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hadrons

. The Hadronic Contribution to ( g – 2) . Andreas Höcker Laboratoire de l’Accélérateur Linéaire, Orsay. Seminar MPI - M ü nchen, 1 March 2005. . . . hadrons. hoecker@lal.in2p3.fr. a  [had].   QED [had]. Outline. The muon magnetic anomaly and hadronic vacuum polarization

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  1. The Hadronic Contribution to (g–2) Andreas Höcker Laboratoire de l’Accélérateur Linéaire, Orsay Seminar MPI - München, 1 March 2005    hadrons hoecker@lal.in2p3.fr A. Höcker – The Hadronic Contribution to (g–2)

  2. a [had] QED [had] Outline • The muon magnetic anomaly and hadronic vacuum polarization • e+e–versus  data • Isospin breaking and radiative corrections • New e+e–data from KLOE (using the radiative return) • A new Standard Model prediction for (g–2) • Appendix (i) : recent ISR cross section results from BABAR • Appendix (ii) : further QCD improvements for (g–2) [SM] A. Höcker – The Hadronic Contribution to (g–2)

  3. Magnetic Anomaly QED Schwinger 1948 (Nobel price 1965) QED Prediction Computed up to 4th order [Kinoshita et al.] (5th order estimated)    Kinoshita-Nio, hep-ph/0402206 corrected K’04 QED Hadronic Weak SUSY... ... or other new physics ? A. Höcker – The Hadronic Contribution to (g–2)

  4. 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 – The Hadronic Contribution to (g–2)

  5. For the Beauty of it: BNL (g–2) Measurement Observed positron rate in successive 100s periods Difference between spin precession and cyclotron frequency (at magic  = 29.3): obtained from fit to: plot taken from: E821 (g –2), hep-ex/0202024 A. Höcker – The Hadronic Contribution to (g–2)

  6. 2001: The First Round of BNL Results on a The E821 (g –2) experiment at BNL published early 2001 a value 3 more precise than the previous CERN and BNL exps. combined: E821 (g –2)PRL 86, 2227-2231 (2001) a(exp) = 11 659 202(16)  10–10 SM BNL compares with Standard Model prediction: a(SM) = 11 659 159.6(6.7)  10–10 Averaging E821 with previous experiments gives: a(exp) – a(SM) = 43(16)  10–10 [2.7 ] BUT: In November 2001, Knecht & Nyffeler have corrected a sign error in the dominant (-pole) contribution from hadronic light-by-light (LBL) scattering, reducing the above discrepancy to LBLS  had a(exp) – a(SM) = 25(16) 10–10 [1.6 ]  Knecht-Nyffeler, hep-ph/0111058; result approved by: Hayakawa-Kinoshita, hep-ph/0112102; Bijnens-Pallante-Prades, hep-ph/0112255  A. Höcker – The Hadronic Contribution to (g–2)

  7. New Physics in a ? Involves (,0) and (, ) loops at mass scale MSUSY (a) statistical fluctuation ? (b) experimental systematic ? (c)theory value incorrect ? (d) new physics ? The points (a-c) are the subject of this talk. 2.7 discrepancy : Concerning (d) : Most fashionable new physics scenario : SUSY Fayet 80, Grifols-Mendez 82, Ellis-Hagelin-Nanopoulos 82, Barbieri-Maiani 82, ... Moroi 96, ... A. Höcker – The Hadronic Contribution to (g–2)

  8. 2002: The Second Round of BNL Results on a The new analysis, first presented at ICHEP’02, achieves 2 times better precision (using 4 more statistics) than the 2001 result: E821 (g –2)PRL 92, 161802 (2004) a(exp) = 11 659 203(7)(5)  10–10 • Error dominated by statistics; systematics are: • 3.6  10–10 from precession frequency • 2.8  10–10 from magnetic field BNL compares WA with SM prediction: (using DH’98 for hadronic vac. pol.) a(exp) – a(SM) = 25(10)  10–10 Experimental and theoretical uncertainties now of similar order ! More work and, in particular, better data needed to achieve a more precise prediction of the hadronic contribution A. Höcker – The Hadronic Contribution to (g–2)

  9. The Muonic (g–2)in the Standard Model 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 theorem) and analyticity  had   ... A. Höcker – The Hadronic Contribution to (g–2)

