# Muon Capture in Deuterium

## TL;DR

This paper investigates the theoretical model dependence of negative muon capture rates in deuterium using potential models, meson exchange currents, and effective field theory, aiming to extract a key low energy constant.

## Contribution

It provides a comparative analysis of different theoretical approaches to determine the low energy constant ^R in muon capture in deuterium.

## Key findings

- Capture rates can be calculated consistently with potential models and meson exchange currents.
- The low energy constant ^R is extracted from the analysis of the doublet transition rate.
- The study highlights the model dependence and the role of effective field theory in muon capture calculations.

## Abstract

Model dependence of the capture rates of the negative muon capture in deuterium is studied starting from potential models and the weak two-body meson exchange currents constructed in the tree approximation and also from an effective field theory. The tree one-boson exchange currents are derived from the hard pion chiral Lagrangians of the $N \Delta \pi \rho \omega a_1$ system. If constructed in conjunction with the one-boson exchange potentials, the capture rates can be calculated consistently. On the other hand, the effective field theory currents, constructed within the heavy baryon chiral perturbation theory, contain a low energy constant $\hat d ^R$ that cannot be extracted from data at the one-particle level nor determined from the first principles. Comparative analysis of the results for the doublet transition rate allows us to extract the constant $\hat d ^R$.