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 → e ννγ and the radiative decays τ → e ννγ and τ → µ ννγ 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-toleading order corrections are important for addressing a tension between BaBar's recent measurement of the branching ratio B(τ → e ννγ) and the Standard Model prediction. In addition, we study various distributions of the process µ → e ννγ and obtain precise predictions for the irreducible background to µ → eγ searches, tailored to the geometry of the MEG detector.

Charged lepton flavour violating processes

“…The first five sections of this write-up are virtually identical to an earlier write-up of a talk [35]. This talk is based on the work presented in [10,12,26,31,33]…”

“…For µ → eγ and µ → 3e this is due to SM processes µ → eγνν and µ → 3eνν in the region where the neutrinos have very little energy. These processes have by now all been calculated at NLO in the electromagnetic coupling, providing reliable predictions to estimate the number of irreducible background events [9][10][11][12][13][14]. For muon conversion, an irreducible background appears through the decay of the muon in orbit.…”

Charged lepton flavor violation

“…For µ → eγ and µ → 3e this is due to SM processes µ → eγνν and µ → 3eνν in the region where the neutrinos have very little energy. These processes have by now all been calculated at NLO in the electromagnetic coupling, providing reliable predictions to estimate the number of irreducible background events [9,10,11,12,13]. For muon conversion, an irreducible background appears through the decay of the muon in orbit.…”

“…This talk is based on the work presented in [10,12,25,30] and I would like to thank my collaborators: first and foremost G. M. Pruna, as well as Y. Ulrich, A. Crivellin and S. Davidson.…”

NLO prediction for the decays $\tau \to \ell \ell'\ell' \nu \bar \nu$ and $\mu \to e e e \nu \bar\nu$

“…The Next-to-Leading Order (NLO) and Next-to-Next-to Leading Order (NNLO) corrections to the muon lifetime were calculated in [23][24][25][26], together with the final state electron's energy spectrum [27] at NNLO, and the tree-level corrections induced by the W -boson propagator [28,29]. Concerning the radiative and the rare muon and tau decays, many tree-level calculations were presented in the last decades [9,14,26,[30][31][32][33], but only recently a complete calculation of the NLO corrections to the muon and tau radiative decays [34,35] and the rare muon five-body decays [36][37][38] were published.…”