Measurements of $\mu\to 3e$ Decay with Polarised Muons as a Probe of New Physics

TL;DR

This paper explores how angular measurements in the polarised muon decay $oldsymbol{\mu^+ o e^+ e^+ e^-}$ can identify new physics operators causing lepton flavor violation, with implications for upcoming experiments like Mu3e.

Contribution

It demonstrates that specific angular observables can distinguish between different effective operators responsible for the decay, enhancing the understanding of potential new physics signals.

Findings

Angular asymmetries can discriminate between most operators.

Helicity measurements can differentiate scalar and vector operators of opposite chirality.

Non-zero T-odd asymmetry indicates T (CP) violation in the decay.

Abstract

Working within the Standard Model effective field theory approach, we examine the possibility to test charged lepton flavour violating (cLFV) new physics (NP) by angular measurements of the outgoing electron and positrons in the polarised $\mu^{+}\to e^{+}e^{+}e^{-}$ decay. This decay is planned to be studied with a sensitivity to the branching ratio of $B_{\mu\to3e}\sim 10^{-15}$ by the Mu3e experiment at PSI. To illustrate the potential of these measurements, we consider a set of eight effective operators generating the decay at the tree level, including dimension-five dipole operators and dimension-six scalar and vector four-fermion operators of different chiralities. We show that if the polarised $\mu^{+}\to e^{+}e^{+}e^{-}$ decay is observed and is induced by a single operator, data from three angular observables - two P-odd asymmetries and one T-odd asymmetry - can allow to discriminate between all considered operators with the exception of scalar and vector operators of opposite chirality. For these two types of operators, the P-odd asymmetry is maximal in magnitude; they can be distinguished, in principle, by measuring the helicities of the outgoing positrons. The observation of a non-zero T-odd asymmetry would indicate the presence in the decay rate of a dipole and vector operator interference term that is T (CP) violating.