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

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.

V1: 28 pages, 5 figures; V2: references added; V3: minor corrections, conclusion unchanged

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