Unitarity Constraints in the standard model with a singlet scalar field

TL;DR

This paper investigates how perturbative unitarity constrains the masses and mixing of scalar fields in the standard model extended with a singlet scalar, impacting vacuum stability, inflation, and dark matter scenarios.

Contribution

It derives unitarity bounds on scalar masses and mixing in the SM with a singlet scalar, considering various VEV and symmetry conditions, and explores implications for inflation and dark matter.

Findings

Upper bounds on singlet scalar mass with VEV depending on mixing.

Higgs mass constrained by unitarity in no-VEV singlet case.

Singlet scalar mass limited by relic abundance and unitarity when considered as dark matter.

Abstract

Motivated by the discovery of a new scalar field and amelioration of the electroweak vacuum stability ascribed to a singlet scalar field embedded in the standard model (SM), we examine the implication of the perturbative unitarity in the SM with a singlet scalar field. Taking into account the full contributions to the scattering amplitudes, we derive unitarity conditions on the scattering matrix which can be translated into bounds on the masses of the scalar fields. In the case that the singlet scalar field develops vacuum expectation value (VEV), we get the upper bound on the singlet scalar mass varying with the mixing between the singlet and Higgs scalars. On the other hand, the mass of the Higgs scalar can be constrained by the unitarity condition in the case that the VEV of the singlet scalar is not generated. Applying the upper bound on the Higgs mass to the scenario of the unitarized Higgs inflation, we discuss how the unitarity condition can constrain the Higgs inflation. The singlet scalar mass is not constrained by the unitarity itself when we impose Z_2 in the model because of no mixing with the Higgs scalar. But, regarding the singlet scalar field as a cold dark matter candidate, we derive upper bound on the singlet scalar mass by combining the observed relic abundance with the unitarity condition.