Calculation of Doublet Capture Rate for Muon Capture in Deuterium within Chiral Effective Field Theory

TL;DR

This paper calculates the muon capture rate in deuterium using chiral effective field theory, highlighting the importance of the low-energy constant d^R and its impact on nuclear weak processes.

Contribution

The study employs chiral EFT with nucleon-nucleon potentials and weak currents to compute muon capture rates, providing insights into the low-energy constant d^R and its role.

Findings

Calculated capture rates show large spread for different d^R values.

Future measurements can constrain d^R and test chiral EFT accuracy.

Results impact calculations of astrophysical weak processes.

Abstract

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.