxLimits on Coupling of µ to νx as Fun tion of mνxPeak sear h testPeak sear h testPeak sear h testPeak sear h testLimits on B(π (or K) → µνx ).VALUE CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •37 ASTIER 02 NOMD π → µX for mX=33.9MeV<6.0 × 10−10 95 38 DAUM 00 CNTR π → µX for mX=33.9MeV39 FORMAGGIO 00 CNTR π → µX for mX=33.9MeV<0.22 90 40 ASSAMAGAN 98 SILI mνx= 0.53 MeV<0.029 90 40 ASSAMAGAN 98 SILI mνx= 0.75 MeV<0.016 90 40 ASSAMAGAN 98 SILI mνx= 1.0 MeV< 46× 10−5 41 BRYMAN 96 CNTR mνx = 3033.91 MeV∼ 1× 10−16 42 ARMBRUSTER95 KARM mνx = 33.9 MeV<4 × 10−7 95 43 BILGER 95 LEPS mνx = 33.9 MeV<7 × 10−8 95 43 BILGER 95 LEPS mνx = 33.9 MeV<2.6 × 10−8 95 43 DAUM 95B TOF mνx = 33.9 MeV<2 × 10−2 90 DAUM 87 mνx=1 MeV<1 × 10−3 90 DAUM 87 mνx=2 MeV<6 × 10−5 90 DAUM 87 3 MeV < mνx < 19.5 MeV<3 × 10−2 90 44 MINEHART 84 mνx=2 MeV<1 × 10−3 90 44 MINEHART 84 mνx=4 MeV<3 × 10−4 90 44 MINEHART 84 mνx=10 GeV<5 × 10−6 90 45 HAYANO 82 mνx=330 MeV<1 × 10−4 90 45 HAYANO 82 mνx=70 MeV<9 × 10−7 90 45 HAYANO 82 mνx=250 MeV

789789789789See key on page 601 LeptonParti le ListingsHeavyNeutral Leptons, Sear hes for<1 × 10−1 90 44 ABELA 81 mνx=4 MeV<7 × 10−5 90 44 ABELA 81 mνx=10.5 MeV<2 × 10−4 90 44 ABELA 81 mνx=11.5 MeV<2 × 10−5 90 44 ABELA 81 mνx=1630 MeV37ASTIER 02 sear h for anomalous pion de ay into a 33.9 MeV neutral parti le. Noeviden e was found and the sensitivity to the bran hing ratio B(π → µX )·B(X →

ν e+ e−) is as low as 3.7× 10−15, depending on the X lifetime.38DAUM 00 sear h for anomalous pion de ay into a 33.9 MeV neutral parti le that might beresponsible for the time-distribution anomaly observed by the KARMEN Collaboration.39 FORMAGGIO 00 sear h for anomalous pion de ay into a 33.9 MeV neutral parti le Q0that might be responsible for the time-distribution anomaly observed by the KARMENCollaboration. In the E815 (NuTeV) experiment at Fermilab no eviden e was found,with sensitivity for the pion bran hing ratio B(π → µQ0)·B(Q0 → visible) as low as10−13.40ASSAMAGAN 98 obtain a limit on heavy neutrino admixture from π+ de ay essentiallyat rest, by measuring with good resolution the momentum distribution of the muons.However, the sear h uses an ad ho shape orre tion. The authors report upper limit for∣∣Uµx ∣∣2 of 0.22 for mν = 0.53 MeV, 0.029 for mν = 0.75 MeV, and 0.016 for mν =1.0 MeV at 90%CL.41BRYMAN 96 sear h for massive un onventional neutrinos of mass mνx in π+ de ay.42ARMBRUSTER 95 study the rea tions 12C(νe ,e−) 12N and 12C(ν,ν′) 12C∗ indu ed byneutrinos from π+ and µ+ de ay at the ISIS neutron spallation sour e at the Rutherford-Appleton laboratory. An anomaly in the time distribution an be interpreted as the de ayπ+ → µ+ νx , where νx is a neutral weakly intera ting parti le with mass ≈ 33.9 MeVand spin 1/2. The lower limit to