Renormalisation-group improved analysis of μ → e processes in a systematic effective-field-theory approach

A bstract In this article, a complete analysis of the three muonic lepton-flavour violating processes μ → e γ, μ → 3 e and coherent nuclear μ → 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.