Gauge-independent $\overline{MS}$ renormalization in the 2HDM

TL;DR

This paper introduces a gauge-independent $ar{MS}$ renormalization scheme for the Two-Higgs-Doublet Model, ensuring physical quantities are gauge-invariant and consistent across calculations, with explicit NLO correction results.

Contribution

It develops a fully consistent $ar{MS}$ renormalization scheme for the 2HDM that maintains gauge independence and can be applied to other extended Higgs models.

Findings

The scheme ensures gauge-independent $S$-matrix elements.

Explicit NLO electroweak corrections are computed.

The method outperforms traditional on-shell schemes in gauge invariance.

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.