Contribution of Nucleon Currents to Radiative Muon Capture by a Proton

Abstract

The observables for the reaction ${\ensuremath{\mu}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}n+\ensuremath{\nu}+\ensuremath{\gamma}$ are calculated for a general ($\mathrm{pn}\ensuremath{\mu}\ensuremath{\nu}$) coupling including all terms of order ($\frac{\ensuremath{\mu}}{M}$) and leading terms of order ${(\frac{\ensuremath{\mu}}{M})}^{2}$, where $\ensuremath{\mu}$ is the meson mass and $M$ the nucleon mass. The nucleon anomalous magnetic moments are handled by the inclusion of a simple Pauli term and all other virtual pion effects are omitted here. The ($\frac{\ensuremath{\mu}}{M}$) terms change the radiative capture rate by as much as 30%. Parity-nonconserving effects are decreased only slightly.