Related papers: Boundedness from below of SU(n) potentials
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…
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…
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.…
A scalar potential of the form $\lambda_{ab} \phi_a^2 \phi_b^2$ is bounded from below if its matrix of quartic couplings $\lambda_{ab}$ is copositive -- positive on non-negative vectors. Scalar potentials of this form occur naturally for…
We investigate the vacuum stability in a scale invariant local $U(1)_\chi$ model with vanishing scalar potential at the Planck scale. We find that it is impossible to realize the Higgs mass of 125\,GeV while keeping the Higgs quartic…
To understand physics beyond the Standard Model (SM) it is important to have the precise knowledge of Higgs boson and top quark masses as well as strong coupling. Recently discovered new boson which is likely to be the SM Higgs with mass…
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 the extension of the Standard electroweak Model through an $SU(2)$ quadruplet of scalars with hypercharge either $3/2$ or $1/2$ (with an additional reflection symmetry in the latter case). We establish, through $\textit{exact…
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 the two Higgs doublet model, there is the possibility that the vacuum where the universe resides in is metastable. We present the tree-level bounds on the scalar potential parameters which have to be obeyed to prevent that situation.…
The most general scalar potential of two real scalar fields and a Higgs boson is a quartic homogeneous polynomial about 3 variables, which defines a 4th order 3 dimensional symmetric tensor. Hence, the boundedness from below of such a…
We consider a five-dimensional supergravity model with SU(5) gauge symmetry and the minimal field content. Studying the arising scalar potential we find that the gauging of the $U(1)_R$ symmetry of the five-dimensional supergravity causes…
We constrain the parameter space of the minimal and gaugino-assisted anomaly mediation, and gaugino mediation models by requiring that the electroweak vacuum corresponds to the deepest minimum of the scalar potential. In the framework of…
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 consider asymptotically anti de Sitter gravity coupled to a scalar field with mass slightly above the Breitenlohner-Freedman bound. This theory admits a large class of consistent boundary conditions characterized by an arbitrary function…
We study the allowed parameter space of the scalar sector in the superweak extension of the standard model (SM). The allowed region is defined by the conditions of (i) stability of the vacuum and (ii) perturbativity up to the Planck scale,…
The scalar potential of the two-Higgs-doublet model (2HDM) may have more than one local minimum and the usually considered vacuum could be located at one of them that could decay to another. This paper studies the condition that the usually…
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…
In this research, we investigate the vacuum structure of an extended standard model with a $U(1)_D$ global symmetry. The scalar sector consists of two $SU(2)$ doublets as well as one complex singlet and one real singlet, resulting in a more…
The vacuum stability lower bound on the mass of the Higgs boson is numerically investigated in an $SU(2)_L \otimes SU(2)_R$ symmetric Yukawa model, which describes two heavy degenerate fermion doublets in the limit of vanishing gauge…