High energy spectrum of internal positrons from radiative muon capture on nuclei

Abstract

The Mu2e and COMET collaborations will search for nucleus-catalyzed muon conversion to positrons (${\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}$) as a signal of lepton number violation. A key background for this search is radiative muon capture where either (1) a real photon converts to an ${e}^{+}{e}^{\ensuremath{-}}$ pair ``externally'' in surrounding material, or (2) a virtual photon mediates the production of an ${e}^{+}{e}^{\ensuremath{-}}$ pair ``internally.'' If the ${e}^{+}$ has an energy approaching the signal region then it can serve as an irreducible background. In this work we describe how the near end point internal positron spectrum can be related to the real photon spectrum from the same nucleus, which encodes all nontrivial nuclear physics.