Vacuum Stability Conditions Research Articles

Vacuum stability conditions of the general two-Higgs-doublet potential

In this paper, we present the novel analytical expressions for the bounded-from-below or the vacuum stability conditions of scalar potential for a general two-Higgs-doublet model by using the concepts of co-positivity and the gauge orbit spaces. More precisely, several sufficient conditions and necessary conditions are established for the vacuum stability of the general 2HDM potential, respectively. We also give an equivalent condition of the vacuum stability of the general 2HDM potential in theory, and then, apply it to derive the analytical necessary conditions of the general 2HDM potential. Meanwhile, the semi-positive definiteness is proved for a class of 4th-order two-dimensional complex tensor.

Higgs–Higgs scattering and the (non-)existence of the Higgsonium

We study the Higgs–Higgs scattering process and the possible emergence of a Higgs–Higgs bound state (Higgsonium) in any Higgs potential with the vacuum expectation value and second derivative matching the corresponding values from the Standard Model (SM). From the tree-level Higgs–Higgs scattering amplitude, we construct the unitarized amplitude using two different unitarization schemes (the well-known on-shell and N/D methods). We reproduce the known result that there is no Higgsonium state in the SM and, in addition, we determine the S-, D-, and G-wave SM scattering lengths, both at tree-level and upon unitarization. In doing so, we refine previous results by checking the convergence of the N/D approach. Next, we extend the calculation for non-SM potentials and investigate under which conditions a formation of a bound state close to the Higgs–Higgs threshold is possible. In this way, the assumption that no Higgsonium exist, imposes certain bounds on the values of the self-interaction parameters that complement those imposed by the vacuum stability condition.

Vacuum stability in the Standard Model with vectorlike fermions

The discovery of Standard-Model like Higgs at 125 GeV may raise more questions than the answers it provides. In particular, the hierarchy problem remains unsolved, and the Standard Model Higgs quartic self-coupling becomes negative below the Planck scale, necessitating new physics beyond the Standard Model. In this work we investigate a popular scenario, extensions of the Standard Model with vector-like fermion fields, such as the ones present in models with extra dimensions or in Higgs composite models, using a model independent approach. Since fermions decrease the Higgs quartic coupling at high energies, only exacerbating the self-coupling problem, we introduce first an additional scalar, which by itself is enough to overcome the vacuum stability limit, and then explore the effects of vector-like fermions in singlet, doublet and triplet representations. For each model, we identify the allowed fermion masses and mixing angles with the third family fermions required to satisfy the vacuum stability condition, and compare different representations. Allowed fermion masses emerge at around 1 TeV, raising hope that these will be found at the LHC. We also examine corrections to oblique parameters S and T from additional scalar and vector-like quarks which also impose constraints on mixing and mass splitting of both sectors., but these restrictions are relatively weak compared to the vacuum stability.

Vacuum stability of conformally invariant scalar dark matter models

We discuss vacuum structure and vacuum stability in classically scale-invariant renormalizable models with a scalar dark matter multiplet of global O(N) symmetry together with an electroweak singlet scalar mediator. Our conformally invariant scalar potential generates the electroweak symmetry breaking via the Coleman-Weinberg mechanism, and the new scalar singlet mediator acquires its mass through radiative corrections of the scalar dark matters as well as of the standard model particles. Taking into account the present collider bounds, we find the region of parameter space where the scalar potential is stable and all the massless couplings are perturbative up to the Planck scale. With the obtained parameter sets satisfying the vacuum stability condition, we present the allowed region of new physics parameters satisfying the recent measurement of relic abundance, and predict the elastic scattering cross section of the new scalar multiplet into target nuclei for a direct detection of the dark matter. We also discuss the collider signatures and future discovery potentials of the new scalars.

Hierarchy problem and the vacuum stability in two-scalar dark matter model

We consider an extension to the Standard Model (SM) with two extra real singlet scalars which interact with the SM Higgs particle. The lighter scalar is taken as the dark matter (DM) candidate. We show that the model successfully explains the relic abundance of the DM in the universe and evades the strong bounds from direct detection experiments while respecting the perturbativity and the vacuum stability conditions. In addition, we study the hierarchy problem within the Veltman approach by solving the renormalization group equations at one-loop. We demonstrate that the addition of the real singlet scalars contributes to the Veltman parameters which in turn results in satisfying the Veltman conditions much lower than the Planck scale $ \Lambda_\text{Pl}$ down to the electroweak scale. Therefore, the presence of the extra scalars solves the fine-tuning problem of the Higgs mass. For the case of the two-scalar DM model we find two representative points in the viable parameter space which satisfy also the Veltman conditions at $\Lambda = 300$ GeV and $\Lambda = 1$ TeV.

Updated constraints on the Georgi-Machacek model and its electroweak phase transition and associated gravitational waves

With theoretical constraints such as perturbative unitarity and vacuum stability conditions and updated experimental data of Higgs measurements and direct searches for exotic scalars at the LHC, we perform an updated scan of the allowed parameter space of the Georgi-Machacek (GM) model. With the refined global fit, we examine the allowed parameter space for inducing strong first-order electroweak phase transitions (EWPTs) and find only the one-step phase transition is phenomenologically viable. Based upon the result, we study the associated gravitational wave (GW) signals and find most of which can be detected by several proposed experiments. We also make predictions on processes that may serve as promising probes to the GM model in the near future at the LHC, including the di-Higgs productions and several exotic scalar production channels.

