Estatus de g-2 del muón

Un escenario para física del sabor

Genaro Toledo

IFUNAM

Mini-workshop on flavor physics: The mexican taste

Outline

The muon magnetic dipole moment

Theoretical and Experimental Status.

The hadronic contribution

– Light by light Scattering

• Upper bound

– Tau ->pi pi nu

• Radiative Corrections

Conclusions.

Magnetic Anomaly

2

aie

e qm

Q

E

D

Magnetic dipole moment

normal anomalous

Dirac theory prediction for

fermions magnetic moment can be

stated from the electromagnetic

vertex.

a g - 2

2≡

Magnetic Anomaly

QED Hadronic Weak SUSY... ... or other new

physics ?

Why Do We Need to Know it so Precisely?

BNL

(2004)

Experimental progress on

precision of (g –2)

Outperforms theory precision

on hadronic contribution

BNL-E-821

a = 1165920.80 ± 0.63 x 10-9

sensitivity to physics scales

L m/sqrt{Da} ≈ 4.2 TeV

Phys. Rev. Lett. 92 161802(04)

BNL E969 approved

Even better accuracy

Magnetic Anomaly QED

Schwinger 1948

QED Prediction:

Computed up to 4th order [Kinoshita et al.]

(5th order estimated)

10

1

11614098.1 41321.810

3014.2 38.2 0.6

n

QED

n

a

0.0011612

a

11658472.9

QED

Contributions to the Standard

Model (SM) Prediction: ha weakQED d2

2

ga aaa

Magnetic Anomaly

Weak

Weak

Electroweak (15.4 ± 0.2) 10 –10

Magnetic Anomaly

Hadronic

Hadronic

Hadronic HO – ( 9.8 ± 0.1) 10 –10

Hadronic LBL + (12.0 ± 3.5) 10 –10

Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002) 071802

Melnikov-Vainshtein, hep-ph/0312226

Davier-Marciano, Ann. Rev. Nucl. Part. Sc. (2004)

Kinoshita-Nio (2006)

Situation at ICHEP-Tau06

ahad [ee ] = (690.9 ± 4.4) 10–10

a [ee ] = (11 659 180.5 ± 4.4had ± 3.5LBL ± 0.2QED+EW) 10–10

a [exp] – a [SM] = (27.5 ± 8.4) 10–10

3.3 “standard

deviations“

BNL E821 (2004)

aexp = (11 659 208.0 6.3) 10 10

.0

The Muonic (g –2)

2

2had

2

4

( )

( )3

m

a R sK

ss

ds

”Dispersion relation“

...

Dominant uncertainty from lowest order hadronic piece.

Can not be calculated from QCD (“first principles”) –

but: we can use experiment (!)

Decreases monotonically with energy giving a strong

weight to the low energy part of the integral

Hadronic

Evaluating the Dispersion Integral

Better agreement

between exclusive

and inclusive (2)

data than in 1997-

1998 analyses

Agreement bet-

ween Data (BES)

and pQCD (within

correlated systematic

errors)

use QCD

use data

use QCD

Hadronic

12%

5%

3%

5%

2%

1%

0%

92% 72%

12 - 5 - 12 (+)3.7 - 5 (+J/, )1.8 - 3.743 (+,)2 > 4 (+KK)

ahad,LO

< 1.8 GeV

2

2

Contributions to the dispersion integral

BABAR preliminar results

M. Davier TAU 08 Workshop

direct relative comparison of cross

sections in the corresponding 2-MeV

BaBar bins (interpolation with 2 bins)

CMD-2, SND, KLOE

Slightly higher

Hadronic

Computing a

FSR correction was missing in Belle, new value 523.5 3.0 2.5

ALEPH-CLEO-OPAL

(DEHZ 2006) (DEHZ 2003) (2008)

BaBar 369.3 0.8 2.2

CMD-2 94-95 362.1 2.4 2.2

CMD-2 98 361.5 1.7 2.9

SND 361.0 1.2 4.7

a (1010)

