Abstract:
In the history of elementary particle physics, the discovery of the Higgs boson at the Large Hadron Collider (LHC) in July 4, 202 is an important breakthrough which completes the Standard Model (SM) of particle physics. Nevertheless, there exist experimental observations which cannot be explained by the SM, like the neutrino oscillations, dark matter, baryon asymmetry etc. With these experimental shortcomings it is evident that there exist some beyond the Standard Model (BSM) physics. There are several ways to extend the SM to explain some of the experimental phenomena which is still to be observed in the state-of-the-art experiment phenomena which is still to be observed in the state-of-the-art experiment like LHC. But the recent Higgs discovery can shed some light in the uncharted territory of theoretical physics. We are living at a minima of the Higgs potential where the Higgs boson mass (mh) measured at the LHC. The stability of the minimum is ensured by the condition that the Higgs quartic coupling should be positive. But recent observation of mh at the LHC indicates that the SM minima does not remain stable up to the Planck scale. This also indicates that there must be some new physics phenomena which will stabilize the minimum. Hence the stability analysis of the BSM scenarios is necessary to constrain parameters of the model. There are other constraints like perturbativity and unitarity of scattering amplitudes of longitudinal gauge boson modes which will also restrict the parameter space.
The BSM models that include many scalar fields possess 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. 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 stability criteria embracing the maximum allowed parameter space.
We study the B-L gauge extension of the Standard Model which contains a singlet scalar and three right-handed neutrinos. The vacuum expectation value of the singlet scalar breaks the U(1)B-L symmetry. The B-L symmetry breaks when the complex singlet scalar acquires a VeV. We studied two different cases of B-l breaking scale. TeV scale and ~1010 GeV. The TeV scale breaking scenario can have signatures at the LHC and we have constrained parameter space of this model. The high scale breaking scenario provides a constrained parameter space where both the issues of vacuum stability and high-scale inflation can be successfully accommodated.
The Left-Right symmetric model (LRSM) is theoretically well motivated and also contains rich phenomenology. We used idea of copositivity to calculate vacuum stability conditions for two variants of the LRSM. We incorporate the unitarity conditions in (LRSM) which can translate into giving a stronger constraint on the model parameters together with the criteria derived from vacuum stability and perturbativity. In this light, we demonstrate the bounds on the masses of the physical scalars present in the model and find the scenario where multiple scalar models are in the reach lf Large Hadron Collider.
We have also studied a variant TeV scale seesaw model in which three additional heavy right handed neutrinos are added to the standard model to generate the quasi-degenerate light neutrinos. This model is theoretically interesting since it can be fully rebuilt from the experimental data of neutrino oscillations except for an in known factor in the Dirac Yukawa coupling. We study the constraints on this coupling coming from meta-stability of electro-weak vacuum. Even stronger bound comes from the lepton flavor violating decays on this model, especially in a heavy neutrino mass scenario which is within the collider reach. Bestowed with these constrained parameters, we explore the production and discovery potential coming from these heavy neutrinos at the 14 TeV run of Large Hadron Collider. Signatures with tri-lepton final state together with backgrounds are considered in a realistic simulation.