the bran hing ratio is a fun tion of the lifetime of thenew massive neutral parti le, and rea hes a minimum of a few × 10−16 for τx ∼ 5 s.43 From experiments of π+ and π− de ay in ight at PSI, to he k the laim of theKARMEN Collaboration quoted above (ARMBRUSTER 95).44π+ → µ+ νµ peak sear h experiment.45K+ → µ+ νµ peak sear h experiment.Peak sear h testPeak sear h testPeak sear h testPeak sear h testLimits on ∣∣Uµ x ∣∣2 as fun tion of mνxVALUE CL% DOCUMENT ID TECN COMMENT


< 110× 10−4 46 BRYMAN 96 CNTR mνx = 3033.91 MeV<2× 10−5 95 47 ASANO 81 mνx=70 MeV<3× 10−6 95 47 ASANO 81 mνx=210 MeV<3× 10−6 95 47 ASANO 81 mνx=230 MeV<6× 10−6 95 48 ASANO 81 mνx=240 MeV<5× 10−7 95 48 ASANO 81 mνx=280 MeV<6× 10−6 95 48 ASANO 81 mνx=300 MeV<1× 10−2 95 CALAPRICE 81 mνx=7 MeV<3× 10−3 95 49 CALAPRICE 81 mνx=33 MeV<1× 10−4 68 50 SHROCK 81 THEO mνx=13 MeV<3× 10−5 68 50 SHROCK 81 THEO mνx=33 MeV<6× 10−3 68 51 SHROCK 81 THEO mνx=80 MeV<5× 10−3 68 51 SHROCK 81 THEO mνx=120 MeV46BRYMAN 96 sear h for massive un onventional neutrinos of mass mνx in π+ de ay.They interpret the result as an upper limit for the admixture of a heavy sterile or otherwise47K+ → µ+ νµ peak sear h experiment.48Analysis of experiment on K+ → µ+ νµ νx νx de ay.49π+ → µ+ νµ peak sear h experiment.50Analysis of magneti spe trometer experiment, bubble hamber experiment, and emulsionexperiment on π+ → µ+ νµ de ay.51Analysis of magneti spe trometer experiment on K → µ, νµ de ay.Peak Sear h in Muon CapturePeak Sear h in Muon CapturePeak Sear h in Muon CapturePeak Sear h in Muon CaptureLimits on ∣∣Uµ x ∣∣2 as fun tion of mνxVALUE DOCUMENT ID COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<1× 10−1 DEUTSCH 83 mνx=45 MeV<7× 10−3 DEUTSCH 83 mνx=70 MeV<1× 10−1 DEUTSCH 83 mνx=85 MeVSear hes for De ays of Massive νSear hes for De ays of Massive νSear hes for De ays of Massive νSear hes for De ays of Massive νLimits on ∣∣Uµ x ∣∣2 as fun tion of mνxVALUE CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<5 × 10−7 90 52 VAITAITIS 99 CCFR mνx=0.28 GeV<8 × 10−8 90 52 VAITAITIS 99 CCFR mνx=0.37 GeV<5 × 10−7 90 52 VAITAITIS 99 CCFR mνx= 0.50 GeV<6 × 10−8 90 52 VAITAITIS 99 CCFR mνx= 1.50 GeV<2 × 10−5 95 53 ABREU 97I DLPH mνx=6 GeV<3 × 10−5 95 53 ABREU 97I DLPH mνx=50 GeV<3 × 10−6 90 GALLAS 95 CNTR mνx = 1 GeV<3 × 10−5 90 54 VILAIN 95C CHM2 mνx = 2 GeV<6.2× 10−8 95 ADEVA 90S L3 mνx=20 GeV<5.1× 10−10 95 ADEVA 90S L3 mνx=40 GeVall values ruled out 95 55 BURCHAT 90 MRK2 mνx < 19.6 GeV<1 × 10−10 95 55 BURCHAT 90 MRK2 mνx = 22 GeV<1 × 10−11 95 55 BURCHAT 90 MRK2 mνx = 41 GeVall values ruled out 95 DECAMP 90F ALEP mνx= 25.042.7 GeV<1 × 10−13 95 DECAMP 90F ALEP mνx= 42.745.7 GeV<5 × 10−3 90 AKERLOF 88 HRS mνx=1.8 GeV<2 × 10−5 90 AKERLOF 88 HRS mνx=4 GeV<3 × 10−6 90 AKERLOF 88 HRS mνx=6 GeV<1 × 10−7 