Bound muon decay spectrum in the leading logarithmic accuracy

TL;DR

This paper calculates the main radiative corrections to the electron spectrum in bound muon decay with leading logarithmic accuracy, improving theoretical predictions relevant for experimental searches for new physics.

Contribution

It provides the first comprehensive calculation of logarithmically enhanced radiative corrections across the entire spectrum in bound muon decay.

Findings

Corrected spectrum aligns well with TWIST experimental results.

Theoretical error is mainly due to nuclear charge distribution uncertainties.

Measurement below the New Physics window can reduce theoretical uncertainties.

Abstract

We compute the dominant, logarithmically enhanced radiative corrections to the electron spectrum in the bound muon decay in the whole experimentally interesting range. The corrected spectrum fits well the TWIST results. The remaining theoretical error, dominated by the nuclear charge distribution, can be reduced in the muon-electron conversion searches by measuring the spectrum slightly below the New Physics signal window.