Mu to e gamma and matching at mW

TL;DR

This paper develops a method to translate experimental limits on muon-to-electron flavor-changing processes into constraints on new physics models at high energy scales, using effective field theory and renormalization group techniques.

Contribution

It constructs a basis of invariant operators, performs one-loop RG running, and matches onto SU(2)-invariant operators at mW to connect low-energy constraints with high-energy physics.

Findings

Constraints on flavor-changing interactions of Z and Higgs are consistent with previous bounds.

The method accurately translates   gamma bounds to high energy scales.

The analysis highlights differences from previous EFT approaches.

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.