  10. Hadronic Vacuum Polarization ... and the running of QED 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 – The Hadronic Contribution to (g–2) ... and equivalently for a [had]

  11. Contributions to the Dispersion Integrals 2 3 (+,) 4 > 4 (+KK) 1.8 - 3.7 3.7 - 5 (+J/, ) 5 - 12 (+) 12 -  < 1.8 GeV had(MZ): ahad: 2[ahad]: 2[had]: with A. Höcker – The Hadronic Contribution to (g–2)

  12. The R Data Situation around 1995 Data density and quality unsatisfactory in some crucial energy regions A. Höcker – The Hadronic Contribution to (g–2)

  13. Improved Determination of the Hadronic Contribution to (g–2) and (MZ ) 2 Eidelman-Jegerlehner’95, Z.Phys. C67 (1995) 585 • Since 1995, improved determination of the dispersion integral: • better data • extended use of QCD • Inclusion of precise  data using SU(2) (CVC) Alemany-Davier-H.’97, Narison’01, Trocóniz-Ynduráin’01, + later works • Extended use of (dominantly) perturbative QCD Martin-Zeppenfeld’95, Davier-H.’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-H.’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 A. Höcker – The Hadronic Contribution to (g–2)

  14. 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 – The Hadronic Contribution to (g–2)

  15. Connection between  Spectral Functions and QCD • Optical theorem (s)  Im(s) • Apply Cauchy’s theorem for “save” (i.e., sufficiently large) s0: kinematic factor spectral function Im(s) Re(s) |s|= |s|=s0 • Use the Adler function to remove unphysical subtractions: • Use global quark-hadron duality in the framework of the Operator Product Expansion (OPE) to predict: D(s)  Dpert(s) + Dq-mass(s) + Dnon-pert(s) • Use analytical moments fn(s)=f(s)·polyn(s) to fix non-perturbative parameters of the OPE ... and then fit s(m) A. Höcker – The Hadronic Contribution to (g–2)

  16. QCD Results from  Decays Evolution of s(m), measured using  decays, to MZ using RGE (4-loop QCD -function & 3-loop quark flavor matching) shows the excellent compatibility of  result with EW fit: s(MZ) = 0.1202 ± 0.0027 (ALEPH’98, theory dominated) s(MZ) = 0.1183 ± 0.0027 (LEP’00, statistics dominated) (analysis also performed by CLEO and OPAL) The  spectral function allows to directly measure the running of s(s0) within s0  [~1...1.8 GeV] A. Höcker – The Hadronic Contribution to (g–2)

  17. 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] • 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-H. 97, Czyż-Kühn’ 01 A. Höcker – The Hadronic Contribution to (g–2)

  18. 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 – The Hadronic Contribution to (g–2)

  19. 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 – The Hadronic Contribution to (g–2)

  20. Comprehensive Re-analyses of ahad in 2002/2003 • 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-H.-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 – The Hadronic Contribution to (g–2)

  21. 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 – The Hadronic Contribution to (g–2)

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

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

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

  26. 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 – The Hadronic Contribution to (g–2)

  27. Comparing the 4 Spectral Functions e+e –  + – 20  data not competitive Large discrepancies between experiments e+e –  2+ 2 – CVC relations:  data not competitive A. Höcker – The Hadronic Contribution to (g–2)

  28. 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 – The Hadronic Contribution to (g–2)

  29. Specific Contributions: Low s Threshold Use Taylor expansion for  + – threshold: • exploiting precise space-like data, r2 = (0.439 ± 0.008) fm2, and fittingc1 and c2 and : • Fit range: • up to 0.35 GeV2 • Integration range: • up to 0.25 GeV2 • Excellent 2 for both  and e+e data • strong anti-correlation between c1 and c2 A. Höcker – The Hadronic Contribution to (g–2)

  30. Specific Contributions: Narrow Resonances Use direct data integration for (782) and (1020) to account for non-resonant contributions. However, careful integration necessary: • trapezoidal rule creates systematics for functions with strong curvature • use phenomenological fit SND, PRD, 072002 (2001) CMD-2, PL B466, 385 (1999); PL B476, 33 (2000) Trapezoidal rule creates bias A. Höcker – The Hadronic Contribution to (g–2)

  31. Specific Contributions: the Charm Region New precise BES data improve cc resonance region: Agreement among experiments A. Höcker – The Hadronic Contribution to (g–2)