90 BERNARDI 88 CNTR mνx=200 MeV<3 × 10−9 90 BERNARDI 88 CNTR mνx=300 MeV<4 × 10−4 90 56 MISHRA 87 CNTR mνx=1.5 GeV<4 × 10−3 90 56 MISHRA 87 CNTR mνx=2.5 GeV<0.9× 10−2 90 56 MISHRA 87 CNTR mνx=5 GeV<0.1 90 56 MISHRA 87 CNTR mνx=10 GeV<8 × 10−4 90 BADIER 86 CNTR mνx=600 MeV<1.2× 10−5 90 BADIER 86 CNTR mνx=1.7 GeV<3 × 10−8 90 BERNARDI 86 CNTR mνx=200 MeV<6 × 10−9 90 BERNARDI 86 CNTR mνx=350 MeV<1 × 10−6 90 DORENBOS... 86 CNTR mνx=500 MeV<1 × 10−7 90 DORENBOS... 86 CNTR mνx=1600 MeV<0.8× 10−5 90 57 COOPER-... 85 HLBC mνx=0.4 GeV<1.0× 10−7 90 57 COOPER-... 85 HLBC mνx=1.5 GeV52VAITAITIS 99 sear h for L0µ → µX . See paper for rather ompli ated limit as fun tionof mνx .53ABREU 97I long-lived νx analysis. Short-lived analysis extends limit to lower masseswith de reasing sensitivity ex ept at 3.5 GeV, where the limit is the same as at 6 GeV.54VILAIN 95C is a sear h for the de ays of heavy isosinglet neutrinos produ ed by neutral urrent neutrino intera tions. Limits were quoted for masses in the range from 0.3 to 24GeV. The best limit is listed above.55BURCHAT 90 in ludes the analyses reported in JUNG 90, ABRAMS 89C, andWENDT 87.56 See also limits on ∣∣U3x∣∣ from WENDT 87.57COOPER-SARKAR 85 also give limits based on model-dependent assumptions for ντ ux. We do not list these. Note that for this bound to be nontrivial, x is not equalto 3, i.e. νx annot be the dominant mass eigenstate in ντ sin e mν3 <70 MeV(ALBRECHT 85I). Also, of ourse, x is not equal to 1 or 2, so a fourth generation wouldbe required for this bound to be nontrivial.Limits on ∣∣Uτ x ∣∣2 as a Fun tion of mνxLimits on ∣∣Uτ x ∣∣2 as a Fun tion of mνxLimits on ∣∣Uτ x ∣∣2 as a Fun tion of mνxLimits on ∣∣Uτ x ∣∣2 as a Fun tion of mνxVALUE CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<1 × 10−2 90 58 ORLOFF 02 CHRM mνx=45 MeV<1.4 × 10−4 90 58 ORLOFF 02 CHRM mνx=180 MeV<0.025 90 ASTIER 01 mνx=45 MeV<0.002 90 ASTIER 01 mνx=140 MeV<2 × 10−5 95 59 ABREU 97I DLPH mνx=6 GeV<3 × 10−5 95 59 ABREU 97I DLPH mνx=50 GeV<6.2 × 10−8 95 ADEVA 90S L3 mνx=20 GeV<5.1 × 10−10 95 ADEVA 90S L3 mνx=40 GeVall values ruled out 95 60 BURCHAT 90 MRK2 mνx < 19.6 GeV<1 × 10−10 95 60 BURCHAT 90 MRK2 mνx = 22 GeV<1 × 10−11 95 60 BURCHAT 90 MRK2 mνx = 41 GeVall values ruled out 95 DECAMP 90F ALEP mνx= 25.042.7 GeV<1 × 10−13 95 DECAMP 90F ALEP mνx= 42.745.7 GeV<5 × 10−2 80 AKERLOF 88 HRS mνx=2.5 GeV<9 × 10−5 80 AKERLOF 88 HRS mνx=4.5 GeV58ORLOFF 02 use the negative result of a sear h for neutral parti les de aying into twoele trons performed by CHARM to get these limits for a mostly isosinglet heavy neutrino.59ABREU 97I long-lived νx analysis. Short-lived analysis extends limit to lower masseswith de reasing sensitivity.60BURCHAT 90 in ludes the analyses reported in JUNG 90, ABRAMS 89C, andWENDT 87.

