Can Galileons solve the muon problem?

TL;DR

This paper investigates whether galileon theories can address the muon problem by analyzing their effects on leptonic bound states and concludes that current constraints make it unlikely.

Contribution

It provides new bounds on galileon contributions to the muonic hydrogen Lamb shift using leptonic bound state data and lepton compositeness constraints.

Findings

Galileon effects are incompatible with experimental bounds unless the scale exceeds 1.33 GeV.

Current constraints prevent galileons from solving the muon problem.

Future measurements of true muonium could tighten these bounds.

Abstract

The leptonic bound states positronium and muonium are used to constrain galileon contributions to the Lamb shift of muonic hydrogen. Through the application of a variety of bounds on lepton compositeness, it is shown that either the assumption of equating the charge radius of a particle with its galileon scale radius is incompatible with experiments or the scale of galileons must be $M>1.33$ GeV, too large to solve the muon problem. The possibility of stronger constraints in the future from true muonium are discussed.