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The Hadronic Contribution to (g–2)

Michel Davier

Laboratoire de l’Accélérateur Linéaire, Orsay

Tau Workshop 2004

September 14 - 17, 2004, Nara, Japan

hadrons

M. Davier – Hadronic Contribution to (g–2)

Magnetic Anomaly

QED

QED Prediction:

Computed up to 4th order [Kinoshita et al.] (5th order estimated)

Schwinger 1948

QED

Hadronic

Weak

SUSY...

... or other new physics ?

M. Davier – Hadronic Contribution to (g–2)

Why Do We Need to Know it so Precisely?

Experimental progress on precision of (g–2)

Outperforms theory pre-cision on hadronic contribution

BNL (2004)

M. Davier – Hadronic Contribution to (g–2)

The Muonic (g–2)

Contributions to the Standard Model (SM) Prediction:

Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD (“first principles”) – but:we can use experiment (!)

The Situation 1995

had

”Dispersion relation“

had

...

M. Davier – Hadronic Contribution to (g–2)

Hadronic Vacuum Polarization

Define: photon vacuum polarization function (q2)

Ward identities: only vacuum polarization modifies electron charge

with:

Leptonic lep(s) calculable in QED. However, quark loops are modified by long-distance hadronic physics, cannot (yet) be calculated within QCD (!)

Way out: Optical Theorem (unitarity) ...

... and the subtracted dispersion relation of (q2) (analyticity)

Im[ ] | hadrons |2

M. Davier – Hadronic Contribution to (g–2)

... and equivalently for a [had]

Improved Determination of the Hadronic Contribution to (g–2) and (MZ )

2

Eidelman-Jegerlehner’95, Z.Phys. C67 (1995) 585

- Since then: Improved determi-nation of the dispersion integral:
- better data
- extended use of QCD

- Inclusion of precise data using SU(2) (CVC)

Alemany-Davier-Höcker’97, Narison’01, Trocóniz-Ynduráin’01, + later works

- Extended use of (dominantly) perturbative QCD

Martin-Zeppenfeld’95, Davier-Höcker’97, Kühn-Steinhauser’98, Erler’98, + others

Improvement in 4 Steps:

- Theoretical constraints from QCD sum rules and use of Adler function

Groote-Körner-Schilcher-Nasrallah’98, Davier-Höcker’98, Martin-Outhwaite-Ryskin’00, Cvetič-Lee-Schmidt’01, Jegerlehner et al’00, Dorokhov’04 + others

- Better data for the e+e– +– cross section

CMD-2’02, KLOE’04

M. Davier – Hadronic Contribution to (g–2)

The Role of Data through CVC – SU(2)

W: I=1 &V,A

CVC: I=1 &V

: I=0,1 &V

e+

hadrons

W

e–

hadrons

Hadronic physics factorizes inSpectral Functions :

fundamental ingredient relating long distance (resonances) to short distance description (QCD)

Isospin symmetry connects I=1 e+e– cross section to vectorspectral functions:

branching fractionsmass spectrum kinematic factor (PS)

M. Davier – Hadronic Contribution to (g–2)

SU(2) Breaking

Electromagnetism does not respect isospin and hence we have to consider isospin breaking when dealing with an experimental precision of 0.5%

- Corrections for SU(2) breaking applied to data for dominant – + contrib.:
- Electroweak radiative corrections:
- dominant contribution from short distance correction SEW to effective 4-fermion coupling (1 + 3(m)/4)(1+2Q)log(MZ /m)
- subleading corrections calculated and small
- long distance radiative correction GEM(s) calculated [ add FSR to the bare cross section in order to obtain – + () ]
- Charged/neutral mass splitting:
- m– m0leads to phase space (cross sec.) and width (FF) corrections
- - mixing (EM – + decay)corrected using FF model
- intrinsic m– m0 and – 0 [not corrected !]
- Electromagnetic decays, like: , , , l+l –
- Quark mass difference mu mdgenerating “second class currents” (negligible)

Marciano-Sirlin’ 88

Braaten-Li’ 90

Cirigliano-Ecker-Neufeld’ 02

Alemany-Davier-Höcker’ 97, Czyż-Kühn’ 01

M. Davier – Hadronic Contribution to (g–2)

Mass Dependence of SU(2) Breaking

Multiplicative SU(2) corrections applied to – – 0 spectral function:

Only 3 and EW short-distance corrections applied to 4 spectral functions

M. Davier – Hadronic Contribution to (g–2)

e+e–Radiative Corrections

Multiple radiative corrections are applied on measured e+e– cross sections

- Situation often unclear: whether or not and if - which corrections were applied
- Vacuum polarization (VP) in the photon propagator:
- leptonic VP in general corrected for
- hadronic VP correction not applied, but for CMD-2 (in principle: iterative proc.)