790790790790LeptonParti le ListingsHeavy Neutral Leptons, Sear hes forLimits on ∣∣Ua x ∣∣2Limits on ∣∣Ua x ∣∣2Limits on ∣∣Ua x ∣∣2Limits on ∣∣Ua x ∣∣2Where a = e, µ from ρ parameter in µ de ay.VALUE CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<1× 10−2 68 SHROCK 81B THEO mνx=10 GeV<2× 10−3 68 SHROCK 81B THEO mνx=40 MeV<4× 10−2 68 SHROCK 81B THEO mνx=70 MeVLimits on ∣∣U1 j×U2 j ∣∣ as Fun tion of mνjLimits on ∣∣U1 j×U2 j ∣∣ as Fun tion of mνjLimits on ∣∣U1 j×U2 j ∣∣ as Fun tion of mνjLimits on ∣∣U1 j×U2 j ∣∣ as Fun tion of mνjVALUE CL% DOCUMENT ID TECN COMMENT• • • We do not use the following data for averages, ts, limits, et . • • •

<3 × 10−5 90 61 BARANOV 93 mνj= 80 MeV<3 × 10−6 90 61 BARANOV 93 mνj= 160 MeV<6 × 10−7 90 61 BARANOV 93 mνj= 240 MeV<2 × 10−7 90 61 BARANOV 93 mνj= 320 MeV<9 × 10−5 90 BERNARDI 86 CNTR mνj=25 MeV<3.6× 10−7 90 BERNARDI 86 CNTR mνj=100 MeV<3 × 10−8 90 BERNARDI 86 CNTR mνj=200 MeV<6 × 10−9 90 BERNARDI 86 CNTR mνj=350 MeV<1 × 10−2 90 BERGSMA 83B CNTR mνj=10 MeV<1 × 10−5 90 BERGSMA 83B CNTR mνj=140 MeV<7 × 10−7 90 BERGSMA 83B CNTR mνj=370 MeV61BARANOV 93 is a sear h for neutrino de ays into e+ e− νe using a beam dump exper-iment at the 70 GeV Serpukhov proton syn hrotron.REFERENCES FOR Heavy Neutral Leptons, Sear hes forREFERENCES FOR Heavy Neutral Leptons, Sear hes forREFERENCES FOR Heavy Neutral Leptons, Sear hes forREFERENCES FOR Heavy Neutral Leptons, Sear hes forBACK 03A JETPL 78 261 H.O. Ba k et al. (Borexino Collab.)Translated from ZETFP 78 707.TRINCZEK 03 PRL 90 012501 M. Trin zek et al.ASTIER 02 PL B527 23 P. Astier et al. (NOMAD Collab.)ORLOFF 02 PL B550 8 J. Orlo et al.ACHARD 01 PL B517 67 P. A hard et al. (L3 Collab.)ACHARD 01B PL B517 75 P. A hard et al. (L3 Collab.)ASTIER 01 PL B506 27 P. Astier et al. (NOMAD Collab.)GALEAZZI 01 PRL 86 1978 M. Galeazzi et al.ABBIENDI 00I EPJ C14 73 G. Abbiendi et al. (OPAL Collab.)DAUM 00 PRL 85 1815 M. Daum et al.FORMAGGIO 00 PRL 84 4043 J.A. Formaggio et al.HOLZSCHUH 00 PL B482 1 E. Holzs huh et al.ABREU 99O EPJ C8 41 P. Abreu et al. (DELPHI Collab.)ACCIARRI 99K PL B461 397 M. A iarri et al. (L3 Collab.)DRAGOUN 99 JP G25 1839 O. Dragoun et al.HOLZSCHUH 99 PL B451 247 E. Holzs huh et al.VAITAITIS 99 PRL 83 4943 A. Vaitaitis et al. (CCFR Collab.)ASSAMAGAN 98 PL B434 158 K. Assamagan et al.HINDI 98 PR C58 2512 M.M. Hindi et al.PDG 98 EPJ C3 1 C. Caso et al. (PDG Collab.)ABREU 97I ZPHY C74 57 P. Abreu et al. (DELPHI Collab.)Also ZPHY C75 580 (erratum)P. Abreu et al. (DELPHI Collab.)BRYMAN 96 PR D53 558 D.A. Bryman, T. Numao (TRIU)BUSKULIC 96S PL B384 439 D. Buskuli et al. (ALEPH Collab.)WIETFELDT 96 PRPL 273 149 F.E. Wietfeldt, E.B. Norman (LBL)

