Antonio Pich IFIC, Valencia Lepton Universality. Lorentz...

Antonio Pich

IFIC, Valencia

International Workshop on Tau-Charm Physics – Charm 2006, Beijing, June 5-7 2006

Lepton Universality. Lorentz Structure

Hadronic Decays: QCD Tests, αs , ms, Vus

New Physics: ν , L , CP

Tau Physics A. Pich - Charm 2006

( )( )

HadronsC

eNR

eτ

ττ

τ ν

τ ν ν

−

− −

Γ → +≡ =

Γ →

C Ccos sind d sθ θ θ= +

1 1Br ( ) 20%2 5C

l lB lNττ ν ν− −≡ → ≈ = =

+

1; 3.642 0.013e

e

B BR

Bμ

τ− −

= = ±

(17.81 0.06) %eB = ±

(17.33 0.06)%Bμ = ±

W

τντ −

, ,e dθμ− −

, ,e uμν νUniversal W Couplings


W

τντ −

,e μ− −

,e μν ν

150.972564 0.000010 (1632.1 1.4) 10 seB

B μ ττ−= =

± ± ×

2 52 2

3( ) ( / )192

FEWll

G ml f m m rττττ ν ν

πΓ → =

3 4 2( ) 1 8 8 12 logf x x x x x x= − + − −

222

2 2( ) 25 31 1 2 0.99602 4 5EW

l

W W

mm mrM M

τ τα ππ

⎡ ⎤⎡ ⎤⎛ ⎞= + − + − =⎜ ⎟ ⎢ ⎥⎢ ⎥⎝ ⎠⎣ ⎦ ⎣ ⎦(Marciano-Sirlin)


150.972564 0.000010 (1632.1 1.4) 10 seB

B μ ττ−= =

± ± ×

( )exp/ 0.9730 0.0047eB Bμ = ±

0.29 MeV0.261776.9mτ+−=


LEPTON UNIVERSALITYLEPTON UNIVERSALITY

e

gg

μ

ggμ

τ


K K

W W

eB

B B

τ μ τ

τ π π μ

τ μ

τ μ

τ τ→

→ →

→ →

→ →

Γ Γ

Γ Γ

1.0004 0.0023

0.9999 0.0036

0.979 0.017

1.039 0.012

±

±

±

±

/g gτ μ

W W

e

e

e

B B

B B

B B

τ μ τ

π μ π

μ

→ →

→ →

→ →

0.9999 0.0020

1.0017 0.0015

0.997 0.011

±

±

±

/ eg gμ

W W e

B

B Bτ μ μ τ

τ

τ τ→

→ →

1.0002 0.0022

1.036 0.013

±

±

/ eg gτ


AssumingAssuming UniversalityUniversality::

/2 2

2 2/

( ) 0.2611

7 0.005( )

K

K K

us

ud

m m Km m

VR

fV f

Rτ

ττ

τ π

π

τ π

τ

τ ντ π δν

δ− −

− −

⎛ ⎞− Γ →= = ±⎜

+⎟⎜ ⎟− Γ →⎝ ⎠

⎟ +⎛ ⎞⎜⎝ ⎠

2 2 3

2 2 3 0.2( )( )

7618 0.0001

41

8K K

K K

us

ud

RR

V fV

m m Km m mfm μ

μ

π

π

π

μπ

μ ν μπ

δδν μ

− −

− −

Γ⎛ ⎞−= = ±⎜ ⎟⎜ ⎟−⎝

⎛ ⎞⎜ ⎟ Γ →

+

⎠

→+⎝ ⎠


l − lν

l −′

lν ′

, ,4 ( ) ( )

2n

nln

ln

l l l lGH g ε σ ωλε ω

εω ν ν′′ ⎡ ⎤′⎡ ⎤= Γ Γ⎣ ⎦ ⎣ ⎦∑

1I ; ; ; , , , ,2

S V T L Rμ μνγ σ ε ω σ λΓ = Γ = Γ = =

Normalization:

( ) ( ) ( )2 2 2 2 2 2 2 2 2 21 34

1

S S S S T T V V V VRR RL LR LL RL LR RR RL LR LL

LL LR RL RR

g g g g g g g g g g

Q Q Q Q

+ + + + + +Γ +∝ + +

≡ ≡ + + +

Standard Model: all ; 1 ; other 0 V nF LLl lG G g gεω′ = = =


,

0.026 0.037

0.017 0.02

(90% CL)

(90

0.047

0.055 % CL)

(90% CL0.03

7

0.002 0.020)5

R

R

Re

e

Q

Q

Qτ μ

τ μ

τ

→

→

→

= − ±

±

= ±

<

=<

<

0.960 (90% CL)VLL e

gμ→

>

( )e eμ μν ν− −→

( 2 , 1 , 1/ 3)S V TN N Nnng Nεω = = =

(90% CL) , eeμ τ→ • →•


probes thehadronic V−A current

Hττ ν− −→

5(1 ) 0H d uμθ γ γ− −

W

τντ −

dθ

u

Hadrons

W

τντ −

dθ

u

Hadrons

e+

γe−

Hadronse+

γe−

Hadrons

e+e−→ H0 probes the hadronic electromagnetic current

0 0q

qH Q q qμγ∑

0

2 1 2EW2 0

1 23cos (1 )( ) ( )(

(1 2 )) 2

C Ie e V

eS dx xV xmx x

eτ

ττ

τ ν στ ν

θπαν + −

− −=

− − →

Γ →Γ

−→

= +∫Isospin :

Only lepton massive enoughto decay into hadrons


0ττ ν π π− −→

( ) ( )0020 2 ( ;0 ) s p pd pF s pu

π ππ πμ

πμ

π π γ −−− ≡ +≡ −

CLEO105 selected events


ee++ee−−→→ππ++ππ−− versus versus ττ−−→→ ννττππ−−ππ00 (CVC)(CVC)

Davier, Höcker, Zhang


Jamin-Pich-Portolés

hep-ph/0605096

ττ−− →→ ννττKK00ππ−− , ν, νττKK−− ππ00


Ιmσ⎧ ⎫⎪ ⎪∼ ⎨ ⎬⎪ ⎪⎩ ⎭e+

γe−

e+

e−

γq

q

( )4 2 2em em em em( ) 0 [ ( ) (0)] 0 ( )iqxq i d x T J x J g q q q qeμν μ ν μν μ νΠ ≡ = − + Π∫

em( had) 12 Im ( )

( )e e s

e eσ π

σ μ μ

+ −

+ − + −

→= Π

→


Ιmσ⎧ ⎫⎪ ⎪∼ ⎨ ⎬⎪ ⎪⎩ ⎭e+

γe−

e+

e−

γq

q


em( had) 12 Im ( )

( )e e s

e eσ π

σ μ μ

+ −

+ − + −

→= Π

→

τν

Wτ −

τν

τ −

Wd,s

u

had Ιmττ ν→ +

⎧ ⎫⎪ ⎪Γ ∼ ⎨ ⎬⎪ ⎪⎩ ⎭


Ιmσ⎧ ⎫⎪ ⎪∼ ⎨ ⎬⎪ ⎪⎩ ⎭e+

γe−

e+

e−

γq

q


2(1) (0)

2

2 20

( + had) Im ( ) Im (12 1 1 2 )( )

m

e

s sdxm

R sm

se

τ

ττ

τ

τ

τπτ ν

τ ν ν

−

− −

⎡ ⎤⎛ ⎞ ⎛ ⎞= − + +⎢ ⎥⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎣ ⎦

Γ →≡ Π Π

Γ → ∫

( )4 2 (1) 2 (0) 2†, , ,( ) 0 [ ( ) (0) ] 0 ( ) ( )ij J ij ij ij J ij J

iqxq i d x T J x J g q q q q q q qeμν μ ν μν μ ν μ νΠ ≡ = − + Π + Π∫

2 2( ) ( ) ( ) ( ) ( ), ,, ,( ) ( ) ( ) ( ) ( )J J J J J

us us V us Aud ud V ud As V s s V s s⎡ ⎤ ⎡ ⎤Π ≡ Π + Π + Π + Π⎣ ⎦⎣ ⎦

em( had) 12 Im ( )