Comparison 0.630-0.958 GeV

Deviation between BNL-E821 and SM

a [exp ] – a [SM ] = (27.5 ± 8.4) 10 –10

(14.0 8.4) 1010

Hadronic

Light by light (LBL) Scattering

Model Prediction (error) x 10-11

Ramsey-Musolf / Wise PRL 89 041601(02) 57(60)

Knecht / Nyffeler PRD 65 073034(02) 80 (40)

Hayakawa / Kinoshita PRL 57 465(98) 90 (15)

Bijnens / Pallante NPB 626 410(02) 83 (32)

Melnikov / Vainshtein PRD 70 113006(04) 136 (25)

Chiral perturbation theory uncertainties ≥ ±10-9

significantly larger than measurement error.

We estimate aLBL(had) at the parton level.

Solid in the heavy quark limit where it matches pQCD but overestimates the

contribution in the chiral limit.

Imply an upper bound for aLBL(had).

In Collaboration with: Jens Erler

Other model estimates agree reasonably but the

error estimates remain rough guesses

M. Hayakawa et al PRL75 790 (95),

PRD 54 3137(96)

J. Bijnens, et al PRL75 1447 (95),

PRL75 3781(E)(95); NPB 474 379(96)

Hadronic LBL

APPLYING TO aLBL(had)

Accounting for model errors and isospin sym. breaking, we obtain

Exact in the limit of infinite mass

Overestimation in the chiral limit(± contribution < 0)

We quote our final result, the 95% CL upper bound:

S. Laporta and E. Remiddi

PLB301 440(93)

Hadronic LBL

aLBL(had)=

Role of data via CVC – SU(2)

hadrons

Whadrons

e+

e–

CVC: I =1 & VW: I =1 & V,A : I =0,1 & V

Hadronic physics factorizes in Spectral Functions :

Isospin symmetry connects I=1 e+e– cross section to vector spectral functions:fundamental

ingredient relating

long distance

(resonances) to

short distance

description (QCD)

Hadronic CVC

24

0

3

, )h()(4

1)v(

m

LO eetdtKeea

2

0

2

3

3

exp

4

3

,

|)(|

|)(|

)(

11))((

)(

)()(

4

1(

02 tf

tf

tGSdt

d

tK

tKtdtKa

EMEWm

LO

10

10

10

10

10

10)7.21.12(

10)7.21.6(

105.7

107.9

100.1

Shifts due to isospin breaking

17

Computing a Hadronic CVC

10

10

10

10

10

10)22.15.23(

10)22.17.1(

1047.7

1021.12

1055.5

VMD

Ours

preliminar

Xral PT

Cirigliano etal

As applied to results of

BELLE (arXiv: 0805.3773)

L L+T,

dttf

tftGee

tK

tKSB EM

EWCVC

2

0

3

00

)(

)()()(

)(

)()(

Dm→

Source IB

-3 MeV 0 MeV +3 MeV

Form factors

+ 1.2 %

- 0.6 %

+ 0.6 %

- 0.5 %

-0.01 %

-0.46 %

LD Radiative

Corrections

+ 0.02 %

- 0.30 %

+ 0.02%

-0.32 %

+0.04 %

-0.34 %

Shifts in (DBCVC/BCVC) due to IB corrections(this work in black, Cirigliano et al in red)

18

Impact on tau branching fraction Hadronic CVC

)(

1,

)(

)(2

0 tGtf

tf

EM

)(,)(

)(2

0 tGtf

tfEM

19

Modifications

Hadronic vacuum polarization is still the dominant systematics for SM

prediction of the muon g – 2

SM prediction for a now differs(preliminar from BABAR)

An upper bound on aLBL(had) restrict interpretation of discrepancy.

Discrepancy with data is vanishing. Isospin breaking corrections

Contributions from new physics are more suppressed

Conclusions

a [exp ] – a [SM ] = (27.5 ± 8.4) 10 –10 (14.0 8.4) 1010

shift -11.4 1010