ARMBRUSTER 95 PL B348 19 B. Armbruster et al. (KARMEN Collab.)BAHRAN 95 PL B354 481 M.Y. Bahran, G.R. Kalb eis h (OKLA)BILGER 95 PL B363 41 R. Bilger et al. (TUBIN, KARLE, PSI)DAUM 95B PL B361 179 M. Daum et al. (PSI, UVA)FARGION 95 PR D52 1828 D. Fargion et al. (ROMA, KIAM, MPEI)GALLAS 95 PR D52 6 E. Gallas et al. (MSU, FNAL, MIT, FLOR)GARCIA 95 PR D51 1458 E. Gar ia et al. (ZARA, SCUC, PNL)HAGNER 95 PR D52 1343 C. Hagner et al. (MUNT, LAPP, CPPM)HIDDEMANN 95 JP G21 639 K.H. Hiddemann, H. Daniel, O. S hwentker (MUNT)VILAIN 95C PL B351 387 P. Vilain et al. (CHARM II Collab.)Also PL B343 453 P. Vilain et al. (CHARM II Collab.)BECK 94 PL B336 141 M. Be k et al. (MPIH, KIAE, SASSO)KONOPLICH 94 PAN 57 425 R.V. Konopli h, M.Y. Khlopov (MPEI)PDG 94 PR D50 1173 L. Montanet et al. (CERN, LBL, BOST+)BAHRAN 93 PR D47 R754 M. Bahran, G.R. Kalb eis h (OKLA)BAHRAN 93B PR D47 R759 M. Bahran, G.R. Kalb eis h (OKLA)BARANOV 93 PL B302 336 S.A. Baranov et al. (JINR, SERP, BUDA)KALBFLEISCH 93 PL B303 355 G.R. Kalb eis h, M.Y. Bahran (OKLA)MORTARA 93 PRL 70 394 J.L. Mortara et al. (ANL, LBL, UCB)OHSHIMA 93 PR D47 4840 T. Ohshima et al. (KEK, TUAT, RIKEN+)ABREU 92B PL B274 230 P. Abreu et al. (DELPHI Collab.)BAHRAN 92 PL B291 336 M.Y. Bahran, G.R. Kalb eis h (OKLA)BRITTON 92 PRL 68 3000 D.I. Britton et al. (TRIU, CARL)Also PR D49 28 D.I. Britton et al. (TRIU, CARL)BRITTON 92B PR D46 R885 D.I. Britton et al. (TRIU, CARL)KAWAKAMI 92 PL B287 45 H. Kawakami et al. (INUS, KEK, SCUC+)MORI 92B PL B289 463 M. Mori et al. (KAM2 Collab.)ALEXANDER 91F ZPHY C52 175 G. Alexander et al. (OPAL Collab.)DELEENER-... 91 PR D43 3611 N. de Leener-Rosier et al. (LOUV, ZURI+)REUSSER 91 PL B255 143 D. Reusser et al. (NEUC, CIT, PSI)SATO 91 PR D44 2220 N. Sato et al. (Kamiokande Collab.)ADEVA 90S PL B251 321 B. Adeva et al. (L3 Collab.)BURCHAT 90 PR D41 3542 P.R. Bur hat et al. (Mark II Collab.)DECAMP 90F PL B236 511 D. De amp et al. (ALEPH Collab.)DEUTSCH 90 NP A518 149 J. Deuts h, M. Lebrun, R. PrieelsJUNG 90 PRL 64 1091 