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High-precision muon decay predictions for ALP searches

by Pulak Banerjee, Antonio Coutinho, Tim Engel, Andrea Gurgone, Adrian Signer, Yannick Ulrich

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Submission summary

Authors (as registered SciPost users): Antonio Coutinho · Tim Engel · Andrea Gurgone · Adrian Signer · Yannick Ulrich
Submission information
Preprint Link: scipost_202211_00021v2  (pdf)
Code repository:
Data repository:
Date accepted: 2023-05-22
Date submitted: 2023-02-27 13:09
Submitted by: Signer, Adrian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • High-Energy Physics - Phenomenology
Approaches: Theoretical, Phenomenological


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 $X$.

Published as SciPost Phys. 15, 021 (2023)

Author comments upon resubmission

We have revised the submission following guidance from the reviewers.

List of changes

The changes we have made as a response to the reviewer's comments are listed in our replies to the report.

Reports on this Submission

Anonymous Report 2 on 2023-3-28 (Invited Report)


I want to thank the authors for their careful and detailed responses to my comments. I was also able to install and run the provided code successfully. The modified version of the paper and the authors' comments provide a clear and sufficient answer to my remarks, and the paper meets the criteria for acceptance. In particular, I agree that uncertainty is reliable for practical applications.

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Anonymous Report 1 on 2023-3-13 (Invited Report)


The second version adequately addresses all the issues arising from the referee reviews. I recommend it for publication.

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