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Antonio Pich
IFIC, CSIC – Univ. Valencia
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 ±±
Tau Physics A. Pich - Beijing 2005
Charged-Current Universality
Lorentz Structure
Neutral-Current Couplings
Neutrinos
Lepton-Flavour Violation
Dipole Moments
Hadronic Decays
QCD Tests: αs , ms , <αs G2> , …
Vus
τ
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
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 = ±
Tau Physics A. Pich - Beijing 2005
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−= =
± ± ×
Tau Physics A. Pich - Beijing 2005
150.972564 0.000010 (1632.1 1.4) 10 seB
B µ ττ−= =
± ± ×
0.29 MeV0.261776.9mτ+−=
( )exp/ 0.9730 0.0047eB Bµ = ±
Tau Physics A. Pich - Beijing 2005
LEPTON UNIVERSALITYLEPTON UNIVERSALITY
e
gg
µ
ggµ
τ
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
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′ = = =
Tau Physics A. Pich - Beijing 2005
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′′ ′ ′ ′ ′′= = = = = = = = =
Tau Physics A. Pich - Beijing 2005
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′
⎡ ⎤ ′≡ + = + − ≡ + = −⎢ ⎥⎣ ⎦
Tau Physics A. Pich - Beijing 2005
,
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→ • →•
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
, 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
Tau Physics A. Pich - Beijing 2005
, 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
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
SensitiveSensitive toto HeavierHeavier ParticlesParticles: : TOP , HIGGSTOP , HIGGS
Tau Physics A. Pich - Beijing 2005
NeutralNeutral –– CurrentCurrent UniversalityUniversalityLEPEWWGLEPEWWG July 2005
EvidenceEvidence ofof ElectroweakElectroweak CorrectionsCorrectionsLowLow ValuesValues ofof MMHH PreferredPreferred
Tau Physics A. Pich - Beijing 2005
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 →
Tau Physics A. Pich - Beijing 2005
TheThe ννττ
Mainz’05:
2.3 eVemν <
(95% CL)
0.19 MeVmµν <
(90% CL)
DONUT: First Direct ντ Observation !
Tau Physics A. Pich - Beijing 2005
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∼
Tau Physics A. Pich - Beijing 2005
, ...ep p d e ν+→
νe
Each second pass through your body
1410 from the SUNeν∼
They also come
from below!
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
Neutrino Neutrino OscillationsOscillations
e µν ν↔
µ τν ν↔
CPRν ?,
NEW PHYSICSNEW PHYSICS
Lepton Mixing
M. Maltoni
Tau Physics A. Pich - Beijing 2005
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.
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
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)
Tau Physics A. Pich - Beijing 2005
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:
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
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)
Tau Physics A. Pich - Beijing 2005
( ) ( ) ( ) ( )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 ⎛ ⎞
⎜ ⎟⎝ ⎠
Tau Physics A. Pich - Beijing 2005
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
Tau Physics A. Pich - Beijing 2005
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)
Tau Physics A. Pich - Beijing 2005
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− −
= = ±
Tau Physics A. Pich - Beijing 2005
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 :
Tau Physics A. Pich - Beijing 2005
0ττ ν π π− −→
( ) ( )0020 2 ( ;0 ) s p pd pF s pu
π ππ πµ
πµ
π π γ −−− ≡ +≡ −
CLEO105 selected events
Tau Physics A. Pich - Beijing 2005
ee++ee−−→→ππ++ππ−− versus versus ττ−−→→ ννττππ−−ππ00 (CVC)(CVC)
Davier, Höcker, Zhang
Tau Physics A. Pich - Beijing 2005
Davier, Höcker, Zhang
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 ±±