Oblique parameters of BSM models with three CP-even neutral scalars

TL;DR

This paper derives formulas for oblique parameters in three BSM models with three CP-even neutral scalars, linking them to mixing matrices, and provides visualizations of parameter constraints.

Contribution

It presents a unified method to compute oblique parameters using mixing matrices for various scalar sector extensions of the Standard Model.

Findings

Formulas for S, T, U, V, W, X in three scalar models

Expressions valid with or without VEVs for scalars

Plots showing allowed mass and mixing angle regions

Abstract

We express the oblique parameters $S$, $T$, $U$, $V$, $W$, and $X$ in terms of the corresponding mixing matrices in the framework of three BSM models with three CP-even neutral scalars. We consider three types of the extension of the scalar sector of the SM with non-standard (i) two real singlet scalars, (ii) one complex doublet and one real singlet scalar, and (iii) two complex doublets. We present the expressions such that one can use these when all the neutral CP-even scalars have VEV, or one of them does not have any VEV. The principal benifit of presenting the oblique parameters in this way is, the sole knowledge of the mixing matrices in the corresponding scalar sector is enough to extract the expression of the oblique parameter of that particular BSM model. This paper also presents some plots, for reference, showing the allowed region of the masses of the three CP-even neutral scalars and the three mixing angles of the three above-mentioned models.