Fully differential NLO predictions for rare and radiative lepton decays

TL;DR

This paper introduces a Monte Carlo program for precise NLO calculations of rare and radiative lepton decays, crucial for background analysis in lepton flavor violation searches and high-precision measurements.

Contribution

It provides the first general-purpose NLO Monte Carlo tool for muon and tau decays, including fully differential corrections and branching ratio predictions.

Findings

NLO QED corrections are around 10%.

The program aids in background discrimination in LFV experiments.

It highlights the importance of differential corrections in precision measurements.

Abstract

We present a general purpose, parton-level Monte Carlo program for the calculation of the radiative ($L\to\nu\bar\nu l+\gamma$) and rare ($L\to\nu\bar\nu l'+ l^+l^-$) muon and tau decays at NLO in the effective Fermi theory. In the case of muon, these processes are irreducible Standard Model backgrounds to searches for lepton flavour violation at the PSI experiments MEG and Mu3e as they become indistinguishable from the corresponding signals when the neutrinos carry little energy. Furthermore, we argue that fully differential NLO corrections are very important for the analysis of measurements aiming at the percent level or better. This is especally true if very stringent phase-space cuts are applied. To illustrate this, we use a tension between BaBar's recent measurement of the radiative tau decay and the Standard Model prediction as an example of such an analysis. Finally, we present the branching ratios of the rare tau decay $\tau\to\nu\bar\nu l' l^+l^-$ at NLO. We generally find that QED corrections of $\mathcal{O}(10\%)$ are very well possible.