1. Muon Magnetic Moment Workshop Glasgow 25 th October 2007 Eduardo de Rafael CPT, CNRS-Luminy Standard Model Prediction of the Muon Anomaly Electroweak and Hadronic Light-by-Light Contributions

2. Summary of SM Contributions to the Muon Anomaly Hadronic Contributions Vacuum Polarization (LO ) Leptonic QED Contributions: Vacuum Polarization (HO ) Electroweak Contributions World Average Experimental Value: Light-by-Light Scattering

3. Electroweak Contributions to Lowest Order Effective Fermi Theory: Electroweak Theory Bardeen, Gastmans, Lautrup ’72; Altarelli, Cabbibo, Maiani ’72; Jackiw, Weinberg’ 72 Bars, Yoshimura ’72; Fujikawa, Lee, Sanda ‘72 Jarlskog ‘71

4. Electroweak Contributions to Two Loops Possible large terms of Separation of LEPTONS and QUARKS no longer possible Bosonic Contributions: Czarnecki, Krause, Marciano ‘95 Gribouk, Czarnecki ‘05 Heinemeyer, Stockinger, Weiglein ‘04 Systematic expansion in: weak mixing angle, and

5. Fermionic Contributions: Czarnecki, Krause, Marciano ‘95 Contribution from Peris, Perrottet, de Rafael ‘ 95 Czarnecki, Krause, Marciano ‘95

6. Contribution from The presence of the light u,d and s quarks spontaneous chiral-symmetry breaking Very interesting New Theoretical issue: pQCD Non-Renormalization Theorems for the non-anomalous component of VVA-triangle Vainshtein ‘ 03 Peris, Perrottet, de Rafael ‘95 Knecht, Peris, Perrottet, de Rafael ‘02 Czarnecki, Marciano, Vainshtein ‘03 Knecht, Peris, Perrottet, de Rafael ‘04

7. In QCD (both pQCD and full physical vacuum QCD): Vainshtein’s theorem (pQCD): Theoretical Comments on the  Z Triangle

8. Summary of SM Contributions to the Muon Anomaly Hadronic Contributions Vacuum Polarization (LO ) Leptonic QED Contributions: Vacuum Polarization (HO ) Electroweak Contributions: World Average Experimental Value: Light-by-Light Scattering

9. Melnikov, Vainshtein ‘03

12. Some Further Comments on Hadronic Light-by-Light Scattering Contribution(s) Light by Light (Melnikov-Vainshtein) Light by Light (Knecht-Nyffeler) More in Arkady’s and Ximo’s talks, this afternoon !! Estimates of the next-to-leading term are all negative Notice the leading term is:

15. Summary of SM Contributions to the Muon Anomaly Hadronic Contributions: Vacuum Polarization (LO) (em-data) Light by Light (Knecht-Nyffeler) Total Standard Model Contribution: Leptonic QED Contributions: Vacuum Polarization (HO) (em-data) Light by Light (Melnikov-Vainshtein) Electroweak Contributions: World average experimental value: There is then a 3.4  discrepancy Light by Light (my estimate) (2006)