Muon Magnetic Moment Workshop
Glasgow 25th October 2007
Standard Model Prediction of the Muon Anomaly
Electroweak and Hadronic Light-by-Light Contributions
Eduardo de Rafael
CPT, CNRS-Luminy
Summary of SM Contributions to the Muon Anomaly
Leptonic QED Contributions:
Hadronic Contributions
Vacuum Polarization (LO)
Light-by-Light Scattering
Vacuum Polarization (HO)
Electroweak Contributions
World Average Experimental Value:
Electroweak Contributions to Lowest Order
Effective Fermi Theory:
Jarlskog ‘71
Electroweak Theory
Bardeen, Gastmans, Lautrup ’72;
Altarelli, Cabbibo, Maiani ’72; Jackiw, Weinberg’ 72
Bars, Yoshimura ’72; Fujikawa, Lee, Sanda ‘72
Electroweak Contributions to Two Loops
Possible large terms of
Separation of LEPTONS and QUARKS no longer possible
Bosonic Contributions:
Czarnecki, Krause , Marciano ‘95
Heinemeyer, Stockinger, Weiglein ‘04
Gribouk, Czarnecki ‘05
Systematic expansion in: weak mixing angle,
and
Fermionic Contributions:
Czarnecki, Krause , Marciano ‘95
Contribution from
Peris, Perrottet, de Rafael ‘ 95
Czarnecki, Krause , Marciano ‘95
Contribution from
The presence of the light u,d and s quarks
spontaneous chiral-symmetry breaking
Peris, Perrottet, de Rafael ‘95
Knecht, Peris, Perrottet, de Rafael ‘02
Czarnecki, Marciano, Vainshtein ‘03
Very interesting New Theoretical issue:
pQCD
Non-Renormalization Theorems
for the non-anomalous component of VVA-triangle
Vainshtein ‘ 03
Knecht, Peris, Perrottet, de Rafael ‘04
Theoretical Comments on the gg Z Triangle
In QCD (both pQCD and full physical vacuum QCD):
Vainshtein’s theorem (pQCD):
Summary of SM Contributions to the Muon Anomaly
Leptonic QED Contributions:
Hadronic Contributions
Vacuum Polarization (LO)
Vacuum Polarization (HO)
Electroweak Contributions:
World Average Experimental Value:
Light-by-Light Scattering
Melnikov, Vainshtein ‘03
Some Further Comments on Hadronic Light-by-Light Scattering Contribution(s)
Light by Light (Knecht-Nyffeler)
Light by Light (Melnikov-Vainshtein)
More in Arkady’s and Ximo’s talks,
this afternoon !!
Notice the leading term is:
Estimates of the next-to-leading term
are all negative
Summary of SM Contributions to the Muon Anomaly
Leptonic QED Contributions:
Hadronic Contributions:
Vacuum Polarization (LO) (em-data) (2006)
Vacuum Polarization (HO) (em-data)
Light by Light (Knecht-Nyffeler)
Light by Light (Melnikov-Vainshtein)
Light by Light (my estimate)
Electroweak Contributions:
Total Standard Model Contribution:
World average experimental value:
There is then a 3.4 s discrepancy