Abstract
We discuss the renormalization of mixing angles for theories with extended scalar sectors. Motivated by shortcomings of existing schemes for mixing angles, we review existing renormalization schemes and introduce new ones based on on-shell conditions or symmetry requirements such as rigid or background-field gauge invariance. Considering in particular the renormalization of the mixing angles in the Two-Higgs-Doublet Model and the Higgs-Singlet Extension of the Standard Model, we compare electroweak corrections within these models for a selection of renormalization schemes. As specific examples, we present next-to-leading-order results on the four-fermion decays of heavy and light CP-even Higgs bosons, H1/H2 → WW/ZZ → 4f , and on electroweak Higgs-boson production processes, i.e. Higgs-strahlung and vector-boson fusion. We find that our new proposals for on-shell and symmetry-based renormalization conditions are well-behaved for the considered benchmark scenarios in both models.
Highlights
After the discovery of a Higgs boson at the Large Hadron Collider (LHC) [1, 2], the investigation of the Higgs sector is still of prime importance for particle physics
While this is phenomenologically unimportant owing to the smallness of the down-type quark masses, the problem has found quite some interest in the literature, and the corresponding theoretical developments have influenced the work on the renormalization of mixing matrices in scalar sectors, which is the subject of this paper
We present first results from a further extension of Prophecy4f18 which covers the decays of the heavy CP-even scalar bosons as well and which supports the on-shell and symmetry-inspired renormalization schemes described in this paper
Summary
After the discovery of a Higgs boson at the Large Hadron Collider (LHC) [1, 2], the investigation of the Higgs sector is still of prime importance for particle physics. For a precise study of such theories, next-to-leading-order (NLO) QCD and electroweak (EW) corrections have to be taken into account This requires a renormalization of these models and the renormalization of mixing angles or, more generally, of mixing matrices. Various proposals were made for a gauge-parameter-independent renormalization of the quark-mixing matrix [10,11,12,13,14,15] These are cumbersome to apply, their generalization beyond one-loop order remains unclear, and/or they potentially lead to singularities in the S-matrix elements for degenerate quark masses. It was suggested to define the quark-mixing matrix counterterm from the quark-field renormalization constants calculated in the ’t Hooft-Feynman gauge [17] Generalizing this idea, it was argued in ref. Generalizing this idea, it was argued in ref. [12] that any renormalization scheme for the quark-mixing matrix may be viewed as a gauge-invariant scheme by definition, in the sense that S-matrix elements remain invariant if the gauge used in the calculation of the loop corrections and all other renormalization constants is changed, while keeping the defining gauge for the renormalization constants of the quark-mixing matrix fixed
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