Antonio Pich IFIC, CSIC – Univ....

Antonio Pich

IFIC, CSIC – Univ. Valencia

[email protected]

Topical Seminar on Frontier of Particle Physics 2005: Heavy Flavor Physics

Beijing, August 13-17 2005

Tau Physics A. Pich - Beijing 2005

BosonsQuarks Leptons

muon

top beauty

photon

gluon

up down electron neutrino e

charm strange neutrino µ

Higgstau neutrino τ

e

µ

τ

ZZ00 WW ±±


Charged-Current Universality

Lorentz Structure

Neutral-Current Couplings

Neutrinos

Lepton-Flavour Violation

Dipole Moments

Hadronic Decays

QCD Tests: αs , ms , <αs G2> , …

Vus

τ


Do not have Strong InteractionsSpin ½Seen as Free ParticlesPointlike 17( few 10 cm)r −< ×

, ,L L L

e

eµ τν ν ν

µ τ− − −

⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠FamilyFamily StructureStructure::

24 6 13

0.5 MeV 106 MeV 1777 MeV

6 10 y 2 10 s 3 10 s

3 eV 0.2 MeV 18 MeVe

e

e

m m m

m m mµ τ

µ τ

µ τ

ν ν ν

τ τ τ− −

= = =

> ⋅ = ⋅ = ⋅

< < <

Why 3 ?WhyWhy 33 ??

The Standard Model A. Pich - CERN Summer Lectures 2005

TheThe heavierheavier leptonsleptons andand are are unstableunstableµ τ

W

µ −µν

e −

eν

W

τντ −

, ,e dθµ− −

, ,e uµν ν

5†

C 5C (1 ) (1 ) h.c.2 2 l

g u d lWµµ

θµγ γ ν γ γ⎡ ⎤− + − +⎣ ⎦=L


W

τντ −

, ,e dθµ− −

, ,e uµν νUniversal W Couplings

C Ccos sind d sθ θ θ= +

( )( )

HadronsC

eNR

eτ

ττ

τ ν

τ ν ν

−

− −

Γ → +≡ =

Γ →

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 µ− −

,e µν ν

2 2

2 2 2´( ´ ) 4 2W WF

W Wll

g gT l l GM q M

ν ν→ ∼ =−

2 2Wq M<<

2 5´( ´ )l l F ll l G mν νΓ → ∼

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−= =

± ± ×


150.972564 0.000010 (1632.1 1.4) 10 seB

B µ ττ−= =

± ± ×

0.29 MeV0.261776.9mτ+−=

( )exp/ 0.9730 0.0047eB Bµ = ±


LEPTON UNIVERSALITYLEPTON UNIVERSALITY

e

gg

µ

ggµ

τ


5

5

( ) 0 2

( ) 0 2 K

p d u i p

K p s u i f p

fµ µ

µ µ

ππ γ γ

γ γ

−

−

≡ −

≡ −

( )2

3 2 2

2 2 /

2

2( ) 1 /( ) 2 1 /

1m mg mg

Rm m m m

τ τ π τ

µ π µ µ πτ π

τ

µ

τ ν ππ ν µ

δ− −

− −

⎛ ⎞Γ → −= ⎜ ⎟⎜ ⎟Γ → −

+⎝ ⎠

( )2

3 2 2

2 2 2

2

/( ) 1 /( ) 2 1 /

1K

KK

K

K m m mK m m m

Rm

gg

τ τ τ

µ µ µ

τ

µτ

τ νν

δµ

− −

− −

⎛ ⎞Γ → −= ⎜ ⎟⎜ ⎟Γ → −⎝ ⎠

+

/ /(0.16 0.14)% ; (0.90 0.22)%KR Rτ π τδ δ= ± = ± Marciano-Sirlin, Decker-Finkemeier


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

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

B

B Bτ µ µ τ

τ

τ τ→

→ →

1.0002 0.0022

1.036 0.013

±

±

/ eg gτ


AssumingAssuming UniversalityUniversality::

