Discerning Singlet and Triplet scalars at the electroweak phase transition and Gravitational Wave

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 the 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 cases are identified by benchmark points, that predict the Gravitational Waves with detectable frequencies in the present and future experiments.Comment: 28 pages, 20 figures, 5 table

Distinguishing Inert Higgs Doublet and Inert Triplet Scenarios

In this article we consider a comparative study between Type-I 2HDM and $Y=0$, $SU(2)$ triplet extensions having one $Z_2$-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 $0.1-0.2$ 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 $\gtrsim 700, \,1176$ GeV for IDM, ITM respectively. Though mass-splitting among $Z_2$-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.Comment: 41 pages, 32 figures and 5 tables, citations added EPJC accepted versio

Exploring CP-violation in Y=0Y=0 inert triplet with real singlet

In this article, we examine the Standard Model extended with a $Y=0$ Higgs triplet and a real singlet. We consider the Higgs triplet to be odd under the $Z_2$ symmetry, and hence the lightest stable particle from the inert triplet becomes the dark matter candidate, whereas the real singlet is considered to be even under the $Z_2$ symmetry. A dimension-5 effective term is introduced with the help of a real singlet, which breaks the CP symmetry and gives an additional source of CP-violation in the fermion sector. The phase transition proceeds in two-steps, with the symmetry breaking in the singlet direction occurring first and later leading to the usual electroweak symmetry breaking minima, while electroweak baryogenesis is associated with the second step. The parameters chosen for the electroweak phase transition are found to be consistent with the Planck scale stability and the perturbativity using two-loop $\beta$-functions. The DM mass bound for inert triplet, i.e., 1.2 TeV (below which it is under abundance), also comes out to be consistent with the strongly first-order phase transition, which was not possible solely with inert triplet. The upper bound on the triplet mass comes out to be $\leq 3.8$ TeV, which satisfies the strongly first-order phase transition. This particular benchmark point also satisfies the correct baryon asymmetry of the Universe $(6.13 \times 10^{-11})$, and the gravitational wave spectrum also lies within the detectable frequency range of LISA $(6.978 \times 10^{-4} - 1.690 \times 10^{-2} )$ Hz and BBO $(2.80\times 10^{-3}-1.096)$ Hz experiments.Comment: 25 pages, 7 figure

Electroweak phase transition with radiative symmetry breaking in Type-II seesaw with inert doublet

We consider the Type-II seesaw model extended with another Higgs doublet, which is odd under the $Z_2$ symmetry. We look for the possibility of triggering the electroweak symmetry breaking via radiative effects. The Higgs mass parameter changes sign from being positive at higher energy scales to negative at lower energy scales in the presence of the TeV scalar triplet. The Planck scale perturbativity is demanded and the electroweak phase transition is studied using two-loop $\beta$-functions. The maximum allowed values for the interaction quartic coupling of the second doublet field and the triplet field with the Higgs field are $\lambda_3=0.15$ and $\lambda_{\Phi_{1\Delta}}=0.50$, respectively. Considering these EW values, the first-order phase transition, i.e., $\phi_{+}(T_c)/T_c\sim 0.6$ is satisfied only for vanishing doublet and triplet bare mass parameters, $m_{\Phi_2}=0.0$ GeV and $m_{\Delta}=0.0$ GeV. The small non-zero induced vacuum expectation value for the scalar triplet also generates the neutrino mass, and the lightest stable neutral particle from the inert doublet satisfies the dark matter constraints for the chosen parameter space. The impact of the thermal corrections on the stability of the electroweak vacuum is also studied, and the current experimental values of the Higgs mass and the top mass lie in the stable region both at the zero temperature and the finite temperature.Comment: 24 pages, 6 figure

Constraining Scalar Doublet and Triplet Leptoquarks with Vacuum Stability and Perturbativity

