Muon Magnetic Moment Workshop Glasgow 25th October 2007

Eduardo de Rafael

CPT, CNRS-Luminy

Standard Model Prediction of the Muon Anomaly Electroweak and Hadronic Light-by-Light Contributions

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

Electroweak Contributions to Lowest Order

Effective Fermi Theory:

Electroweak Theory

Bardeen, Gastmans, Lautrup ’72;

Altarelli, Cabbibo, Maiani ’72; Jackiw, Weinberg’ 72Bars, Yoshimura ’72; Fujikawa, Lee, Sanda ‘72

Jarlskog ‘71

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

Fermionic Contributions:

Czarnecki, Krause , Marciano ‘95

Contribution from

Peris, Perrottet, de Rafael ‘ 95Czarnecki, Krause , Marciano ‘95

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

In QCD (both pQCD and full physical vacuum QCD):

Vainshtein’s theorem (pQCD):

Theoretical Comments on the Z Triangle

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

Melnikov, Vainshtein ‘03

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:

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)