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 ${\Gamma }_{\mu d}^{1/2}=399.1\pm 7.6\pm 4.4$ s${}^{-1}$ for capture from the atomic doublet state, and ${\Gamma }_{\mu d}^{3/2}=12.31\pm 0.47\pm 0.04$ s${}^{-1}$ for capture from the quartet state.

Comments: 17 pages, 3 figures