Challenges for an axion explanation of the muon $g-2$ measurement

TL;DR

This paper critically examines the viability of axion-like particles as an explanation for the muon g-2 anomaly, highlighting significant theoretical and phenomenological challenges that undermine this hypothesis.

Contribution

It provides an updated analysis of axion couplings, including two-loop effects, and discusses the difficulties in generating these couplings at low scales with minimal new matter.

Findings

Axion decay constant must be around tens of GeV, conflicting with the need for low-scale coupling generation.

Scenarios require new charged matter at or below the weak scale and Higgs-mixing scalars, posing phenomenological issues.

Additional contributions to muon g-2 from these models challenge the validity of the axion effective theory.

Abstract

The discrepancy between the muon $g-2$ measurement and the Standard Model prediction points to new physics around or below the weak scale. It is tantalizing to consider the loop effects of a heavy axion (in the general sense, also known as an axion-like particle) coupling to leptons and photons as an explanation for this discrepancy. We provide an updated analysis of the necessary couplings, including two-loop contributions, and find that the new physics operators point to an axion decay constant on the order of 10s of GeV. This poses major problems for such an explanation, as the axion couplings to leptons and photons must be generated at low scales. We outline some possibilities for how such couplings can arise, and find that these scenarios predict new charged matter at or below the weak scale and new scalars can mix with the Higgs boson, raising numerous phenomenological challenges. These scenarios also all predict additional contributions to the muon $g-2$ itself, calling the initial application of the axion effective theory into question. We conclude that there is little reason to favor an axion explanation of the muon $g-2$ measurement relative to other models postulating new weak-scale matter.