Fully differential NLO predictions for the radiative decay of muons and taus

Abstract

We present a general purpose Monte Carlo program for the calculation of the radiative muon decay $μ\to e\,ν\barνγ$ and the radiative decays $τ\to e\, ν\barνγ$ and $τ\toμ\,ν\barνγ$ at next-to-leading order in the Fermi theory. The full dependence on the lepton masses and polarization of the initial-sate lepton are kept. We study the branching ratios for these processes and show that fully-differential next-to-leading order corrections are important for addressing a tension between BaBar's recent measurement of the branching ratio $\mathcal{B}(τ\to e\, ν\barνγ)$ and the Standard Model prediction. In addition, we study various distributions of the process $μ\to e\,ν\barνγ$ and obtain precise predictions for the irreducible background to $μ\to e γ$ searches, tailored to the geometry of the MEG detector.