- Initial state radiation (ISR)
- corrected by experiments

- Final state radiation (FSR) [we need e+e– hadrons () in disper-sion integral]
- usually, experiments obtain bare cross section so that FSR has to be added “by hand”; done for CMD-2, (supposedly) not done for others

M. Davier – Hadronic Contribution to (g–2)

2002/2003 Analyses of ahad

- Motivation for new work:
- New high precision e+e– results (0.6% sys. error) around from CMD-2 (Novosibirsk)
- New results from ALEPH using full LEP1 statistics
- New R results from BES between 2 and 5 GeV
- New theoretical analysis of SU(2) breaking

CMD-2 PL B527, 161 (2002)

ALEPH CONF 2002-19

BES PRL 84 594 (2000); PRL 88, 101802 (2002)

Cirigliano-Ecker-Neufeld

JHEP 0208 (2002) 002

- Outline of the 2002/2003 analyses:
- Include all new Novisibirsk (CMD-2, SND) and ALEPH data
- Apply (revisited) SU(2)-breaking corrections to data
- Identify application/non-application of radiative corrections
- Recompute all exclusive, inclusive and QCD contributions to dispersion integral; revisit threshold contribution and resonances
- Results, comparisons, discussions...

Davier-Eidelman-Höcker-Zhang

Eur.Phys.J. C27 (2003) 497; C31 (2003) 503

Hagiwara-Martin-Nomura-Teubner, Phys.Rev. D69 (2004) 093003 (no data)

Jegerlehner,

hep-ph/0312372 (no data)

M. Davier – Hadronic Contribution to (g–2)

Comparing e+e– +– and –0

Correct data for missing - mixing (taken from BW fit) and all other SU(2)-breaking sources

Remarkable agreement

But: not good enough...

...

M. Davier – Hadronic Contribution to (g–2)

The Problem

Relative difference between and e+e– data:

zoom

M. Davier – Hadronic Contribution to (g–2)

––0: Comparing ALEPH, CLEO, OPAL

Shape comparison only. SFs normalized to WA branching fraction (dominated by ALEPH).

- Good agreement observed between ALEPH and CLEO
- ALEPH more precise at low s
- CLEO better at high s

M. Davier – Hadronic Contribution to (g–2)

Testing CVC

Infer branching fractions from e+e– data:

Difference: BR[ ] – BR[e+e– (CVC)]:

leaving out CMD-2 :

B0 = (23.69 0.68) %

(7.4 2.9) % relative discrepancy!

M. Davier – Hadronic Contribution to (g–2)

New Precise e+e–+– Data from KLOE Using the „Radiative Return“

Overall: agreement with CMD-2

Some discrepancy on peak and above ...

...

M. Davier – Hadronic Contribution to (g–2)

The Problem (revisited)

Relative difference between and e+e– data:

zoom

No correction for ± –0 mass (~ 2.3 ± 0.8 MeV) and width (~ 3 MeV) splitting applied

Davier, hep-ex/0312064

Jegerlehner, hep-ph/0312372

M. Davier – Hadronic Contribution to (g–2)

Evaluating the Dispersion Integral

use data

Agreement bet-ween Data (BES) and pQCD (within correlated systematic errors)

use QCD

Better agreement between exclusive and inclusive (2) data than in 1997-1998 analyses

use QCD

M. Davier – Hadronic Contribution to (g–2)

Results: the Compilation (including KLOE) Contributions to ahad[in 10–10]from the different energy domains:

M. Davier – Hadronic Contribution to (g–2)

Discussion

- The problem of the + – contribution :
- Experimental situation:
- new, precise KLOE results in approximate agreement with latest CMD-2 data
- data without m() and () corr. in strong disagreement with both data sets
- ALEPH, CLEO and OPAL spectral functions in good agreement within errors
- Concerning the remaining line shape discrepancy (0.7- 0.9 GeV2):
- SU(2) corrections: basic contributions identified and stable since long; overall correction applied to is (– 2.2 ± 0.5)%, dominated by uncontroversial short distance piece; additional long-distance corrections found to be small
- lineshape corrections cannot account for the difference above 0.7 GeV2

The fair agreement between KLOE and CMD-2 invalidates the use of data until a better understanding of the discrepancies is achieved

M. Davier – Hadronic Contribution to (g–2)

Preliminary Results

Hadronic contribution from higher order : ahad [(/)3]= – (10.0 ± 0.6) 10–10

Hadronic contribution from LBL scattering: ahad [LBL] = + (12.0 ± 3.5) 10–10

inclu-ding:

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

Melnikov-Vainshtein, hep-ph/0312226

.0

Davier-Marciano, to appear Ann. Rev. Nucl. Part. Sc.

BNL E821 (2004):

aexp = (11 659 208.0 5.8) 1010

not yet published

Observed Difference with Experiment:

not yet published

preliminary

M. Davier – Hadronic Contribution to (g–2)

Conclusions and Perspectives

- Hadronic vacuum polarization is dominant systematics for SM prediction of the muon g–2
- New data from KLOE in fair agreement with CMD-2 with a (mostly) independent technique
- Discrepancy with data (ALEPH & CLEO & OPAL) confirmed
- Until /e+e– puzzle is solved, use only e+e– data in dispersion integral
- We find that the SM prediction differs by 2.7 [e+e–] from experiment (BNL 2004)

- Future experimental input expected from:
- New CMD-2 results forthcoming, especially at low and large +–masses
- BABAR ISR: +– SF over full mass range, multihadron channels (2+2– and +–0 already available)

M. Davier – Hadronic Contribution to (g–2)

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