Can Galileons solve the muon problem?

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.