Mu to e gamma and matching at mW

Several experiments search for μ- e flavour change, for instance in μ->e conversion, μ-> e γ, and μ-> 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 μ-> e γbound is translated to the scale M, where it constrains two sums of operators. The constraints differ from those obtained in previous EFT analyses of μ-> e γ, 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.

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