In this article we consider a comparative study between Type-I 2HDM and $$Y=0$$Y=0, SU(2) triplet extensions having one $$Z_2$$Z2-odd doublet and triplet that render the desired dark matter(DM). For the inert doublet model (IDM) either a neutral scalar or pseudoscalar can be the DM, whereas for inert triplet model (ITM) it is a CP-even scalar. The bounds from perturbativity and vacuum stability are studied for both the scenarios by calculating the two-loop beta functions. While the quartic couplings are restricted to $$0.1-0.2$$0.1-0.2 for a Planck scale perturbativity for IDM, these are much relaxed (0.8 ) for ITM. The RG-improved potentials by Coleman-Weinberg show the regions of stability, meta-stability and instability of the electroweak vacuum. The constraints coming from DM relic, the direct and indirect experiments like XENON1T, LUX and H.E.S.S., Fermi-LAT allow the DM mass $$\gtrsim 700, \,1176$$≳700,1176 GeV for IDM, ITM respectively. Though mass-splitting among $$Z_2$$Z2-odd particles in IDM is a possibility for ITM we have to rely on loop-corrections. The phenomenological signatures at the LHC show that the mono-lepton plus missing energy with prompt and displaced decays in the case of IDM and ITM can distinguish such scenarios at the LHC along with other complementary modes.

We consider the extension of the Standard Model (SM) with an inert Higgs doublet that also contains two or three sets of SU(2)L triplet fermions with hypercharge zero and analyze the stability of electroweak vacuum for the scenarios. The model represents a Type-III inverse seesaw mechanism for neutrino mass generation with a Dark matter candidate. An effective potential approach calculation with two-loop beta function have been carried out in deciding the fate of the electroweak vacuum. Weak gauge coupling g2 shows a different behaviour as compared to the Standard Model. The modified running of g2, along with the Higgs quartic coupling and Type-III Yukawa couplings become crucial in determining the stability of electroweak vacuum. The interplay between two and three generations of such triplet fermions reveals that extensions with two generations is favoured if we aspire for Planck scale stability. Bounds on the Higgs quartic couplings, Type-III Yukawa and number of triplet fermion generations are drawn for different mass scale of Type-III fermions. The phenomenologies of inert doublet and Type-III fermions at the LHC and other experiments are commented upon.

We analyze the vacuum stability in the inert Higgs doublet extension of the Standard Model (SM), augmented by right-handed neutrinos (RHNs) to explain neutrino masses at tree level by the seesaw mechanism. We make a comparative study of the highand low-scale seesaw scenarios and the effect of the Dirac neutrino Yukawa couplings on the stability of the Higgs potential. Bounds on the scalar quartic couplings and Dirac Yukawa couplings are obtained from vacuum stability and perturbativity considerations. These bounds are found to be relevant only for low-scale seesaw scenarios with relatively large Yukawa couplings. The regions corresponding to stability, metastability and instability of the electroweak vacuum are identified. These theoretical constraints give a very predictive parameter space for the couplings and masses of the new scalars and RHNs which can be tested at the LHC and future colliders. The lightest non-SM neutral CP-even/odd scalar can be a good dark matter candidate and the corresponding collider signatures are also predicted for the model.

In this article we examine the prospect of first order phase transition with a Y=0 real SU (2) triplet extension of the Standard Model, which remains odd under Z 2 , considering the observed Higgs boson mass, perturbative unitarity, dark matter constraints, etc. Especially we investigate the role of Higgs-triplet quartic coupling considering one-and two-loop beta functions and compare the results with the complex singlet extension case. It is observed that at one-loop level, no solution can be found for both, demanding the Planck scale perturbativity. However, for a much lower scale of 10 4 GeV, the singlet case predicts first order phase transition consistent with the observed Higgs boson mass. On the contrary, at the two-loop, both the scenarios foresee strongly first order phase transition consistent with the observed Higgs mass with upper bounds of 310, 909 GeV on the triplet and singlet masses, respectively. This puts the triplet in apparent contradiction with the observed dark matter relic bound and thus requires additional field for that. The preferred regions of the parameter space in both the cases are identified by benchmark points, that predict the Gravitational Waves with detectable frequencies in present and future experiments.

We investigate the constraints on the leptoquark Yukawa couplings and the Higgs-leptoquark quartic couplings for scalar doublet leptoquark $$\widetilde{R}_2$$ R ~ 2 , scalar triplet leptoquark $$\varvec{S}_3$$ S 3 and their combination with both three generations and one generation with respect to perturbative unitarity and vacuum stability. The perturbative unitarity of all the dimensionless couplings is studied via one- and two-loop beta functions. New $$SU(2)_L$$ S U ( 2 ) L multiplets in terms of these leptoquarks are introduced to fabricate Landau poles at the two-loop level in the gauge coupling $$g_2$$ g 2 at $$10^{19.7}$$ 10 19.7 GeV and $$10^{14.4}$$ 10 14.4 GeV, respectively, for the $$\varvec{S}_3$$ S 3 and $$\widetilde{R}_2+\varvec{S}_3$$ R ~ 2 + S 3 models with three generations. However, such Landau poles cease to exist for $$\widetilde{R}_2$$ R ~ 2 and any of these extensions with both one and two generations up to Planck scale. The Higgs-leptoquark quartic couplings acquire severe constraints to protect Planck scale perturbativity, whereas leptoquark Yukawa couplings acquire some upper bound in order to respect Planck scale stability of Higgs vacuum. The Higgs quartic coupling at the two-loop level constrains the leptoquark Yukawa couplings for $$\widetilde{R}_2,\varvec{S}_3, \,\widetilde{R}_2+\varvec{S}_3$$ R ~ 2 , S 3 , R ~ 2 + S 3 with values "Equation missing" with three generations. In the effective potential approach, the presence of any of these leptoquarks with any number of generations pushes the metastable vacuum of the Standard Model to the stable region.