  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.
