Can galileons solve the muon problem?

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 is discussed. [ABSTRACT FROM AUTHOR]