The $\mu\to e\gamma$ decay in a systematic effective field theory approach with dimension 6 operators

TL;DR

This paper systematically analyzes the $$ decay using effective field theory with dimension 6 operators, computing one-loop effects, and deriving constraints on Wilson coefficients at various energy scales.

Contribution

It introduces an automated one-loop computational framework for $$ decay within EFT, including operator mixing and renormalisation-group evolution effects.

Findings

Derived limits on Wilson coefficients from $$ decay data.

Demonstrated operator mixing effects under renormalisation-group flow.

Applied method to $ au$ lepton-flavour violating decays.

Abstract

We implement a systematic effective field theory approach to the benchmark process $\mu\to e \gamma$, performing automated one-loop computations including dimension 6 operators and studying their anomalous dimensions. We obtain limits on Wilson coefficients of a relevant subset of lepton-flavour violating operators that contribute to the branching ratio $\mu\to e \gamma$ at one-loop. In addition, we illustrate a method to extract further constraints induced by the mixing of operators under renormalisation-group evolution. This results in limits on the corresponding Wilson coefficients directly at the high scale. The procedure can be applied to other processes as well and, as an example, we consider also lepton-flavour violating decays of the $\tau$.