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 $\hat{I}¼\to e\hat{I}½\bar{\hat{I}}½{\hat{I}}^3$ and the radiative decays $\ddot{I}„\to e\hat{I}½\bar{\hat{I}}½{\hat{I}}^3$ and $\ddot{I}„\to \hat{I}¼\hat{I}½\bar{\hat{I}}½{\hat{I}}^3$ 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 $\mathcal{B}(\ddot{I}„\to e\hat{I}½\bar{\hat{I}}½{\hat{I}}^3)$ and the Standard Model prediction. In addition, we study various distributions of the process $\hat{I}¼\to e\hat{I}½\bar{\hat{I}}½{\hat{I}}^3$ and obtain precise predictions for the irreducible background to $\hat{I}¼\to e{\hat{I}}^3$ searches, tailored to the geometry of the MEG detector.

14 pages, 5 figures, published version