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hadrons

. The Hadronic Contribution to ( g – 2) . Michel Davier Laboratoire de l’Accélérateur Linéaire, Orsay. Tau Workshop 2004 September 1 4 - 17 , 2004, Nara , Japan. . . . hadrons. davier@lal.in2p3.fr. Magnetic Anomaly. QED. QED Prediction:

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hadrons

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  1. The Hadronic Contribution to (g–2) Michel Davier Laboratoire de l’Accélérateur Linéaire, Orsay Tau Workshop 2004 September 14 - 17, 2004, Nara, Japan    hadrons davier@lal.in2p3.fr M. Davier – Hadronic Contribution to (g–2)

  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)

  3. 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)

  4. 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)

  5. 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]

  6. 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)

  7. 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 vectorspectral functions: branching fractionsmass spectrum kinematic factor (PS) M. Davier – Hadronic Contribution to (g–2)

  8. 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+2Q)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–  m0leads 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 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)

  9. 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)

  10. 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)

  11. 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 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)

  12. 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)

  13. The Problem Relative difference between  and e+e– data: zoom M. Davier – Hadronic Contribution to (g–2)

  14. ––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)

  15. Testing CVC Infer branching fractions from e+e– data: Difference: BR[ ] – BR[e+e– (CVC)]: leaving out CMD-2 : B0 = (23.69  0.68) %  (7.4  2.9) % relative discrepancy! M. Davier – Hadronic Contribution to (g–2)

  16. 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)

  17. 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)

  18. 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)

  19. Results: the Compilation (including KLOE) Contributions to ahad[in 10–10]from the different energy domains: M. Davier – Hadronic Contribution to (g–2)

  20. 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)

  21. Preliminary Results 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: 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): aexp = (11 659 208.0  5.8) 1010 not yet published Observed Difference with Experiment: not yet published preliminary M. Davier – Hadronic Contribution to (g–2)

  22. 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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