Muon capture on the deuteron in chiral effective field theory

Abstract

We consider the capture of a muon on a deuteron. An uncertainty analysis of the dominant channels is important for a careful analysis of forthcoming experimental data. We quantify the theoretical uncertainties of chiral effective-field-theory predictions of the muon-deuteron capture rate from the relevant neutron-neutron partial wave channels in the final state. We study the dependence on the cutoff used to regularize the interactions, low-energy constants calibrated using different fitting data and strategies, and truncation of the effective-field-theory expansion of the currents. Combining these approaches gives as an estimate of ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\mu}d}^{1/2}=399.1\ifmmode\pm\else\textpm\fi{}7.6\ifmmode\pm\else\textpm\fi{}4.4\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for capture from the atomic doublet state, and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\mu}d}^{3/2}=12.31\ifmmode\pm\else\textpm\fi{}0.47\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for capture from the quartet state and the first and second uncertainties given here are due to the effective field theory truncation error and the uncertainty in the axial radius, respectively.