antonio pich ific, valencia lepton universality. lorentz...
TRANSCRIPT
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
Tau Physics A. Pich - Charm 2006
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)
Tau Physics A. Pich - Charm 2006
150.972564 0.000010 (1632.1 1.4) 10 seB
B μ ττ−= =
± ± ×
( )exp/ 0.9730 0.0047eB Bμ = ±
0.29 MeV0.261776.9mτ+−=
Tau Physics A. Pich - Charm 2006
LEPTON UNIVERSALITYLEPTON UNIVERSALITY
e
gg
μ
ggμ
τ
Tau Physics A. Pich - Charm 2006
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
Tau Physics A. Pich - Charm 2006
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 →
+
⎠
→+⎝ ⎠
Tau Physics A. Pich - Charm 2006
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 - Charm 2006
,
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 - Charm 2006
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
Tau Physics A. Pich - Charm 2006
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 - Charm 2006
ee++ee−−→→ππ++ππ−− versus versus ττ−−→→ ννττππ−−ππ00 (CVC)(CVC)
Davier, Höcker, Zhang
Tau Physics A. Pich - Charm 2006
Tau Physics A. Pich - Charm 2006
Tau Physics A. Pich - Charm 2006
Jamin-Pich-Portolés
hep-ph/0605096
ττ−− →→ ννττKK00ππ−− , ν, νττKK−− ππ00
Tau Physics A. Pich - Charm 2006
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
→
Tau Physics A. Pich - Charm 2006
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
→
τν
Wτ −
τν
τ −
Wd,s
u
had Ιmττ ν→ +
⎧ ⎫⎪ ⎪Γ ∼ ⎨ ⎬⎪ ⎪⎩ ⎭
Tau Physics A. Pich - Charm 2006
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∫
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 ∼ ⎨ ⎬⎪ ⎪⎩ ⎭
Tau Physics A. Pich - Charm 2006
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
Tau Physics A. Pich - Charm 2006
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
Tau Physics A. Pich - Charm 2006
(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− =
± ±
Tau Physics A. Pich - Charm 2006
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 , …
Tau Physics A. Pich - Charm 2006
Non-Perturbative
Perturbativeat s = mτ
2
Rτ
Chiral Sum Rules:
02 2
2
,
/ , '/A
f m m
F rπ ππ
π ε ε
± −
Tau Physics A. Pich - Charm 2006
(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
Tau Physics A. Pich - Charm 2006
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
Tau Physics A. Pich - Charm 2006
TheThe ννττ
Mainz’05:
DONUT: First Direct ντ Observation !
2.3 eVemν <
(95% CL)
0.19 MeVmμν <
(90% CL)
Tau Physics A. Pich - Charm 2006
Neutrino Neutrino OscillationsOscillations
CPRν ?,
NEW PHYSICSNEW PHYSICS
Lepton Mixinge μν ν↔
μ τν ν↔
M. Maltoni
Tau Physics A. Pich - Charm 2006
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.
Tau Physics A. Pich - Charm 2006
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 - Charm 2006
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
Tau Physics A. Pich - Charm 2006
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 - Charm 2006
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 - Charm 2006
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−= ± ×
Tau Physics A. Pich - Charm 2006
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)
Tau Physics A. Pich - Charm 2006
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
Tau Physics A. Pich - Charm 2006
Davier, Höcker, Zhang