High-precision muon decay predictions for ALP searches

TL;DR

This paper provides highly precise theoretical predictions for muon decay spectra, including advanced corrections and resummations, to improve searches for rare muon decays involving axion-like particles in experiments.

Contribution

It introduces an improved calculation of the muon decay spectrum with higher-order corrections and resummations, enhancing the accuracy for experimental searches.

Findings

Enhanced precision in muon decay spectrum predictions.

Quantified the impact of theoretical uncertainties on experimental sensitivities.

Provided tools for better interpretation of muon decay experiments.

Abstract

We present an improved theoretical prediction of the positron energy spectrum for the polarised Michel decay $\mu^+\to e^+ \nu_e\bar{\nu}_\mu$. In addition to the full next-to-next-to-leading order correction of order $\alpha^2$ in the electromagnetic coupling, we include logarithmically enhanced terms at even higher orders. Logarithms due to collinear emission are included at next-to-leading accuracy up to order $\alpha^4$. At the endpoint of the Michel spectrum, soft photon emission results in large logarithms that are resummed up to next-to-next-to-leading logarithmic accuracy. We apply our results in the context of the MEG II and Mu3e experiments to estimate the impact of the theory error on the branching ratio sensitivity for the lepton-flavour-violating decay $\mu^+\to e^+ X$ of a muon into an axion-like particle $X$.