1 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)     hadrons The Hadronic Contribution to (g – 2)  Michel Davier Laboratoire de l’Accélérateur Linéaire, Orsay Tau Workshop 2004 September , 2004, Nara, Japan

2 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Magnetic Anomaly Schwinger 1948 QED Prediction: Computed up to 4 th order [Kinoshita et al.] (5 th order estimated)    QEDQED QEDHadronicWeakSUSY or other new physics ?

3 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Why Do We Need to Know it so Precisely? BNL (2004) Experimental progress on precision of (g –2)  Outperforms theory pre- cision on hadronic contribution

4 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  The Muonic (g –2)  Contributions to the Standard Model (SM) Prediction: Source (a)(a) Reference QED ~ 0.3  10 –10 [Schwinger ’48 & others] Hadrons ~ (15  4)  10 –10 [Eidelman-Jegerlehner ’95 & others] Z, W exchange ~ 0.4  10 –10 [Czarnecki et al. ‘95 & others] The Situation 1995 ”Dispersion relation“    hadhad had ... Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD (“first principles”) – but: we can use experiment (!)

5 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Hadronic Vacuum Polarization Define: photon vacuum polarization function   (q 2 ) 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)... Im[ ]  | hadrons | 2... and the subtracted dispersion relation of   (q 2 ) (analyticity)... and equivalently for a  [had]

6 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Improved Determination of the Hadronic Contribution to (g –2)  and  (M Z )2 Energy [GeV]Input 1995Input after m  - 1.8Data Data (e + e – &  ) + QCD 1.8 – J/  DataQCD J/  -  DataData + QCD  - 40 DataQCD 40 -  QCD Eidelman-Jegerlehner’95, Z.Phys. C67 (1995) 585 Improvement in 4 Steps: Inclusion of precise  data using SU(2) (CVC) Extended use of (dominantly) perturbative QCD Theoretical constraints from QCD sum rules and use of Adler function Alemany-Davier-Höcker’97, Narison’01, Trocóniz-Ynduráin’01, + later works Martin-Zeppenfeld’95, Davier-Höcker’97, Kühn-Steinhauser’98, Erler’98, + others Groote-Körner-Schilcher-Nasrallah’98, Davier-Höcker’98, Martin-Outhwaite- Ryskin’00, Cvetič-Lee-Schmidt’01, Jegerlehner et al’00, Dorokhov’04 + others Since then: Improved determi- nation of the dispersion integral: better data extended use of QCD Better data for the e + e –   +  – cross section CMD-2’02, KLOE’04

7 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  The Role of  Data through CVC – SU(2) hadrons   W  e+e+ e –e – CVC: I =1 & V W: 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: branching fractions mass spectrum kinematic factor (PS) fundamental ingredient relating long distance (resonances) to short distance description (QCD)

8 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  SU(2) Breaking Corrections for SU(2) breaking applied to  data for dominant  –  + contrib.: Electroweak radiative corrections: dominant contribution from short distance correction S EW to effective 4-fermion coupling  (1 + 3  (m  )/4  )(1+2  Q  )log(M Z /m  ) subleading corrections calculated and small long distance radiative correction G EM (s) calculated [ add FSR to the bare cross section in order to obtain  –  + (  ) ] Charged/neutral mass splitting: m  –  m  0 leads to phase space (cross sec.) and width (FF) corrections  -  mixing (EM    –  + decay) corrected using FF model intrinsic m  –  m  0 and   –    0 [not corrected !] Electromagnetic decays, like:     ,    ,    ,   l + l – Quark mass difference m u  m d generating “second class currents” (negligible) Electromagnetism does not respect isospin and hence we have to consider isospin breaking when dealing with an experimental precision of 0.5% Cirigliano-Ecker-Neufeld’ 02 Marciano-Sirlin’ 88 Braaten-Li’ 90 Alemany-Davier-Höcker’ 97, Czyż-Kühn’ 01

9 Tau Workshop, Nara, Sept 14-17, 2004M. 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

10 Tau Workshop, Nara, Sept 14-17, 2004M. 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.) 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 Initial state radiation (ISR) corrected by experiments

