The muon g−2

Abstract

The muon anomalous magnetic moment is one of the most precisely measured quantities in particle physics. In a recent experiment at Brookhaven it has been measured with a remarkable 14-fold improvement of the previous CERN experiment reaching a precision of 0.54ppm. Since the first results were published, a persisting "discrepancy" between theory and experiment of about 3 standard deviations is observed. It is the largest "established" deviation from the Standard Model seen in a "clean" electroweak observable and thus could be a hint for New Physics to be around the corner. This deviation triggered numerous speculations about the possible origin of the "missing piece" and the increased experimental precision animated a multitude of new theoretical efforts which lead to a substantial improvement of the prediction of the muon anomaly aµ = (gµ − 2)/2. The dominating uncertainty of the prediction, caused by strong interaction effects, could be reduced substantially, due to new hadronic cross section measurements in electron-positron annihilation at low energies. Also the recent electron g − 2 measurement at Harvard contributes substantially to the progress in this field, as it allows for a much more precise determination of the fine structure constant α as well as a cross check of the status of our theoretical understanding.In this report we review the theory of the anomalous magnetic moments of the electron and the muon. After an introduction and a brief description of the principle of the muon g − 2 experiment, we present a review of the status of the theoretical prediction and in particular discuss the role of the hadronic vacuum polarization effects and the hadronic light-by-light scattering correction, including a new evaluation of the dominant pion-exchange contribution. In the end, we find a 3.2 standard deviation discrepancy between experiment and Standard Model prediction. We also present a number of examples of how extensions of the electroweak Standard Model would change the theoretical prediction of the muon anomaly aµ. Perspectives for future developments in experiment and theory are briefly discussed and critically assessed. The muon g − 2 will remain one of the hot topics for further investigations.

Baryons as relativistic three-quark bound states

“…In any case, even if the smaller radius turned out to be the correct one this does still not explain the larger radius inferred from atomic spectroscopy. The second and third explanations, on the other hand, highlight the similarity of the proton radius puzzle with the muon g-2 problem [684]. In both cases it is the muon measurement that deviates from the established or expected result.…”

“…Its experimental value is extremely precisely measured but differs from the Standard Model prediction by 3σ. The main uncertainties enter through QCD via the hadronic vacuum polarisation and HLbL amplitude, with a typical theoretical estimate a HVP µ = 685.1(4.3) × 10 −10 and a HLbL µ = 11.6(3.9) × 10 −10 [684]. Although they are much smaller than the QED corrections they dominate the theoretical uncertainty by far.…”

Predictions for the neutrino parameters in the minimal gauged $$\hbox {U}(1)_{L_\mu -L_\tau }$$ U ( 1 ) L μ - L τ model

“…An attractive feature of this a e-mail: asai@hep-th.phys.s.u-tokyo.ac.jp class of models is that the muon g − 2 anomaly [5][6][7][8] may be explained by the loop contribution of the U(1) L μ −L τ gauge boson if its mass lies around the weak scale or lower [9][10][11][12], though this possibility is severely restricted by the searches of the neutrino trident production process [13][14][15][16]. These models may also explain anomalies in flavor physics [15,17] and offer promising candidates for dark matter in the Universe [18][19][20][21][22].…”

Pseudoscalar meson transition form factors in nonperturbative QCD approach

“…The theoretical studies of the muon AMM g − 2 (see for review [6][7][8][9][10]), the rare decays of light pseudoscalar mesons into lepton pairs [5,[11][12][13][14] and the comparison with the experimental results, offer an important low-energy tests of the SM.…”