Isotope dependence of muon decay in orbit

TL;DR

This paper calculates the electron-energy spectra from muon decay in orbit across all stable isotopes to improve background understanding for upcoming muon-to-electron conversion experiments.

Contribution

It provides precise calculations of muon decay spectra in orbit for all stable isotopes, accounting for nuclear charge distribution uncertainties, aiding experimental background analysis.

Findings

Spectra calculated for all stable isotopes.

Uncertainty estimates due to nuclear charge distribution.

Results support background studies for future experiments.

Abstract

The decay $\mu^-\to e^- \bar{\nu}_e\nu_\mu$ of a muon that is bound to a nucleus poses an unavoidable background for experiments such as Mu2e, COMET, and DeeMe searching for lepton-flavor-violating $\mu^-\to e^-$ conversion and thus requires a precise understanding. We calculate the electron-energy spectra of muon decays in orbit near the electron energy endpoint for all stable isotopes and estimate uncertainties due to the nuclear charge distribution. Our results enable background studies of mixed or enriched target materials that are necessary for the next generation of $\mu^-\to e^-$ conversion experiments.