Radiative corrections to inverse muon decay for accelerator neutrinos

Abstract

Inverse muon decay ($\nu_\mu e^- \to \nu_e \mu^-$) is a promising tool to constrain neutrino fluxes with energies $E_{\nu} \ge 10.9~\mathrm{GeV}$. Radiative corrections introduce percent-level distortions to energy spectra of outgoing muons and depend on experimental details. In this paper, we generalize the calculation of radiative corrections in muon decay to the scattering processes $\nu_\mu e^- \to \nu_e \mu^-$ and $\bar{\nu}_e e^- \to \bar{\nu}_\mu \mu^-$. We evaluate virtual and real $\mathrm{O} \left( \alpha \right)$ contributions and present the muon energy spectrum for both channels, double-differential distributions in muon energy and muon scattering angle, in photon energy and photon scattering angle, and photon energy spectrum for the dominant $\nu_\mu e^- \to \nu_e \mu^-$ process. We discuss how radiative corrections modify experimentally interesting distributions.Comment: 21 pages, 8 figures, v2, structure changed, new cross sections adde