Vacuum Stability vs. Positivity in Real Singlet Scalar Extension of the Standard Model

TL;DR

This paper investigates the constraints on a real singlet scalar extension of the Standard Model, focusing on vacuum stability, positivity, and perturbativity up to the Planck scale, revealing a tightly constrained parameter space and possible scalar masses.

Contribution

It provides a comprehensive analysis of vacuum stability and positivity conditions in the singlet scalar extension, delineating the viable parameter space up to the Planck scale.

Findings

Viable parameter space is strongly constrained for various singlet VEVs.

Singlet scalar mass can range from a few GeV to less than a TeV.

Vacuum stability conditions significantly restrict model parameters.

Abstract

We assume a generic real singlet scalar extension of the Standard Model living in the vacuum $(v,w)$ at the electroweak scale with $v=246$ GeV and $w$ being respectively the Higgs and the singlet scalar vacuum expectation values. By requiring {\it absolute} vacuum stability for the vacuum $(v,w)$, the positivity condition and the perturbativity up to the Planck scale, we show that the viable space of parameters in the model is strongly constrained for various singlet scalar vacuum expectation values $w=0.1, 1, 10, 100$ TeV. Also, it turns out that the singlet scalar mass can be from a few GeV up to less than TeV.