( )e e s

e eσ π

σ μ μ

+ −

+ − + −

→= Π

→

τν

Wτ −

τν

τ −

Wd,s

u

had Ιmττ ν→ +

⎧ ⎫⎪ ⎪Γ ∼ ⎨ ⎬⎪ ⎪⎩ ⎭


1 2 (1) 2 (0) 2

012 (1 ) (1( + had) Im ( ) Im (

)2 )

()

edx xR x mx m x

eτ

τ τ ττ

τ ντ ν ν

π−

− −

Γ →≡ Π⎡ ⎤= − + +⎣ Π ⎦Γ → ∫

(0 1) 2 (0) 22

| | 16 (1 ) ( ( ) ( )1 2 ) 2

xR xmi dx xmx x xτ τ τπ +

=⎡ ⎤= − + −⎣ ⎦Π Π∫

Braaten-Narison-Pich

( )( )

/ 22

( , ) ( )( )

( )

JJ D D

DD n

C s Os

sμ μ

=Π =

−∑ OPE

( )EW EW P NP , , ,1C V A SR N S R R Rττ τ τδ δδ = + ++ +′= +

EW W PE N1.0194 ; 0.00 0.004 0.00210 ;S δ δ′= = = − ±

2 3P 5.20 26 ... (20 ; /% )sa a a a mτ τ τ τ τδ α π= + + + ≡≈

(fitted from data)

Im(s)

Re(s)

2mτ


Similar predictions for and the moments, , ,, ,V A SR R Rτ τ τ

0

0 200

( ) 1lk

skl s s dRR s dss m ds

ττ

τ

⎛ ⎞⎛ ⎞≡ − ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠∫

Different sensitivity to power corrections through k , l

The non-perturbative contribution to Rτ can be obtainedfrom the invariant-mass distribution of the final hadrons:

NP 0.004 0.002δ = − ± ALEPH, CLEO, OPAL


(ALEPH 2005), , ,1.787 0.013 ; 1.695 0.013 ; 3.482 0.014V A V AR R Rτ τ τ += ± = ± = ±

2( ) 0.345 0.010s mτα = ±

2( ) 0.1215 0.0012Zs Mα = ±

2width( ) 0.1186 0.0027Z Zs Mα = ±

The most precise test ofAsymptotic Freedom

2 2( ) ( )

0.0029 0.0010 0.0027

ZZ Z

Z

s sM Mτ

τ

α α− =

± ±


SPECTRAL FUNCTIONSSPECTRAL FUNCTIONS(0 1)

1 ,v ( ) 2 Im ( )ud Vs sπ += Π (0 1)1 ,a ( ) 2 Im ( )ud As sπ += Π

Important information:

v1(s) CVC , aτhad , α-1(MZ) = 128.95 ± 0.05 , …


Non-Perturbative

Perturbativeat s = mτ

2

Rτ

Chiral Sum Rules:

02 2

2

,

/ , '/A

f m m

F rπ ππ

π ε ε

± −


(k,l) ALEPH OPAL

(0,0) 0.39 ± 0.14 0.26 ± 0.12

(1,0) 0.38 ± 0.08 0.28 ± 0.09

(2,0) 0.37 ± 0.05 0.30 ± 0.07

(3,0) 0.40 ± 0.04 0.33 ± 0.05

(4,0) 0.40 ± 0.04 0.34 ± 0.04

StrangeStrange SpectralSpectral FunctionFunction: SU(3) : SU(3) BreakingBreaking

2 2

2 2 2, , ( )24 ( )

kl klkl

kls

usud

V A Ss

R R m mRmVV

τ

τ

τ ττδ α+≡ − ≈ Δ

2 GeV

( ) 84 23 MeV

( ) 81 22 MeVs

s

m m

mτ = ±

= ±Gámiz-Jamin-Pich-Prades-Schwab


Gámiz-Jamin-Pich-Prades-Schwab

Strong sensitivity to Vus

2 GeV( ) 81 22 MeVsm = ±(k≠0,l=0)

Taking as input (from non τ sources) :2 GeV( ) 95 20 MeVsm = ±

(k=0,l=0)

exp th0.2208 0.0033 0.0009usV = ± ± ( )3

0.2233 0.0028lKusV = ±

Simultaneous ms & Vus fit possible with better dataThe τ could give the most precise Vus determination

τ OPAL dataτ ALEPH data

S / P SR Jamin 06


TheThe ννττ

Mainz’05:

DONUT: First Direct ντ Observation !

