Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions

We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization conditions as far as possible and on (MS) over bar prescriptions for the remaining field-mixing parameters where no distinguished on-shell condition exists and make contact to existing schemes in the literature. In particular, we treat the tadpole diagrams in different ways and discuss issues of gauge independence and perturbative stability in the considered schemes. The renormalization group equations for the (MS) over bar parameters are solved in each scheme, so that a consistent renormalization scale variation can be performed. We have implemented all Feynman rules including counterterms and the renormalization conditions into a FEYNARTS model file, so that amplitudes and squared matrix elements can be generated automatically. As an application we compute the decay of the light, CP-even Higgs boson of the Two-Higgs-Doublet Model into four fermions at next-to-leading order. The comparison of different schemes and the investigation of the renormalization scale dependence allows us to test the perturbative consistency in each of the renormalization schemes, and to get a better estimate of the theoretical uncertainty that arises due to the truncation of the perturbation series.