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.

6 pages, 1 figure, Changed to match journal version

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• One-loop corrections to vector Galileon theory
• Hadronic Vacuum Polarization in True Muonium
• Discovering True Muonium in $K_L\to ({\mu }^{+}{\mu }^{-})\gamma$
• Stars disformally coupled to a shift-symmetric scalar field
• Hyperfine Splitting in True Muonium to $\mathcal{O}(m_{\mu }{\alpha }^6)$: Two Photon Annihilation Contribution from Other Flavors
• High Resolution Nonperturbative Light-Front Simulations of the True Muonium Atom
• Applying Bayesian Inference to Galileon Solutions of the Muon Problem
• Nonperturbative True Muonium on the Light Front with TMSWIFT