2.3 eVemν <

(95% CL)

0.19 MeVmμν <

(90% CL)


Neutrino Neutrino OscillationsOscillations

CPRν ?,

NEW PHYSICSNEW PHYSICS

Lepton Mixinge μν ν↔

μ τν ν↔

M. Maltoni


mν ≠ 0 NEW PHYSICS

Standard Model + Direct (singlet) νiR : Sterile νiR

New Interactions ?

Small Majorana Mass: mν > 0.05 eV Λ / cij < 1015 GeV

4d

SM ddd

cL L O−= +Λ∑Low-Energy Effective Field Theory:

21h.c. h.c. ;2

vL Lij ij

it c c

i j i jj ijLc

M MLc

φ φ ν ν− ⎯⎯⎯→ ≡Λ

+Λ

− +SSB

2 *)( iφ τ φ≡1 SU(2)L ⊗ U(1)Y Invariant Operator with d=5

CPLepton Number Violation. Lepton Mixing.


LEPTON MIXINGLEPTON MIXING

{ }†CC h.c.

2 L L L Li j i j

ji i

ij j

g W l u V dμμ

μν γ γ= + +∑ UL

Lepton Flavour Violation

Mixing Structure U ≠ V : (M.C. González-García)

1 1(1 ) (1 )2 2

1 1 1(1 ) (1 0.2 0) ; ;2 2 2

1 1 1(1 ) (1 )2 2 2

.2i j

λ λ ε

λ ε λ ε

λ ε λ ε

λ ε

⎡ ⎤+ −⎢ ⎥⎢ ⎥⎢ ⎥∼ − − + + −⎢ ⎥⎢ ⎥⎢ ⎥− − − + +⎢ ⎥⎣ ⎦

∼ <U

Open Questions: ν Masses (Dirac, Majorana). Leptonic

Leptogenesis (Baryon Asymmetry)

CP


LEPTON FLAVOUR VIOLATIONLEPTON FLAVOUR VIOLATION90% CL Upper Limits on Br(l − → X −) [BABAR / BELLE]

Decay U.L. Decay U.L. Decay U.L.

