Abstract
We present a consistent renormalization scheme for the CP-conserving Two-Higgs-Doublet Model based on $\overline{MS}$ renormalization of the mixing angles and the soft-$Z_2$-symmetry-breaking scale $M_{sb}$ in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent $S$-matrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general $R_{\xi}$-gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the $\overline{MS}$ renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence.
Highlights
The discovery of a Higgs boson at the Large Hadron Collider (LHC) [1, 2] was a tremendous success for elementary particle physics
We present a consistent renormalization scheme for the CP-conserving TwoHiggs-Doublet Model based on MS renormalization of the mixing angles and the soft-Z2symmetry-breaking scale Msb in the Higgs sector
We show that tadpole renormalization schemes that are commonly used in literature in combination with MS renormalization lead to gauge-dependent predictions, while the use of the FJ Tadpole Scheme ensures gauge independence
Summary
The discovery of a Higgs boson at the Large Hadron Collider (LHC) [1, 2] was a tremendous success for elementary particle physics. If parameters are renormalized in the MS scheme, it becomes crucial to define all bare physical parameters and counterterms, like for instance the mass counterterms of the EW gauge bosons or Higgs bosons, in a gauge-independent way This in turn requires a consistent treatment of tadpoles. We generalize this scheme, which we dub FJ Tadpole Scheme, and apply it to the 2HDM in order to allow for a consistent gauge-independent MS renormalization of the mixing angles α and β as well as the soft-breaking scale Msb. We stress that the FJ Tadpole Scheme as introduced here provides a consistent universal description of tadpoles in arbitrary theories with spontaneous symmetry breaking (SSB), such as general multi-Higgs models. In the appendices we present results for the Higgs-tadpole counterterms in the 2HDM, proof the gauge dependence of the MS renormalization of β in popular tadpole schemes, and illustrate the tadpole contributions to the two-loop Higgs-boson self-energy
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