Abstract
Using the automation program GoSam, fully differential NLO corrections were obtained for the rare decay of the muon $\mu\to e\nu\bar\nu ee$. This process is an important Standard Model background to searches of the Mu3e collaboration for lepton-flavour violation, as it becomes indistinguishable from the signal $\mu\to 3e$ if the neutrinos carry little energy. With our NLO program we are able to compute the branching ratio as well as custom-tailored observables for the experiment. With minor modifications, related decays of the tau can also be computed.
Highlights
The rare decay of the muon μ → eννee is not one of those Standard Model processes that has been in the limelight in the past decades
The branching ratio B = (3.4 ± 0.4) × 10−5 has been measured more than thirty years ago by the SINDRUM collaboration [1, 2] in the context of searches for the lepton-flavour violating process μ → 3e
For the corresponding decay τ → eννee a measurement B = (2.8 ± 1.5) × 10−5 is available from CLEO [3], but for other leptonic five-body decays of the τ only upper limits exist
Summary
The rare decay of the muon μ → eννee is not one of those Standard Model processes that has been in the limelight in the past decades. Several tree-level calculations of the branching ratios for the various rare decays have been made long ago [4,5,6]. A realistic background study benefits from a fully differential description of the rare muon decay This requires the computation of the corresponding matrix elements and their implementation in a Monte Carlo program. The squared matrix elements at tree level for the unpolarized rare muon decay and a study of the energy spectrum have been published less than ten years ago [10]. The paper is organized as follows: in section 2 we will discuss our methodology Since this is a standard NLO calculation we focus on changes to GoSam that were necessary to compute the required one-loop matrix elements.
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