1 / 23

hadrons

. The Hadronic Contribution to ( g – 2) . Andreas Höcker Laboratoire de l’Accélérateur Linéaire, Orsay. ICHEP 2004 August 16 - 22, 2004, Beijing, China. . . . hadrons. hoecker@lal.in2p3.fr. Magnetic Anomaly. QED. Schwinger 1948 (Nobel price 1965). QED Prediction:

halima
Download Presentation

hadrons

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Hadronic Contribution to (g–2) Andreas Höcker Laboratoire de l’Accélérateur Linéaire, Orsay ICHEP 2004 August 16 - 22, 2004, Beijing, China    hadrons hoecker@lal.in2p3.fr A. Höcker – Hadronic Contribution to (g–2)

  2. Magnetic Anomaly QED Schwinger 1948 (Nobel price 1965) QED Prediction: Computed up to 4th order [Kinoshita et al.] (5th order estimated [Mohr, Taylor])    Kinoshita-Nio, hep-ph/0402206 corrected K’04 QED Hadronic Weak SUSY... ... or other new physics ? [see talk by A. Vainstein] A. Höcker – 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) A. Höcker – 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“, uses unitarity (optical theoreme) and analyticity  had   see backup slides ! A. Höcker – Hadronic Contribution to (g–2)

  5. Improved Determination of the Hadronic Contribution to (g–2) and (MZ ) 2 Eidelman-Jegerlehner’95, Z.Phys. C67 (1995) 585 • Since 1995, 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 See submitted abstract 6-0842 • Better data for the e+e–  +– cross section (!) CMD-2’02, KLOE’04 A. Höcker – Hadronic Contribution to (g–2)

  6. 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) A. Höcker – Hadronic Contribution to (g–2)

  7. 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 +– contribution: • 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 • intrinsicm–  m0 and –  0 [not corrected so far – can be measured] • Electromagnetic decays, like:     ,    ,    ,   l+l – • Quark mass difference mu  md generating “second class currents” (negligible) Marciano-Sirlin’ 88 Braaten-Li’ 90 Cirigliano-Ecker-Neufeld’ 02 Alemany-Davier-Höcker’ 97, Czyż-Kühn’ 01 A. Höcker – Hadronic Contribution to (g–2)

  8. Mass Dependence of SU(2) Breaking Multiplicative SU(2) corrections applied to –   – 0 spectral function: not shown: short distance correction Only  3 and EW short-distance corrections applied to 4 spectral functions A. Höcker – Hadronic Contribution to (g–2)

  9. 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 dispersion 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 A. Höcker – Hadronic Contribution to (g–2)

  10. 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  ) Troconiz-Yndurain, hep-ph/0402285 A. Höcker – Hadronic Contribution to (g–2)

  11. 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... ... A. Höcker – Hadronic Contribution to (g–2)

  12. The Problem Relative difference between  and e+e– data: z o o m zoom A. Höcker – Hadronic Contribution to (g–2)

  13. New Precise e+e–+– Data from KLOE Using the „Radiative Return“ KLOE Collaboration, hep-ex/0407048 Overall: fair agreement with CMD-2 Some discrepancy on  peak and above ... ... A. Höcker – Hadronic Contribution to (g–2)

  14. The Problem (revisited) Correction for ± –0 mass (~2.3 ± 0.8 MeV) and width (~2.9 MeV) splitting applied Davier, hep-ex/0312064 Jegerlehner, hep-ph/0312372 Relative difference between  and e+e– data: zoom z o o m A. Höcker – Hadronic Contribution to (g–2)

  15. Evaluating the Dispersion Integral Agreement bet-ween Data (BES) and pQCD (within correlated systematic errors) use data Better agreement between exclusive and inclusive (2) data than in 1997-1998 analyses use QCD use QCD A. Höcker – Hadronic Contribution to (g–2)

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

  17. 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 line shape discrepancy: • 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 correctionsimproves, but cannot correct difference above 0.7 GeV2 The fair agreement between KLOE and CMD-2 devalidates the use of data until a better understanding of the discrepancies is achieved A. Höcker – Hadronic Contribution to (g–2)

  18. Preliminary Results Czarnecki-Marsiano-Vainshtein + others Weak contribution : aweak = +(15.4 ± 0.3) 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 a SMinclu-ding: Knecht-Nyffeler,Phys.Rev.Lett. 88 (2002) 071802 Melnikov-Vainshtein, hep-ph/0312226 BNL E821 (2004): aexp = (11 659 208.0  5.8) 1010 not yet published not yet published Observed Difference with Experiment: preliminary A. Höcker – Hadronic Contribution to (g–2)

  19. 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, we 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: +–spectral function over full mass range, multihadron channels (2+2– and +–0 already available [see talk by E. Solodov, this session]) • New proposal submitted by E821 Collaboration aiming at precision of 2.4 10–10 • Ambitious muon g–2 project at J-PARC, Japan, aiming at (0.1 – 0.2) (BNL-E821) A. Höcker – Hadronic Contribution to (g–2)

  20. Backup Slides A. Höcker – Hadronic Contribution to (g–2)

  21. 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 A. Höcker – Hadronic Contribution to (g–2) ... and equivalently for a [had]

  22. 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! A. Höcker – Hadronic Contribution to (g–2)

  23. ––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 A. Höcker – Hadronic Contribution to (g–2)

More Related