Related papers: Vacuum Stability Conditions From Copositivity Crit…
We find analytical vacuum stability or bounded below conditions for general scalar potentials of a few fields. After a brief review of copositivity we go beyond it. We discuss the vacuum stability conditions of the general potential of two…
We consider a two-component scalar dark matter model in this work, where the scalars are stabilized by extra $Z_2 \times Z'_2$ symmetry. To guarantee the stability of the vacuum, we consider the copositive criteria and different choices of…
We derive analytic necessary and sufficient conditions for the vacuum stability of the left-right symmetric model by using the concepts of copositivity and gauge orbit spaces. We also derive the conditions sufficient for successful symmetry…
By applying the concepts of copositivity and using the gauge orbit spaces on the scalar potential, we derive analytic necessary and sufficient conditions which guarantee the boundedness of the scalar potential in all the directions in the…
We discuss vacuum structure and vacuum stability in classically scale-invariant renormalizable models with a scalar dark matter multiplet of global O(N) symmetry together with an electroweak singlet scalar mediator. Our conformally…
The orbit space for a scalar field in a complex square matrix representation obtains a Minkowski space structure from the Cauchy-Schwarz inequality. It can be used to find vacuum stability conditions and minima of the scalar potential. The…
By applying copositivity criterion to the scalar potential of the economical $3-3-1$ model, we derive necessary and sufficient bounded-from-below conditions at tree level. Although these are a large number of intricate inequalities for the…
We will revise one of the methods given in the literature to determine the necessary and sufficient conditions that the parameters must satisfy to have a stable scalar potential in the general two-Higgs doublet model. We will give a…
Vacuum stability requires that the scalar potential is bounded from below. Whether or not this is true depends on the scalar quartic interactions alone, but even so the analysis is arduous and has only been carried out for a limited set of…
We consider the addition to the Standard Model of a scalar $SU(2)$ multiplet $\Delta_n$ with dimension $n$ going from $1$ to $6$. The multiplet $\Delta_n$ is assumed to have null vacuum expectation value and an arbitrary (free) hypercharge.…
The stability requirements for a noncommutative scalar field coupled to gravity is investigated through the positive energy theorem. It is shown that for a noncommutative scalar with a polynomial potential, the stability conditions are…
Tree-level dynamical stability of scalar field potentials in renormalizable theories can in principle be expressed in terms of positivity conditions on quartic polynomial structures. However, these conditions cannot always be cast in a…
We analyze the one-loop vacuum stability and perturbativity bounds on a singlet extension of the Standard Model (SM) scalar sector containing a scalar dark matter candidate. We show that the presence of the singlet-doublet quartic…
The mathematical model of multiple microscopic particles potentials corresponds to a fourth order symmetric tensor with a particular structure in particle physics. In this paper, we mainly dedicate to the study of copositivity for a class…
The inert scalar doublet model of dark matter can be valid up to the Planck scale. We briefly review the bounds on the model in such a scenario and identify parameter spaces that lead to absolute stability and metastability of the…
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…
We consider a noncommutative scalar field with a covariantly constant noncommutative parameter in a curved space-time background. For a potential as a noncommutative polynomial it is shown that the stability conditions are unaffected by the…
We summarize our analysis for the vacuum stability of the superweak extension of the standard model. The parameter space allowed by the $W$-boson mass measurements and collider searches for a new scalar particle are also presented. The…
The most general $SU(2)\times U(1)_Y$-symmetric quartic potential with two Higgs doublets, subject to an only softly broken discrete symmetry $(\phi_1,\phi_2)\to(-\phi_1,\phi_2)$, is considered. At tree-level, analytic bounds on the…
In this work, we study the vacuum stability of the classical unstable $\left( -\phi^{4}\right) $ scalar field potential. Regarding this, we obtained the effective potential, up to second order in the coupling, for the theory in $1+1$ and…