Calculation of doublet capture rate for muon capture in deuterium within chiral effective field theory

Abstract The doublet capture rate Λ 1 / 2 of the negative muon capture in deuterium is calculated employing the nuclear wave functions generated from accurate nucleon–nucleon ( NN ) 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 ˆ R ( c D ), which cannot be determined from the purely two-nucleon data, was extracted recently from the triton β -decay and the binding energies of the three-nucleon systems. The calculated values of Λ 1 / 2 show a rather large spread for the used values of the d ˆ R . Precise measurement of Λ 1 / 2 in the future will not only help to constrain the value of d ˆ R , but also provide a highly nontrivial test of the nuclear chiral EFT framework. Besides, the precise knowledge of the constant d ˆ 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.