11 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  2002/2003 Analyses of a  had 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 Cirigliano-Ecker-Neufeld JHEP 0208 (2002) 002 ALEPH CONF CMD-2 PL B527, 161 (2002) 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 BES PRL (2000); PRL 88, (2002) Hagiwara-Martin-Nomura-Teubner, Phys.Rev. D69 (2004) (no  data) Jegerlehner, hep-ph/ (no  data)

12 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Comparing e + e –   +  – and    –  0  Remarkable agreement But: not good enough Correct  data for missing  -  mixing (taken from BW fit) and all other SU(2)-breaking sources

13 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  The Problem zoom Relative difference between  and e + e – data:

14 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)   –   –  0  : Comparing ALEPH, CLEO, OPAL Good agreement observed between ALEPH and CLEO ALEPH more precise at low s CLEO better at high s Shape comparison only. SFs normalized to WA branching fraction (dominated by ALEPH).

15 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Testing CVC Infer  branching fractions from e + e – data: Difference: BR[  ] – BR[e + e – (CVC) ]: Mode  (  – e + e – ) „Sigma“  –   –  0  ±  –   – 3  0  – 0.08 ±  –  2  –  +  0  ± leaving out CMD-2 : B  0 = (23.69  0.68) %  (7.4  2.9) % relative discrepancy!

16 Tau Workshop, Nara, Sept 14-17, 2004M. 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...

17 Tau Workshop, Nara, Sept 14-17, 2004M. 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 Jegerlehner, hep-ph/ Davier, hep-ex/

18 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Evaluating the Dispersion Integral Better agreement between exclusive and inclusive (  2) data than in analyses Agreement bet- ween Data (BES) and pQCD (within correlated systematic errors) use QCD use data use QCD

19 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Results: the Compilation (including KLOE) Contributions to a  had [in 10 –10 ] from the different energy domains: ModesEnergy [GeV] e+e –e+e –  Low s expansion2m  – ± 1.7 ± 1.2 rad 56.0 ± 1.6 ± 0.3 SU(2) [  +  – (DEHZ’03) ] 2m  – 1.8[ ± 4.9 ± 1.6 rad ]464.0 ± 3.0 ± 2.3 SU(2)  +  – (incl. KLOE) 2m  – ± 4.1 ± 1.6 rad –  + – 20 + – 20 2m  – ± 1.3 ± 0.2 rad 21.4 ± 1.3 ± 0.6 SU(2) 2  + 2  – 2m  – ± 0.9 ± 0.2 rad 12.3 ± 1.0 ± 0.4 SU(2)  (782) 0.3 – ± 1.0 ± 0.3 rad –  (1020) 1.0 – ± 0.8 ± 0.2 rad – Other exclusive2m  – ± 1.5 ± 0.3 rad – J / ,  (2S) 3.08 – ± 0.4 ± 0.0 rad – R [QCD]1.8 – ± 0.5 ± 0.0 rad – R [data]3.7 – ± 0.3 ± 0.0 rad – R [QCD] 5.0 –  9.9 ± 0.2 theo – Sum (incl. KLOE) 2m  –  ± 5.3 ± 3.5 rad ± 5.0 ± 0.8 rad ± 2.8 SU(2)

20 Tau Workshop, Nara, Sept 14-17, 2004M. 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 ( GeV 2 ): 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 GeV 2 The fair agreement between KLOE and CMD-2 invalidates the use of  data until a better understanding of the discrepancies is achieved

21 Tau Workshop, Nara, Sept 14-17, 2004M. Davier – Hadronic Contribution to (g – 2)  Preliminary Results a  had [ee ]= (693.4 ± 5.3 ± 3.5)  10 –10 a  [ee ]= ( ± 6.3 had ± 3.5 LBL ± 0.3 QED+EW )  10 –10 Hadronic contribution from higher order : a  had [(  /  ) 3 ] = – (10.0 ± 0.6)  10 –10 Hadronic contribution from LBL scattering: a  had [ LBL ] = + (12.0 ± 3.5)  10 –10 inclu- ding: a  [exp ] – a  [SM ]= (25.2 ± 9.2)  10 –10  2.7 „standard deviations“ Observed Difference with Experiment: BNL E821 (2004): a  exp = (  5.8) 10  10 Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002) Melnikov-Vainshtein, hep-ph/ not yet published preliminary Davier-Marciano, to appear Ann. Rev. Nucl. Part. Sc.

22 Tau Workshop, Nara, Sept 14-17, 2004M. 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)