Abstract
The 2 Higgs Doublet Model of type III has renormalisable Lepton Flavour-Violating couplings, and its one- and two-loop (“Barr–Zee”) contributions to $$\mu \rightarrow e \gamma $$ 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. It is found that the dominant two-loop “Barr–Zee” contributions arise mostly in two-loop matching and running, and that dimension-eight operators might be numerically relevant.
Highlights
This exercise was born from a puzzle: experiments that search for μ ↔ e flavour change constrain a long list of QCD×QED-invariant four-fermion operators, some of which turn out to be of dimension eight when SU(2) invariance is imposed
It is common, when describing New Physics from above mW with Effective Field Theory(EFT) [1,2], to use the SU(2)-invariant basis of dimension 6 operators given by Buchmuller and Wyler [3] and pruned in [4]
In the context of B physics, Alonso et al [7] and Aebischer et al [8] calculated the coefficients of the enlarged operator basis below mW, given a selection of SU(2)-invariant operators above mW
Summary
This exercise was born from a puzzle: experiments that search for μ ↔ e flavour change constrain a long list of QCD×QED-invariant four-fermion operators, some of which turn out to be of dimension eight when SU(2) invariance is imposed It is common, when describing New Physics from above mW with Effective Field Theory(EFT) [1,2], to use the SU(2)-invariant basis of dimension 6 operators given by Buchmuller and Wyler [3] and pruned in [4]. In the context of B physics, Alonso et al [7] and Aebischer et al [8] calculated the coefficients of the enlarged operator basis below mW , given a selection of SU(2)-invariant operators above mW This exercise only agrees approximatively with [7], as discussed in Sect.
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