On the Fate of Electroweak Vacuum and Order of Phase Transition in Beyond Standard Model Scenarios

In this article, we consider an extension of the Standard Model (SM) with a singlet and a \(Y=0\) triplet under SU(2). Both singlet and the triplet are considered odd under a discrete \(Z_2\) symmetry and hence, does not take part in the electroweak symmetry breaking (EWSB). The lightest stable neutral particle from the singlet and the triplet becomes the cold dark matter candidate. The bounds on the mass parameter for the singlet and the triplet are computed from strong first-order phase transition (FOPT) consistent with the measured Higgs boson mass and the Planck scale perturbative unitarity. The upper mass bound on the singlet mass comes out to be \(\lesssim 909\) GeV and for the triplet, the upper bound comes out to be \(\lesssim 320\) GeV using two-loop \(\beta -\) functions and one-loop potential. Including two-loop contribution to the thermal masses for two-loop \(\beta -\) functions, the mass bound for singlet still remains the same while the mass bound for the triplet reduces to 259 GeV. The Gravitational wave (GW) signatures for the first-order phase transition are also studied.