Looking for an axion in a haystack of muons

The search for axion-like particles $X$ in muon decays is an excellent opportunity for the MEG II and Mu3e experiments to extend their horizons beyond ${\mu }^{+}\to e^{+}\gamma$ and ${\mu }^{+}\to e^{+}{e}^{-}{e}^{+}$. A suitable process for both experiments is the two-body decay ${\mu }^{+}\to e^{+}X$, whose only signature is a monochromatic peak close to the kinematic endpoint of the positron energy spectrum of the ${\mu }^{+}\to e^{+}{\nu }_e{\bar{\nu }}_{\mu }$ background. The hunt for such an elusive signal in a vast amount of irreducible background requires extremely accurate theoretical predictions to be implemented in a Monte Carlo event generator. This work presents a new state-of-the-art computation of ${\mu }^{+}\to e^{+}{\nu }_e{\bar{\nu }}_{\mu }$ for polarised muons, accomplished with the McMule framework. The calculation includes next-to-next-leading order QED corrections and logarithmically enhanced terms at even higher orders. The results are also used to estimate the sensitivity of both experiments on the branching ratio of ${\mu }^{+}\to e^{+}X$, in order to evaluate the impact of the theoretical error.