We investigate the constraints on the leptoquark Yukawa couplings and Higgs-leptoquark quartic couplings for scalar doublet leptoquark $\tilde{R}_2$, scalar triplet leptoquark $\vec S_3$ and their combination with both three generations and one generation from perturbative unitarity and vacuum stability. Perturbative unitarity of all the dimensionless couplings have been studied via one- and two-loop beta-functions. Introduction of new $SU(2)$ multiplets in terms of these leptoquarks fabricate Landau poles at two-loop level in the gauge coupling $g_2$ at $10^{19.7}$ GeV and $10^{14.4}$ GeV, respectively for $\vec S_3$ and $\tilde{R}_2+\vec S_3$ models with three generations. However, such Landau pole ceases to exist for $\tilde{R}_2$ and any of these extensions with both one and two generations till Planck scale. The Higgs-leptoquark quartic couplings acquire severe constraints to protect Planck scale perturbativity, whereas leptoquark Yukawa couplings get some upper bound in order to respect Planck scale stability of Higgs Vacuum. The Higgs quartic coupling at two-loop constraints the leptoquark Yukawa couplings for $\tilde{R}_2,\vec S_3, \,\tilde{R}_2+\vec S_3$ with values $\lesssim 1.30, 3.90, 1.00$ 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.Comment: 45 pages, 56 figures, 2 table

Scrutinizing Vacuum Stability in IDM with Type-III Inverse seesaw

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 $g_2$ shows a different behaviour as compared to the Standard Model. The modified running of $g_2$, 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.Comment: 38 pages, 32 figures, 1 table, Published versio

Neutrino Mass Model and Dark Matter with Y=0Y=0 Inert Triplet Scalar

We study a one-loop induced neutrino mass model with an inert isospin triplet scalar field of $Y=0$ and heavier Majorana right-handed fermions. We show numerical analysis of neutrino oscillation and lepton flavor violations and demonstrate our allowed regions in cases of normal and inverted hierarchies. Then, we move on to the discussion of dark matter (DM) candidates to satisfy the relic density where we have two candidates; fermionic DM (FDM) and bosonic DM (BDM). And, we classify four cases NH+FDM, NH+BDM, IH+FDM, IH+BDM and search for each of the allowed points in the model.Comment: 15 pages, 6 figures, two table

Vacuum Stability in Inert Higgs Doublet Model with Right-handed Neutrinos

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 high- and 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. 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.Comment: 38 pages and 44 figures, citation and text added, JHEP accepted versio

Electroweak symmetry breaking of standard model in SU(2) doublet extension

The long-awaited Higgs particle with mass around 125 GeV has been observed at the LHC. Considering it as the standard model Higgs boson and if there is no new physics between electroweak scale and Planck scale, then we don’t have a stable vacuum. Here, we give a brief review of the Standard Model vacuum stability and some other theoretical issues in the standard model. Possible ways to enhance the vacuum stability are also discussed. The Standrd Model (SM) is a guage theory which explains all the interactions nicely but leaves the particles massless. Higgs mechanism gives mass to all the particles in Standard Model except neutrinos, photon and gluons through Spontaneous symmetry breaking. Motivations from different sectors: such as baryon asymmetry, dark matter, supersymmetry and many more lead to extension of SM Higgs sector. We discuss theoretical and phenomenological aspects of Two Higgs Doublet Model. This extension has flavor changing neutral currents which are strongly constrained by experiment. Various strategies are discussed to eliminate these flavor changing neutral currents by imposing a discrete Z2 symmetry. In particular, scenarios with natural flavor conservation are investigated, including the so-called type I and type II models as well as leptonspecific and flipped models.

Numerical Study of Cattaneo–Christov Heat Flux on Water-Based Carreau Fluid Flow over an Inclined Shrinking Sheet with Ternary Nanoparticles

Due to their capacity to create better thermal conductivity than standard nanofluids, hybrid nano-fluids and modified nanofluids have notable applications in aerospace, energy materials, thermal sensors, antifouling, etc. This study aims to the modified and hybrid nanofluid flow with the Carreau fluid over a sloped shrinking sheet. The Cattaneo–Christov heat flux also takes into account. To determine the thermal efficiency of the heat, three different kinds of nanomaterials, copper oxide (CuO), copper (Cu), and alumina (Al2O3), are used. The similarity alteration commutes the insolubility of the model into ODEs. The conclusions are attained by program writing in MATLAB software and dealing with them through the bvp4c solver with the shooting method. The skin-friction amount decreases with the inclined sheet and local Weissenberg parameter for both modified and hybrid nanofluid. An upsurge thermal relaxation parameter declines the skin-friction coefficient for modified nanofluid flow and increases the skin-friction coefficient for hybrid nanofluid flow. The heat transfer rate is upsurged with modified and hybrid nanofluid for thermal relaxation parameter. Furthermore, the presentation includes the development of skin friction coefficient and Nusselt number values for specific parameters. Through benchmarking, numerical solutions are validated using certain limiting situations that were previously published findings, and typically solid correlation is shown