C. Jung et al. (Mark II Collab.)ABRAMS 89C PRL 63 2447 G.S. Abrams et al. (Mark II Collab.)ENQVIST 89 NP B317 647 K. Enqvist, K. Kainulainen, J. Maalampi (HELS)FISHER 89 PL B218 257 P.H. Fisher et al. (CIT, NEUC, PSI)AKERLOF 88 PR D37 577 C.W. Akerlof et al. (HRS Collab.)BERNARDI 88 PL B203 332 G. Bernardi et al. (PARIN, CERN, INFN+)CALDWELL 88 PRL 61 510 D.O. Caldwell et al. (UCSB, UCB, LBL)OLIVE 88 PL B205 553 K.A. Olive, M. Sredni ki (MINN, UCSB)SREDNICKI 88 NP B310 693 M. Sredni ki, R. Watkins, K.A. Olive (MINN, UCSB)AHLEN 87 PL B195 603 S.P. Ahlen et al. (BOST, SCUC, HARV+)DAUM 87 PR D36 2624 M. Daum et al. (SIN, UVA)GRIEST 87 NP B283 681 K. Griest, D. Se kel (UCSC, CERN)Also NP B296 1034 (erratum) K. Griest, D. Se kel (UCSC, CERN)MISHRA 87 PRL 59 1397 S.R. Mishra et al. (COLU, CIT, FNAL+)OBERAUER 87 PL B198 113 L.F. Oberauer, F. von Feilitzs h, R.L. MossbauerWENDT 87 PRL 58 1810 C. Wendt et al. (Mark II Collab.)AZUELOS 86 PRL 56 2241 G. Azuelos et al. (TRIU, CNRC)BADIER 86 ZPHY C31 21 J. Badier et al. (NA3 Collab.)BERNARDI 86 PL 166B 479 G. Bernardi et al. (CURIN, INFN, CDEF+)DORENBOS... 86 PL 166B 473 J. Dorenbos h et al. (CHARM Collab.)ALBRECHT 85I PL 163B 404 H. Albre ht et al. (ARGUS Collab.)APALIKOV 85 JETPL 42 289 A.M. Apalikov et al. (ITEP)Translated from ZETFP 42 233.COOPER-... 85 PL 160B 207 A.M. Cooper-Sarkar et al. (CERN, LOIC+)MARKEY 85 PR C32 2215 J. Markey, F. Boehm (CIT)OHI 85 PL 160B 322 T. Ohi et al. (TOKY, INUS, KEK)MINEHART 84 PRL 52 804 R.C. Minehart et al. (UVA, SIN)BERGSMA 83 PL 122B 465 F. Bergsma et al. (CHARM Collab.)BERGSMA 83B PL 128B 361 F. Bergsma et al. (CHARM Collab.)BRYMAN 83B PRL 50 1546 D.A. Bryman et al. (TRIU, CNRC)DEUTSCH 83 PR D27 1644 J.P. Deuts h, M. Lebrun, R. Prieels (LOUV)GRONAU 83 PR D28 2762 M. Gronau (HAIF)SCHRECK... 83 PL 129B 265 K. S hre kenba h et al. (ISNG, ILLG)HAYANO 82 PRL 49 1305 R.S. Hayano et al. (TOKY, KEK, TSUK)ABELA 81 PL 105B 263 R. Abela et al. (SIN)ASANO 81 PL 104B 84 Y. Asano et al. (KEK, TOKY, INUS, OSAK)CALAPRICE 81 PL 106B 175 F.P. Calapri e et al. (PRIN, IND)SHROCK 81 PR D24 1232 R.E. Shro k (STON)SHROCK 81B PR D24 1275 R.E. Shro k (STON)SHROCK 80 PL 96B 159 R.E. Shro k (STON)

LEPTONS - Institute of Physics · 7 × 10 23 68 REUSSER 91 CNTR Ge K-shell disapprance ea > 2 × 10...

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