2 22 22

2 2/

2

/

( ) (7.12 0.27)1

10( 1) K

K

K

us

ud

V fV

m m Km

Rmf R

τ π

τ

τ

τπ

τ π

τ

τ ντ ν π

δδ

− −−

− −

⎛ ⎞− Γ →= = ± ×⎜ ⎟⎜ ⎟−

⎛ ⎞⎜ ⎟⎝ ⎠ →⎠

+

Γ⎝ +

2 22 22

2 3

2 3

2 (7.602 0.0( )(

311

0)

5) 1KK

K K

us

ud

V RR

KfV f

m m mm m m

µ

µ

π µ

µ π

π

π

νπ

δδ

µν µ

−

− −−

−Γ⎛ ⎞−= = ± ×⎜ ⎟⎜ ⎟−⎝

⎛ ⎞⎜ ⎟⎝ ⎠

+→ +→

Γ⎠

Marciano


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′ = = =


MichelMichel ParametersParameters4

2 2 2 203

2

02 ( ) cos

2c s)

o 3(l l

l l ll Fd G

d x dx A xm x x x xω θ

πξ

θ′→

′⎧ ⎫= − − −

Γ⎨ ⎬⎩ ⎭

P

max 2 20( ) / 2 ; / ; /l l l l l lE m m m x E x mω ω ω′ ′ ′ ′≡ = + ≡ ≡

( )2 2 20 0 0

2 2(1 ) (4 3 ) (1 ) ;( ) 1 4 4 19 3

( )x x x x x x x x x xF x A xρ η δ= − + − − + − = − + − + −

lν

l −′

lν ′

l−

2 52 2

3 ( / )192 E

l ll l W

ll l

m f m rG mπ

′′→ ′=Γ

2 32 2

2 2

2 2 ( ) 1 9 9 6 (1 ) log( / )1 4 ;( / )

l l l ll l l

l l lg z z z z z z z

m g m mm f m m

G G η′ ′′ ′

′

= + − − + +⎧ ⎫

+⎨ ⎬⎩

≡⎭

Standard Model: 3 ; 0 ; 14

ρ δ η η α β ξ ξ ξ′′ ′ ′ ′ ′′= = = = = = = = =


MichelMichel ParametersParameters4

2 2 2 203

2

02 ( ) cos

2c s)

o 3(l l

l l ll Fd G

d x dx A xm x x x xω θ

πξ

θ′→

′⎧ ⎫= − − −

Γ⎨ ⎬⎩ ⎭

P

max 2 20( ) / 2 ; / ; /l l l l l lE m m m x E x mω ω ω′ ′ ′ ′≡ = + ≡ ≡

( )2 2 20 0 0

2 2(1 ) (4 3 ) (1 ) ;( ) 1 4 4 19 3

( )x x x x x x x x x xF x A xρ η δ= − + − − + − = − + − + −

lν

l −′

lν ′

l−

2 2

2 2

2 2 2

2 2 2

1414

1 3

1 16 1 1634 3 3 91 16 1 1634 3 3 91 16 1 1654 3 3 91 16 1 1654

4

31 34 3 9

S VLL LL LL

S VRR RR RR

S V TLR LR LR LR

S V TRL RL RL RL

Q g g

Q g g

Q g g g

Q g g g

ρ ξ ξδ ξ ξ

ρ ξ ξδ ξ ξ

ρ ξ ξδ ξ ξ

ρ ξ ξδ

⎛ ⎞′ ′′= − + − + + +⎜ ⎟⎝ ⎠⎛ ⎞′ ′′= − + + − − +⎜ ⎟⎝ ⎠⎛ ⎞′ ′′= − + − + −⎜ ⎟⎝ ⎠

= +

= +

= + +

= − − ++ + = − ξ ξ⎛ ⎞′ ′′−⎜ ⎟⎝ ⎠

1 16 11 ; (1 )2 3 9 2R RRR LR RR RLl lQ Q Q Q Q Qξ ξδ ξ′

⎡ ⎤ ′≡ + = + − ≡ + = −⎢ ⎥⎣ ⎦


,

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→ • →•


ν

ν

e+

e−Z

e+

µ −

µ +

γ Ze−,

Flavour Conserving

.

