# Renormalisation-group improved analysis of $\mu\to e$ processes in a systematic effective-field-theory approach

## TL;DR

This paper performs a comprehensive renormalisation-group analysis of muon-to-electron lepton-flavour violating processes within an effective field theory, providing analytic tools and exploring phenomenological constraints from experimental data.

## Contribution

It introduces a systematic EFT approach with full RG evolution for muonic LFV processes, including explicit evolution matrices and phenomenological analysis.

## Key findings

- Wilson coefficients are more constrained when RG effects are included.
- Correlations among operators are identified with current and future data.
- Rates are expressed as functions of Wilson coefficients at any scale up to m_W.

## Abstract

In this article, a complete analysis of the three muonic lepton-flavour violating processes $\mu\to e \gamma$, $\mu\to 3e$ and coherent nuclear $\mu\to e$ conversion is performed in the framework of an effective theory with dimension six operators defined below the electroweak symmetry breaking scale $m_W$. The renormalisation-group evolution of the Wilson coefficients between $m_W$ and the experimental scale is fully taken into account at the leading order in QCD and QED, and explicit analytic and numerical evolution matrices are given. As a result, muonic decay and conversion rates are interpreted as functions of the Wilson coefficients at any scale up to $m_W$. Taking the experimental limits on these processes as input, the phenomenology of the mixing effects is investigated. It is found that a considerable set of Wilson coefficients unbounded in the simplistic tree-level approach are instead severely constrained. In addition, correlations among operators are studied both in the light of current data and future experimental prospects.