Ordinary Muon Capture in Hydrogen Reexamined

TL;DR

This paper recalculates the muon capture rate in hydrogen using advanced chiral perturbation theory, including radiative and proton-size corrections, achieving results that align well with recent experimental measurements.

Contribution

It provides a systematic, high-precision theoretical calculation of muon capture in hydrogen up to NNLO, incorporating all relevant corrections with predictive power.

Findings

Calculated capture rate $oxed{ ext{710} ext{ s}^{-1}}$ with small uncertainty

Results agree with recent high-precision experimental data

Demonstrates predictive capability of chiral perturbation theory for low-energy processes

Abstract

The rate of muon capture in a muonic hydrogen atom is calculated in heavy-nucleon chiral perturbation theory up to next-to-next-to leading order. To this order, we present the systematic evaluation of all the corrections due to the QED and electroweak radiative corrections and the proton-size effect. Since the low-energy constants involved can be determined from other independent sources of information, the theory has predictive power. For the hyperfine-singlet $\mu p$ capture rate $\Gamma_0$, our calculation gives $\Gamma_0=710 \,\pm 5\,s^{-1}$, which is in excellent agreement with the experimental value obtained in a recent high-precision measurement by the MuCap Collaboration.