μ−→ e−γ 1.2 ⋅ 10−11 μ−→ e−e+e− 1.0 ⋅ 10−12 μ−→ e−γγ 7.2 ⋅ 10−11

τ−→ e−γ 1.1 ⋅ 10−7 τ−→ e−e+e− 2.0 ⋅ 10−7 τ−→ e−e+μ− 1.9 ⋅ 10−7

τ−→ μ−γ 6.8 ⋅ 10−8 τ−→ e−μ+μ− 2.0 ⋅ 10−7 τ−→ μ−e+μ− 1.3 ⋅ 10−7

τ−→ e−e−μ+ 1.1 ⋅ 10−7 τ−→ μ−μ+μ− 1.9 ⋅ 10−7 τ−→ e−π0 1.9 ⋅ 10−7

τ−→ μ−π0 4.1 ⋅ 10−7 τ−→ e−η’ 10 ⋅ 10−7 τ−→ μ−η’ 4.7 ⋅ 10−7

τ−→ e−η 2.3 ⋅ 10−7 τ−→ μ−η 1.5 ⋅ 10−7 τ−→ e−Κ* 3.0 ⋅ 10−7

τ−→ e−ΚS 5.6 ⋅ 10−8 τ−→ μ−ΚS 4.9 ⋅ 10−8 τ−→ μ−ρ0 2.0 ⋅ 10−7

τ−→e−K+K− 1.4 · 10−7 τ−→e−K+π− 1.6 · 10−7 τ−→e−π+K− 3.2 · 10−7

τ−→μ−K+K− 2.5 · 10−7 τ−→μ−K+π− 3.2 · 10−7 τ−→μ−π+K− 2.6 · 10−7

τ−→e−π+π− 1.2 · 10−7 τ−→μ−π+π− 2.9 · 10−7 τ−→Λπ− 0.7 ⋅ 10−7

τ−→e+K−K− 1.5 · 10−7 τ−→e+K−π− 1.8 · 10−7 τ−→e+π−π− 2.0 · 10−7

τ−→μ+K−K− 4.4 · 10−7 τ−→μ+K−π− 2.2 · 10−7 τ−→μ+π−π− 0.7 · 10−7


LEPTON FLAVOUR VIOLATIONLEPTON FLAVOUR VIOLATION

eff S 2Mi

ii

iL L l l f fC ′ ′⎡ ⎤⎡ ⎤= + Γ Γ⎣ ⎦Λ ⎣ ⎦∑

Present Experimental Limits :

μ : Br ∼ 10−12 Λ / Ci½ ∼ 175 TeV

τ : Br ∼ 10−7 Λ / Ci½ ∼ 5 TeV

J/ψ : Br (J/ψ → μ e) < 1.1 ⋅ 10−6 ; Br (J/ψ → μ τ) < 2.0 ⋅ 10−6

Br (J/ψ → τ e) < 8.3 ⋅ 10−6 BES (90% CL)

Z : Br (Z → μ e) < 1.7 ⋅ 10−6 ; Br (Z → μ τ) < 1.2 ⋅ 10−5

Br (Z → τ e) < 9.8 ⋅ 10−6 LEP (95% CL)


AnomalousAnomalous MagneticMagnetic MomentMoment

2l ll

g em

μ ≡

1 ( 2)2l la g≡ −

1 2 2 3(QED) ( / ) ( / ) ( / , / )e e e e ea A A m m A m m A m m m mμ τ μ τ= + + +

(2) (4) (6) (8)2 3 4

i i i i iA A A A Aα α α απ π π π

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + + + + ⋅⋅ ⋅⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (8)

1 1.7283 (35)A = −

(6)2

6( / ) 7.373 941 58 (28) 10eA m mμ−= − ×

(Kinoshita–Nio)

11(115 965 218.59 0.38) 10ea −= ± × 1 137.035 998 83 0.000 000 51α− = ±

Atom Interferometry + Cesium D1 Line: 1 137.036 000 3 0.000 001 0α− = ±

1 137.035 999 13 0.000 000 45α−< > = ±World Average:


AnomalousAnomalous MagneticMagnetic MomentMoment

2l ll

g em

μ ≡

1 ( 2)2l la g≡ −

1010 x aμth = 11 658 470.4 ± 1.5 QED Kinoshita-Nio

+ 15.4 ± 0.2 EW Czarnecki-Marciano-Vainshtein+ 703.1 ± 8.8 hvp (711.0 ± 5.8)τ , (693.4 ± 6.4)e+e− Davier et al− 9.8 ± 0.1 hvp NLO Krause, Hagiwara et al+ 12.0 ± 3.5 light-by-light Melnikov-Vainshtein, Knech et al

= 11 659 191.1 ± 9.6 (11 659 199.0 ± 6.9)τ , (11 659 181.4 ± 7.5)e+e−

aμexp - aμ

th = 1.5 σ 1.0 σ 2.8 σ

10exp (BNL-E821)(11 659 208.0 6.0) 10aμ−= ± ×


σ ∼

HadronicHadronic VacuumVacuum PolarizationPolarization ContributionContribution toto aaμμ

Davier et al

hadττ ν→ +Γ ∼

F. Jegerlehner

aμ

Contributing E regionsand associated errors(grey) scaled up by 10αQED(MZ)


SUMMARYSUMMARY

The τ is an ideal laboratory to test the Standard Model

Lepton Universality tested to rather good accuracy

V-A Structure verified in μ→e , but not yet in τ→e,μGood limits on τR→e,μ

Wonderful QCD laboratory to study the hadronic V, A currents

- Exclusive: χPT , Resonance structure, …- Inclusive: αs , ms , Vus , <αs G2>, …

Information needed in s,c,b decays (CKM, CP, …)

Open questions in g-2

First hints of New Physics: Non-zero ν masses and mixings

There is an exciting future ahead


Davier, Höcker, Zhang

Antonio Pich IFIC, Valencia Lepton Universality. Lorentz...

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