Hadronic corrections to muon anomalous magnetic moment within the instanton liquid model

Abstract

The current status of the muon anomalous magnetic moment problem is briefly presented. The corrections to muon anomaly coming from the effects of hadronic vacuum polarization, Z * γγ * effective vertex and light-by-light scattering are estimated within the instanton model of QCD vacuum. The study of anomalous magnetic moments (AMM) of leptons, a = (g S −2)/2, have played an important role in the development of the standard model (SM). At present accuracy the electron AMM due to small electron mass is sensitive only to quantum electrodynamic (QED) contributions. The theoretical error [1] is dominated by the uncertainty in the input value of the QED coupling α ≡ e 2 /(4π). Thus, the electron AMM provides the best observable for determining the fine coupling constant α −1 = 137.035 998 83(51).(Compared to the electron, the muon AMM has a relative sensitivity to heavier mass scales which is typically proportional to (m µ /m e ) 2 . 1 At present level of accuracy, the muon AMM gives an experimental sensitivity to virtual W and Z gauge bosons as well as a potential sensitivity to other, as yet unobserved, particles in the few hundred GeV/c 2 mass range. The muon AMM is known to an unprecedented accuracy of order of 1 ppm. The * Presented at XLV Cracow School of Theoretical Physics, Zakopane, Poland June 3-12, 2005. 1 The τ -lepton AMM due to τ 's highest mass is the best for searching for manifestation of effects beyond SM, however, τ -lepton is short living particle, so it is not easy to make experiment with good enough accuracy.(1)

Standard Model Predictions for the Muon

“…Let us hope that progress of theory will allow a calculation of a had µ from first principles (QCD, Lattice). One can mention here a new approach in the QCD instanton model [ 68] or calculations on the lattice, where there are encouraging estimates of a had,LO µ , e.g., [ 69] (667 ± 20) · 10 −10 or attempts to estimate a had,LBL µ [ 70], see also Ref. [ 71] discussing successes and difficulties of this approach.…”

Standard Model Prediction for the Muon Anomalous Magnetic Moment

“…One can mention here a new approach in the QCD instanton model [38] or calculations on the lattice [39].…”