The high energy spectrum of internal positrons from radiative muon capture on nuclei

TL;DR

This paper investigates the high-energy internal positron spectrum from radiative muon capture on nuclei, linking it to the real photon spectrum to better understand backgrounds in muon-to-positron conversion experiments.

Contribution

It establishes a relationship between the internal positron spectrum and the real photon spectrum in radiative muon capture, aiding background estimation for lepton number violation searches.

Findings

The internal positron spectrum near the endpoint can be derived from the real photon spectrum.

This relationship helps in modeling backgrounds for muon conversion experiments.

The work provides a theoretical framework connecting nuclear physics to experimental backgrounds.

Abstract

The Mu2e and COMET collaborations will search for nucleus-catalyzed muon conversion to positrons ($\mu^-\rightarrow e^+$) 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 $e^+ e^-$ pair "externally" in surrounding material, or 2) a virtual photon mediates the production of an $e^+e^-$ 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 non-trivial nuclear physics.