Effective-field-theory predictions of the muon-deuteron capture rate

TL;DR

This paper assesses the theoretical uncertainties in chiral effective-field-theory predictions of the muon-deuteron capture rate, crucial for interpreting upcoming experimental results, by analyzing various sources of error.

Contribution

It provides a detailed quantification of the main theoretical uncertainties affecting muon-deuteron capture rate predictions using chiral effective field theory.

Findings

Uncertainty of about 4.6 s^{-1} from EFT truncation.

Uncertainty of about 3.9 s^{-1} from axial radius of the nucleon.

Uncertainties are comparable to experimental precision.

Abstract

We quantify the theoretical uncertainties of chiral effective-field-theory predictions of the muon-deuteron capture rate. Theoretical error estimates of this low-energy process is important for a reliable interpretation of forthcoming experimental results by the MuSun collaboration. Specifically, we estimate the three dominant sources of uncertainties that impact theoretical calculations of this rate: those resulting from uncertainties in the pool of fit data used to constrain the coupling constants in the nuclear interaction, those due to the truncation of the effective field theory, and those due to uncertainties in the axial radius of the nucleon. For the capture rate into the ${}^1S_0$ channel, we find an uncertainty of approximately $4.6~s^{-1}$ due to the truncation in the effective field theory and an uncertainty of $3.9~s^{-1}$ due to the uncertainty in the axial radius of the nucleon, both of which are similar in size to the targeted experimental precision.