Mu to e gamma in the 2 Higgs Doublet Model: an exercise in EFT

The 2 Higgs Doublet Model (2HDM) of type III has renormalisable Lepton Flavour-Violating couplings, and its one and two-loop ("Barr-Zee") contributions to $μ\to e γ$ are known. In the decoupling limit, where the mass scale M of the second doublet is much greater than the electroweak scale, the model can be parametrised with an Effective Field Theory(EFT) containing dimension six operators. The $1/M^2$ terms of the exact calculation are reproduced in the EFT, provided that the four-fermion operator basis below the weak scale is enlarged with respect to the SU(2)-invariant Buchmuller-Wyler list. The two-loop "Barr-Zee" contributions are located in the EFT, showing that two-loop matching and running would be required to obtain the most important contributions, and that dimension eight operators can be numerically relevant.

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