Mu to e gamma and matching at mW

Abstract: Several experiments search for \mu - e flavour change, for instance in \mu ->e conversion, \mu-> e \gamma, and \mu -> 3e. This paper studies how to translate these experimental constraints from low energy to a New Physics scale M >> mW. A basis of QCD and QED-invariant operators (as appropriate below mW) is constructed, then run to mW with one-loop RGEs of QCD and QED. At mW, these operators are matched onto SU(2)-invariant dimension-six operators, which can continue to run up with electroweak RGEs. As an example, the \mu-> e \gamma bound is translated to the scale M, where it constrains two sums of operators. The constraints differ from those obtained in previous EFT analyses of \mu -> e \gamma, but reproduce the expected bounds on flavour-changing interactions of the Z and the Higgs, because the matching at mW is pragmatically performed to the loop order required to get the "leading" contribution.