The anomalous magnetic moment of the muon in the Standard Model

Abstract

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant α and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including O(α 5 ) with negligible numerical uncertainty. The electroweak contribution is suppressed by (m µ /M W ) 2 and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at O(α 2 ) and is due to hadronic vacuum polarization, whereas at O(α 3 ) the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads a SM µ = 116 591 810(43) × 10 −11 and is smaller than the Brookhaven measurement by 3.7σ. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

Light-quark contribution to the leading hadronic vacuum polarization term of the muon g−2 from twisted-mass fermions

“…There are a number of complementary theoretical efforts underway to better understand and quantify these hadronic corrections, including dispersive methods, lattice QCD, and effective field theories, as well as a number of different experimental efforts to provide inputs to dispersive, datadriven evaluations. A concerted effort of the theory community to improve upon and scrutinize the existing SM results has been made possible thanks to the formation of the Muon 𝑔 − 2 Theory Initiative and a Whitepaper summarizing the current theory status has been recently finalized [8]. The main outcome is that for 𝑎 HVP 𝜇 the overall lattice precision is not yet competitive with respect to the one of the dispersive results, while recent lattice estimates of the HLbL term are consistent with the phenomenological and dispersive findings within the current level of precision and rule out the HLbL contribution as an explanation for the current tension between theory and experiment.…”

Muon g-2 and other observables in models with extended Higgs and matter sectors

“…Thus, the 4.2σ anomaly, ∆a exp µ ≡ a exp µ − a SM µ = (2.51 ± 0.59) × 10 −9 [1,2], points to a multi-TeV scale of new physics for order one couplings, and it extends to about 50 TeV for couplings close to the perturbativity limit.…”

Constraining Light Mediators via Detection of Coherent Elastic Solar Neutrino Nucleus Scattering

“…The Muon (g − 2) Collaboration at Fermi National Laboratory [83] has just published a new result on the anomalous muon magnetic moment, and when combined with the old result from Brookhaven National Laboratory [84], induces 4.2σ inconsistency with the SM prediction [85]. Among the numerous and diverse solutions [86,87] to the muon (g − 2) anomaly, the light vector mediator with the L µ − L τ gauge symmetry is regarded as a viable and simple model [88][89][90][91].…”