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

In this article, a complete analysis of the three muonic lepton-flavour violating processes mu -> e gamma, mu -> 3e and coherent nuclear mu -> 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.