Basis-independent methods for the two-Higgs-doublet model III: The CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U

TL;DR

This paper develops basis-independent methods to analyze custodial symmetry and oblique parameters in the two-Higgs-doublet model, clarifying symmetry constraints, mass degeneracies, and experimental bounds on model parameters.

Contribution

It provides basis-independent expressions for custodial symmetry constraints in the 2HDM and computes oblique parameters for the most general CP-violating case.

Findings

Custodial symmetry imposes CP-conservation and additional constraints on the 2HDM.

In the custodial symmetry limit, contributions to T and U parameters vanish.

Experimental bounds on S and T constrain the 2HDM parameter space.

Abstract

In the Standard Model, custodial symmetry is violated by the hypercharge U(1) gauge interactions and the Yukawa couplings, while being preserved by the Higgs scalar potential. In the two-Higgs doublet model (2HDM), the generic scalar potential introduces new sources of custodial symmetry breaking. We obtain a basis-independent expression for the constraints that impose custodial symmetry on the 2HDM scalar potential. These constraints impose CP-conservation on the scalar potential and vacuum, and in addition add one extra constraint on the scalar potential parameters. We clarify the mass degeneracies of the 2HDM that arise as a consequence of the custodial symmetry. We also provide a computation of the "oblique" parameters (S, T, and U) for the most general CP-violating 2HDM in the basis-independent formalism. We demonstrate that the 2HDM contributions to T and U vanish in the custodial symmetry limit, as expected. Using the experimental bounds on S and T from precision electroweak data, we examine the resulting constraints on the general 2HDM parameter space.