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. . . . hadrons. The Muon g – 2 Challenging e + e – and Tau Spectral Functions. Andreas Hoecker ( * ) (CERN) Moriond QCD and High Energy Interactions, La Thuile, Italy, 8 – 15 March, 2008. The “Problem”. QED. Hadronic. Weak. SUSY. The Muon Anomalous Magnetic Moment.

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hadrons

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  1.    hadrons The Muon g–2 Challenging e+e– and Tau Spectral Functions Andreas Hoecker(*) (CERN) Moriond QCD and High Energy Interactions, La Thuile, Italy, 8 – 15 March, 2008 A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  2. The “Problem” A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  3. QED Hadronic Weak SUSY... The Muon Anomalous Magnetic Moment • Diagrams contributing to the magnetic moment ... or some unknown type of new physics ? A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  4. Experimental Progress: from CERN to BNL Miller-de Rafael-Roberts, Rept.Prog.Phys.70:795,2007 [ hep-ex/0602035]  Current world average:aexp=11 659 208.0 ± 5.4 ± 3.3 × 10–10 Dominated by by BNL-E821: [PRD73(06)072003, hep-ex/0602035] A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  5. Confronting Experiment with Theory The Standard Model prediction of a is decomposed in its main contributions: of which the hadronic contribution has the largest uncertainty A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  6. had  Dispersion relation, uses unitarity (optical theorem) and analyticity  had ... (see digression)   The Hadronic Contribution to (g–2) Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD (“first principles”) – but:we can use experiment (!) A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  7. digression: 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 ... and equivalently for a [had] ... and equivalently for a [had] A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  8. Panoramic View of Inputs to Dispersion Integral use data Agreement between Data (BES) and pQCD (within correlated systematic errors) QCD use QCD A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  9. Contributions to the Dispersion Integrals 2 3 (+,) 4 > 4 (+KK) 1.8 - 3.7 3.7 - 5 (+J/, ) 5 - 12 (+) 12 -  < 1.8 GeV ahad,LO 2 2[ahad,LO] 2 A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  10. W e m u s t c o n c e n t r a t e o n 2 - p i o n C h a n n e l A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  11. Overview of e+e– +–() Data DEHZ preliminary update ICHEP 06 DEHZ 03  ISR Novosibirsk & Orsay experiments: Energy scan method KLOE at DAΦNE: Radiative return method e+ hadrons e A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  12. e+e– Radiative Corrections Desired measured e+e– cross sections: with FSR included but ISR & VP corrected • 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 procedure) • Initial state radiation (ISR) • corrected by experiments • Final state radiation (FSR) [need e+e–  hadrons () in disp. 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. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  13. Comparing e+e– +–() Data Green band corresponds to combined data used in the numerical integration Good agreement in general – varying precision  Need to see ratio plots to appreciate differences A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  14. Comparison of Recent e+e– +–() Data CMD2 & KLOE measurements compared to fit to SND data CMD2 / SND KLOE / SND Relative systematic error of SND Whereas CMD2 and SND are in good agreement, KLOE shows a significantly different energy dependence.  Needs clarification before using KLOE data A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  15. U s i n g a l s o T a u D a t a v i a t h e c o n s e r v e d v e c t o r c u r r e n t A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  16. Using also Tau 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 : Isospin symmetry connects I =1 e+e– cross section to vectorspectral functions: Experimentally:  and e+e– data are complementary with resp. to normalisation and shape uncertainties branching fractionsmass spectrum kinematic factor (PS) A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  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% • Radiative corrections:SEW ~ 2% (short distance), GEM(s) (long distance) • Charged/neutral mass splitting: m –  m 0, - mixing, m, –  m,0 • Electromagnetic decays:    ,    ,    ,   l+l – • Quark mass difference: mu  md negligible Marciano-Sirlin’ 88 Braaten-Li’ 90 Cirigliano-Ecker-Neufeld’ 02 Alemany-Davier-Höcker 97, Czyż-Kühn’ 01 A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  18. Comparing e+e– +– and ––0 e+e– data corrected for vacuum polarisation and initial state radiation Correct  data for missing - mixing (taken from BW fit) and all other SU(2)-breaking sources Remarkable agreement But: not good enough... ... A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  19. The Problem Relative difference between  and e+e– data (form factors) z o o m zoom  Clear difference on s dependence in particular for s at 0.7 – 1.0 GeV2 A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  20. Another Way to Look at the Data Infer branching fractions (more robust than spectral functions) from e+e– data: Difference: BR[ ] – BR[e+e– (CVC)]: e+e– data for  –  +  0 0 not satisfactory A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  21. Results: the Compilation (including newest data) Contributions to ahad,LO[in 10–10]from the different energy domains: A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  22. And the Complete Result DEHZ (Tau 2006) BNL E821 (2004): aexp = (11 659 208.0  6.3) 1010 Observed Difference with Experiment: A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  23. c o m m e n t s a n d p e r s p e c t i v e s A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  24. c o m m e n t s • Will the tau-based result still move ? • Tau spectral functions unchanged: final results from ALEPH, CLEO, OPAL • Waiting for final Belle results, BABAR forthcoming • Revisiting SU(2)-breaking corrections: • Improved long-distance correction GEM(s) [ vertex,  not accounted for previously] • → decays: large effects from soft/virtual ’s: (0 – ±)  1.8 MeV ! • Re-evaluation of expected effects from pion and rho mass and width differences; improved estimate of – mixing available • [ Suggestion to compare “dressed” quantities did not enthuse theorists ] • Expected improvements should reduce tau-based result by  – 1010–10 • Improvements for e+e–: • Awaiting BABAR’s ISR result, and normalised result from KLOE A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  25. a p p e n d i x (A) t h e B A B A R I S R p r o g r a m m e A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  26. ISR Rsdiative Return Cross Section Results from BABAR • 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. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  27. The e+e–+–0 Cross Section • Cross section above  resonance : DM2 missed a resonance ! compatible with (1650) [m  1.65 GeV,   0.22 GeV] SND BABAR DM2 contribution to ahad (<1.8 GeV) : • all before BABAR [10–10] 2.45  0.26  0.03 • all + BABAR [10–10] 2.79  0.19  0.01 • all + BABAR – DM2 [10–10] 3.25  0.09  0.01 A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  28. The e+e–2+2– Cross Section Good agreement with direct ee measurements Most precise result above 1.4 GeV contribution to ahad (<1.8 GeV) • all before BABAR [10–10] 14.20  0.87  0.24 • all + BABAR [10–10] 13.09  0.44  0.00 A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  29. BaBar ISR: 33 BABAR BABAR contribution to ahad (<1.8 GeV) : • all before BABAR [10–10] 0.10  0.10 • all + BABAR [10–10] 0.108  0.016 A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  30. BABAR ISR: 222 BABAR BABAR contribution to ahad (<1.8 GeV) : • all before BABAR [10–10] 1.42  0.30  0.03 • all + BABAR [10–10] 0.89  0.09 A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  31. a p p e n d i x (B) P r e l i m i n a r y r e s u l t s f r o m B e l l e A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

  32. digression: Preliminary – –0 Results from Belle • Preliminary spectral function presented by Belle at EPS 2005 • High statistics: see significant dip at 2.4 GeV2 for first time in  data ! • Discrepancies with ALEPH/CLEO at large mass and with e+e– data at low mass A. Hoecker: Muon g – 2: Tau and e+e– spectral functions

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