The $\mu^-d$ capture rate in effective field theory

Abstract

Muon capture on the deuteron is studied in heavy baryon chiral perturbation theory (HBChPT). It is found that by far the dominant contribution to $\mu d$ capture comes from a region of the final three-body phase-space in which the energy of the two neutrons is sufficiently small for HBChPT to be applicable. The single unknown low-energy constant having been fixed from the tritium beta decay rate, our calculation contains no free parameter. Our estimate of the $\mu d$ capture rate is consistent with the existing data. The relation between $\mu d$ capture and the $\nu d$ reactions, which are important for the SNO experiments, is briefly discussed.