Same interaction for both lepton helicities

NC Universality:

Different coupling to and

Left-handed neutrinos only

3 Families with light (nearly massless) neutrinos

;e Z eµ γ µ ±→ → ∓

( ; 0)eQ Q Q Qµ τ ν= = =

Z Rl LlZee Z Z Zg g g gµµ ττ νν= = ≠

lg Qγ ∼

γ


, Z f fe e γ+ − → →

e+

, Zγe− f

f

f

f

e− +eθ

2

2 2f f(1 cos ) cos - (1 cos ) cos

8Ad

d sN B Ch Dσ α θ θ θ θ⎡ ⎤= + + + +⎣ ⎦Ω

2

f( )1 ; 1 ; 1C

Zql

s MN N N hαπ

⎧ ⎫= = + + = ±⎨ ⎬

⎩ ⎭

2

2

2 2 2 2

2 2

2 2

2

2

f f f

f f f

f f f

f f f

1 2 Re( ) +

4 Re( ) +

v ν (v ) (v )

v v

v (v ) v

v v

8

2 Re( ) + 2

4 Re( ) + (v )4

e e e

e e e

e e e

e e e

A a a

B a a a a

C a a a

D a a a

χ χ

χ χ

χ χ

χ χ

+ +

+

+

= +

=

=

=

2

2 /2 2F Z

Z Z Z

G M ss M i s M

χπα

=− + Γ


, Z f fe e γ+ − → →

e+

, Zγe− f

f

f

f

e− +eθ

2

2 2f f(1 cos ) cos - (1 cos ) cos

8Ad

d sN B Ch Dσ α θ θ θ θ⎡ ⎤= + + + +⎣ ⎦Ω

f f

f f

( ) ( ) 2

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

F B

F B1 1

( 1) ( 1)

1 1 1 1F F B B

1 1 1 1F F B B

f

( )

( )

( )

38

4;3

38

h h

h h

BsA

Cs A

N NN N

s

N N N NN N

sN A

N

N

A

D

σ σ π ασσ σ

=+ =−

=+ =−

+ − + −

+ − + −

−+

−+

− − +−

+

≡ =

≡ =

+ +

− =

≡ =

A

A

A

FB

Pol

PolFB


2Z(s = M )Z Peak

f22 f; ( f f12 )ZZ

eM

Zπσ Γ ΓΓ ≡ Γ →

Γ=

f f3 34

( ) ( ) ( ); ;4e es s s= = =A A AP P P PPol

FB Pol FB

L R

L Rf;( ) ( ) 3

4es sσ σσ σ

−−

≡ =+

−=AA P PLRLR FB

f ff f 2 2

f f

2 vv

( ) aAsa

−≡ − ==

+A PPolFinal Final PolarizationPolarization OnlyOnly AvailableAvailable forfor f = τ

lP21v 1 4sin 1

2l θ= − + SensitiveSensitive toto HigherHigher OrderOrder CorrectionsCorrections


SensitiveSensitive toto HeavierHeavier ParticlesParticles: : TOP , HIGGSTOP , HIGGS


NeutralNeutral –– CurrentCurrent UniversalityUniversalityLEPEWWGLEPEWWG July 2005

EvidenceEvidence ofof ElectroweakElectroweak CorrectionsCorrectionsLowLow ValuesValues ofof MMHH PreferredPreferred


HOW MANY NEUTRINOS ?HOW MANY NEUTRINOS ?

e( hadrons)Zσ →

Th

( invisible)

2.9840 0.0082

( )i i

ZZ

Nν ν ν

= ±

Γ →=

Γ →

( invisible) ( all) ( visible)Z Z ZΓ → ≡ Γ → − Γ →


TheThe ννττ

Mainz’05:

2.3 eVemν <

(95% CL)

0.19 MeVmµν <

(90% CL)

DONUT: First Direct ντ Observation !


νe

, ...ep p d e ν+→

• Weakly Interacting Particles

• Among most abundant

particles in the Universe

• Each second pass through

your body

1410 from the SUNeν∼


, ...ep p d e ν+→

νe

Each second pass through your body

1410 from the SUNeν∼

They also come

from below!


Measured < Predictedeν eν

CC:

ES:NC:

e

x x

x x

d p p e

e ed p n

ν

ν νν ν

−

− −

+ → + +

+ → ++ → +

•

+••

SNOSNO

( , , )x e µ τ=

,e µ τν ν→Neutrino Neutrino OscillationsOscillations


Neutrino Neutrino OscillationsOscillations

e µν ν↔

µ τν ν↔

CPRν ?,

NEW PHYSICSNEW PHYSICS

Lepton Mixing

M. Maltoni


mν ≠ 0 NEW PHYSICS

Standard Model + Direct (singlet) νiR : Sterile νiR

New Interactions ?

