  The doublet capture rate of the negative muon capture in deuterium is
calculated employing the nuclear wave functions generated from accurate
nucleon-nucleon potentials constructed at next-to-next-to-next-to-leading order
of heavy-baryon chiral perturbation theory and the weak meson exchange current
operator derived within the same formalism. All but one of the low-energy
constants that enter the calculation were fixed from pion-nucleon and
nucleon-nucleon scattering data. The low-energy constant d^R (c_D), which
cannot be determined from the purely two-nucleon data, was extracted recently
from the triton beta-decay and the binding energies of the three-nucleon
systems. The calculated values of the doublet capture rates show a rather large
spread for the used values of the d^R. Precise measurement of the doublet
capture rate in the future will not only help to constrain the value of d^R,
but also provide a highly nontrivial test of the nuclear chiral EFT framework.
Besides, the precise knowledge of the constant d^R will allow for consistent
calculations of other two-nucleon weak processes, such as proton-proton fusion
and solar neutrino scattering on deuterons, which are important for
astrophysics.
