Copositive Criteria and Boundedness of the Scalar Potential

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 123-127 GeV has a submissive impact on the stability of the new physics beyond standard model (BSM). The beyond standard model scenarios that include many scalar fields posses scalar potential with many quartic couplings. Due to the complicated structures of such scalar potentials it is indeed difficult to adjudge the stability of the vacuum. Thus one needs to formulate a proper prescription for computing the vacuum stability criteria. In this paper we have used the idea of copositive matrices to deduce the conditions that guarantee the boundedness of the scalar potential. We have discussed the basic idea behind the copositivity and then used that to determine the vacuum stability criteria for the Left-Right symmetric models with doublet, and triplet scalars and Type-II seesaw. As this idea is based on the strong mathematical arguments it helps to compute simple and unique stability criteria embracing the maximum allowed parameter space.