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

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

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 3.9 ⋅ 10−7 τ−→ e−e+e− 1.5 ⋅ 10−7 τ−→ e−e+µ− 1.2 ⋅ 10−7

τ−→ µ−γ 6.8 ⋅ 10−8 τ−→ e−µ+µ− 1.4 ⋅ 10−7 τ−→ µ−e+µ− 0.7 ⋅ 10−7

τ−→ e−e−µ+ 0.6 ⋅ 10−7 τ−→ µ−µ+µ− 0.8 ⋅ 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−→ pγ 3.0 ⋅ 10−7

τ−→e−K+K− 1.4 · 10−7 τ−→e−K+π− 1.7 · 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− 2.7 · 10−7

τ−→µ+K−K− 4.8 · 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≡ −

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

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


HadronicHadronic VacuumVacuum PolarizationPolarization ContributionContribution toto aaµµ

Davier et al

σ ∼

hadττ ν→ +Γ ∼

F. Jegerlehner

aµ

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


( ) ( ) ( ) ( )2222

22

2 1Q

Q QQ Q

Qαα

+ Π + Π +T ∼∼

SCREENINGSCREENING

DecreasesDecreases atat LargeLarge DistancesDistances( ) 22 2Increases with QQ qα ≡ −

EffectiveEffective ((RunningRunning)) CouplingCoupling::

( ) ( ) 2

2

22

1 log3

1 Qm

QQ α

π

α αα−

= ≈− Π ⎛ ⎞

⎜ ⎟⎝ ⎠


TheThe PhotonPhoton CouplesCouples toto Virtual Virtual PairsPairsf f

VacuumVacuum PolarizedPolarized DielectricDielectric MediumMedium

1 2 1 2 1(45)( ) 137.03599913 ; ( ) 128.95 0.05Zem Mα α α− − −= = = ±

( and contributions included )l l− + qq


ElectromagneticElectromagnetic andand WeakWeak MomentsMoments2 2

2 321 5 3

2 ; (( )

0) ; (0( )

) ( ) )(2 2l

l ll

F q F qT l l e q l F q i q q l F a e F d

m mµµ µν µν

ν νγ ε γ σ σ γ⎡ ⎤

⎡ ⎤ = + +⎢ ⎥⎣ ⎦⎢

=⎥

=⎣ ⎦

de = (0.07 ± 0.07) x 10−26 e cm ; dµ = (3.7 ± 3.4) x 10−19 e cm

From e+e−→ τ+τ− , τ+τ−γ , e+e−τ+τ− data: (95% CL)

−0.042 < aτ < 0.016 [ aτth = 0.0011773 (3) ]

−2.2 < Re(dτ ) < 4.5 ; −2.5 < Im(dτ ) < 0.8 ( x 10−17 e cm)

Weak Moments:

0.00114 < Re(awτ) < 0.00114 ; 0.00265 < Im(aw

τ) < 0.00265

−3.56 < Re(dwτ) < 2.26 ; −6.9 < Im(dw

τ) < 7.7 ( x 10−18 e cm)


C Ccos sind d sθ θ θ= +

W

τντ −

dθ

u

Hadronsτ

Only lepton massive enough to decay into hadrons

( )( )

HadronsC

eR N

eτ

ττ

τ ν

τ ν ν

−

− −

Γ → +≡ ≈

Γ →

13.642 0; .013e

e

B BR

Bµ

τ− −

= = ±


W

τντ −

dθ

u

Hadrons

W

τντ −

dθ

u

Hadronsprobes the

hadronic V−A current

Hττ ν− −→

5(1 ) 0H d uµθ γ γ− −

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 :


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


Davier, Höcker, Zhang


BosonsQuarks Leptons

muon

top beauty

photon

gluon

up down electron neutrino e

charm strange neutrino µ

Higgstau neutrino τ

e

µ

τ

ZZ00 WW ±±

Antonio Pich IFIC, CSIC – Univ....

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