High-precision muon decay predictions for ALP searches

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 $X$.

arXiv comment37 pages, 14 figures, published version

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• Searching for new physics at $\mu \to e$ facilities with ${\mu }^{+}$ and ${\pi }^{+}$ decays at rest
• A compact frozen-spin trap for the search for the electric dipole moment of the muon
• Improved muon decay simulation with McMule and Geant4
• Direct Detection of Ultralight Dark Matter via Charged Lepton Flavor Violation
• Looking for an axion in a haystack of muons
• Loop-Level Lepton Flavor Violation and Diphoton Signals in the Minimal Left-Right Symmetric Model