Partial muon capture rates in $A=3$ and $A=6$ nuclei with chiral effective field theory

TL;DR

This paper presents ab initio calculations of muon capture rates in light nuclei using chiral effective field theory, providing insights into nuclear matrix elements relevant for neutrinoless-double beta decay research.

Contribution

It introduces a novel application of chiral effective field theory to compute muon capture rates in $^3$He and $^6$Li with advanced Monte Carlo methods, including analysis of three-nucleon interactions.

Findings

Capture rates are sensitive to three-nucleon forces.

Regularization cutoffs significantly affect results.

Energy range of scattering data impacts interaction fits.

Abstract

Searches for neutrinoless-double beta decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless-double beta decays take place at momentum transfers on the order of 100 MeV/$c$ and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate these currents. In this work, we present results of {\it ab initio} calculations of partial muon capture rates for $^3$He and $^6$Li nuclei using variational and Green's Function Monte Carlo computational methods. We estimate the impact of the three-nucleon interactions, the cutoffs used to regularize two-nucleon ($2N$) interactions, and the energy range of $2N$ scattering data used to fit these interactions.