Muon capture on the deuteron in chiral effective field theory

TL;DR

This paper calculates the muon capture rate on deuterons using chiral effective field theory, providing uncertainty estimates crucial for interpreting upcoming experimental results.

Contribution

It offers a detailed uncertainty analysis of muon-deuteron capture rates within chiral EFT, including cutoff, low-energy constants, and truncation effects.

Findings

Capture rate from doublet state: 399.1 ± 7.6 ± 4.4 s⁻¹

Capture rate from quartet state: 12.31 ± 0.47 ± 0.04 s⁻¹

Quantified theoretical uncertainties for upcoming experiments.

Abstract

We consider the capture of a muon on a deuteron. An uncertainty analysis of the dominant channels is important for a careful analysis of forthcoming experimental data. We quantify the theoretical uncertainties of chiral effective-field-theory predictions of the muon-deuteron capture rate from the relevant neutron-neutron partial wave channels in the final state. We study the dependence on the cutoff used to regularize the interactions, low-energy constants calibrated using different fitting data and strategies, and truncation of the effective-field-theory expansion of the currents. Combining these approaches gives as an estimate of $\Gamma^{1/2}_{\mu d} = 399.1 \pm 7.6 \pm 4.4$ s$^{-1}$ for capture from the atomic doublet state, and $\Gamma^{3/2}_{\mu d} = 12.31 \pm 0.47 \pm 0.04$ s$^{-1}$ for capture from the quartet state.