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 Z2 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.
Highlights
Lagrangian can modify the production and/or decay rates of the Higgs field [15, 16] and supply solutions for dark matter [17, 18], baryogenesis via the first order electroweak phase transition [19] and the unitarity problem of the Higgs inflation [20]
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
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
Summary
The full Lagrangian considered in this paper consists of the SM Lagrangian LSM and extra terms associated with the singlet scalar S, L. We consider two cases depending on whether the singlet scalar S develops VEV or not. As will be shown later, the implications on the unitarity condition depend on whether the VEV of S is developed or not. Substituting these into the Lagrangian, we obtain mixing terms between two neutral fields h and s which are superpositions of two physical states (h1, h2) given as follows:. It is important to notice that there are no bi-linear mixing terms (∼ hs) between h and s because the singlet s does not develop the VEV. In this case, the mass of singlet scalar s is given by m2s μ2s v2 2. Requiring that the vacuum is located at the global minimum of the potential, we get the inequality given by 0 < μ2s < λSλHS v2
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