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

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

  34. New Preliminary Result Czarnecki-Marciano-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 – The Hadronic Contribution to (g–2)

  35. a p p e n d i x (i) I S R w i t h B A B A R A. Höcker – The Hadronic Contribution to (g–2)

  36. Radiative Return Cross Section Results from BABAR ISR The Radiative Return : benefit from huge luminosities at B and Factories to perform continuous cross section measurements H is radiation function • High PEP-II luminosity at s = 10.58 GeV  precise measurement of the e+e– cross section0 at low c.m. energieswith BABAR • Comprehensive program at BABAR • Results for +0, preliminary results for 2+2, K+K+, 2K+2Kfrom 89.3 fb–1 A. Höcker – The Hadronic Contribution to (g–2)

  37. The e+e–+–0 Cross Section Cross section above  resonance : DM2 missed a resonance SND compatible with (1650) [m  1.65 GeV,   0.22 GeV] BABAR DM2 coverage of wide region in this experiment - no point-to-point normalization problems consistent with SND data E C.M. < 1.4 GeV inconsistent with DM2 results overall normalization error ~ 5% up to 2.5 GeV A. Höcker – The Hadronic Contribution to (g–2)

  38. The e+e–2+2– Cross Section Good agreement with direct ee measurements. Most precise result above 1.4 GeV A. Höcker – The Hadronic Contribution to (g–2)

  39. The e+e–K+K–+– Cross Section Systematic error – 15% (mainly model dependence) J/ Much more precise than previous measurement Substantial resonance sub-structures observed: K*(890)Kdominant f, KK contribute strongly K*2(1430)K seen A. Höcker – The Hadronic Contribution to (g–2)

  40. Impact on (g–2) Contributions to ahad (1010) • from 2+ 2 (s = 0.56 – 1.8 GeV) : from all e+e exp. : 14.21  0.87exp  0.23rad from all  data : 12.35  0.96exp  0.40SU(2) from BABAR : 12.95  0.64exp  0.13rad • from +–0 (s = 1.055 – 1.8 GeV) : from all e+e exp. : 2.45  0.26exp  0.03rad from BABAR : 3.31  0.13exp  0.03rad Many more modes to come; aim for systematic errors 1% (in +) Several B(J/  X) measurements better than current world average A. Höcker – The Hadronic Contribution to (g–2)

  41. 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) • The difference is within the range of possible SUSY contributions • 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 – The Hadronic Contribution to (g–2)

  42. a p p e n d i x (ii) Q C D i m p r o v e m e n t s f o r ahad A. Höcker – The Hadronic Contribution to (g–2)

  43. Extend the Use of QCD • The inclusion of  data has reduces the error on ahadby 40% • However, no significant improvement for had(MZ) ...how can we further improve – in particular: had(MZ) ? Inclusive hadronicdecayshave shown that QCD is safely applicable at m1.8 GeV/c2 ALEPH (1993, 1998) CLEO(1994) OPAL(1998) HINT: Why not also for e+e– ? ... Do equivalent QCD analysis as for decays using spectral moments of [e+e–  hadrons](s) TEST: The combined fit of spectral moment to e+e– data showed consistent OPE prediction and revealed small non-perturbative contributions at s0=1.8 GeV A. Höcker – The Hadronic Contribution to (g–2)

  44. Data Driven QCD Sum Rules • The use of  data and extended QCD reduces the error on ahadby 51% • and provides a 60% (!) reduction of the error on had(MZ) ...however, there exist domains for which no theoretical constraints are used so far... we can thus still increase our information budget ! USE: Modified Dispersion Integral: DataTheory where the Pnare (analytic) polynomials that approximate the kernel f(s) and thus reduce the data piece of the integral replaced by known theory. No new assumptions ! An optimization procedure minimizes the total experimental and (conservative) theoretical error A. Höcker – The Hadronic Contribution to (g–2)

  45. b a c k u p A. Höcker – The Hadronic Contribution to (g–2)

  46. Changes in the Input Data ee data : problems found by CMD-2 Collaboration in their analysis : 2.2-2.7% luminosity correction from change in Bhabha 1.2-1.4% change in  both changes affect event separation ee /  /  0.6% systematic error unchanged (!)  and  contributions re-evaluated (new SND, corrected CMD-2)  data : no change (precision improved slightly with new L3 result on B0) A. Höcker – The Hadronic Contribution to (g–2)

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