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.

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 $\hat d ^R$.