Imprint of SUSY in radiative B -meson decays

We study supersymmetric (SUSY) effects on $C_7(\mu_b)$ and $C'_7(\mu_b)$ which are the Wilson coefficients (WCs) for $b \to s \gamma$ at b-quark mass scale $\mu_b$ and are closely related to radiative $B$-meson decays. The SUSY-loop contributions to $C_7(\mu_b)$ and $C'_7(\mu_b)$ are calculated at leading order (LO) in the Minimal Supersymmetric Standard Model (MSSM) with general quark-flavour violation (QFV). For the first time we perform a systematic MSSM parameter scan for the WCs $C_7(\mu_b)$ and $C'_7(\mu_b)$ respecting all the relevant constraints, i.e. the theoretical constraints from vacuum stability conditions and the experimental constraints, such as those from $K$- and $B$-meson data and electroweak precision data, as well as recent limits on SUSY particle masses and the 125 GeV Higgs boson data from LHC experiments. From the parameter scan we find the following: (1) The MSSM contribution to Re($C_7(\mu_b)$) can be as large as $\sim \pm 0.05$, which could correspond to about 3$\sigma$ significance of New Physics (NP) signal in the future LHCb and Belle II experiments. (2) The MSSM contribution to Re($C'_7(\mu_b)$) can be as large as $\sim -0.08$, which could correspond to about 4$\sigma$ significance of NP signal in the future LHCb and Belle II experiments. (3) These large MSSM contributions to the WCs are mainly due to (i) large scharm-stop mixing and large scharm/stop involved trilinear couplings, (ii) large sstrange-sbottom mixing and large sstrange-sbottom involved trilinear couplings and (iii) large bottom Yukawa coupling $Y_b$ for large $\tan\beta$ and large top Yukawa coupling $Y_t$. In case such large NP contributions to the WCs are really observed in the future experiments at Belle II and LHCb Upgrade, this could be the imprint of QFV SUSY (the MSSM with general QFV).

Vacuum stability conditions and potential minima for a matrix representation in lightcone orbit space

The orbit space for a scalar field in a complex square matrix representation obtains a Minkowski space structure from the Cauchy–Schwarz inequality. It can be used to find vacuum stability conditions and minima of the scalar potential. The method is suitable for fields such as a bidoublet, an SU(2) triplet or SU(3) octet. We use the formalism to find the vacuum stability conditions for the left-right symmetric potential of a bidoublet and left and right Higgs doublets.

Copositivity for 3rd-Order Symmetric Tensors and Applications

The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of 4th order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity of 3th order 2 dimensional (3 dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th order tensors, the analytically sufficient conditions of copositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for $\mathbb{Z}_3$ scalar dark matter.

Analytical expressions of copositivity for fourth-order symmetric tensors

In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are fourth-order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of fourth-order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for fourth-order 2-dimensional symmetric tensors. For fourth-order 3-dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) copositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for fourth-order 2-dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for fourth-order 2-dimensional symmetric tensors. Finally, these results may be applied to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson.

Complex scalar dark matter in the gauged two-Higgs-doublet model

The complex scalar dark matter (DM) candidate in the gauged two Higgs doublet model (G2HDM), stabilized by a peculiar hidden parity ($h$-parity), is studied in detail. We explore the parameter space for the DM candidate by taking into account the most recent DM constraints from various experiments, in particular, the PLANCK relic density measurement and the current DM direct detection limit from XENON1T. We separate our analysis in three possible compositions for the mixing of the complex scalar. We first constrain our parameter space with the vacuum stability and perturbative unitarity conditions for the scalar potential, LHC Higgs measurements, plus Drell-Yan and electroweak precision test constraints on the gauge sector. We find that DM dominated by composition of the inert doublet scalar is completely excluded by further combining the previous constraints with both the latest results from PLANCK and XENON1T. We also demonstrate that the remaining parameter space with two other DM compositions can be further tested by indirect detection like the future CTA gamma-ray telescope.

Constraints from Spectrum of Scalar Fields in the 3-3-1 Model with CKM Mechanism

The vacuum stability conditions are implemented for the 3-3-1 model of observed fermion masses and mixings. We show that for the Higgs squared mass matrices, the condi- tions for semi-definition of the diagonal elements are most important since other constraints are followed from the first ones.

Correlation between the decays h0 → γγ/gg in the MSSM with quark flavor violation

We study the loop-induced decays [Formula: see text] and [Formula: see text] in the Minimal Supersymmetric Standard Model (MSSM) with quark flavor violation (QFV), identifying [Formula: see text] with the Higgs boson with a mass of 125 GeV, where [Formula: see text] and [Formula: see text] are photon and gluon, respectively. We perform a MSSM parameter scan and a detailed analysis around a fixed reference point respecting theoretical constraints from vacuum stability conditions and experimental constraints, such as those from [Formula: see text]-meson data and electroweak precision data, as well as recent limits on Supersymmetric (SUSY) particle masses from LHC experiments. We find that (i) the relative deviation of the decay width [Formula: see text] from the Standard Model value, [Formula: see text], can be large and negative, [Formula: see text], (ii) the analogous deviation of [Formula: see text] is strongly correlated, [Formula: see text] for [Formula: see text], (iii) the relative deviation of the width ratio [Formula: see text] from the SM value, [Formula: see text], can be large (up to [Formula: see text]20%), (iv) the deviations can be large due to the up-type squark loop contributions, (v) the SUSY QFV parameters can have a significant effect on these deviations. Such large deviations can be observed at a future [Formula: see text] collider like ILC. Observation of the deviation patterns as shown in this study would favor the MSSM with flavor-violating squark mixings and encourage to perform further studies in this model.

Signatures of synchrotron radiation from the annihilation of dark matter at the Galactic Centre

We propose a fermionic dark matter model by extending Standard Model with a Dirac fermion and a real pseudoscalar. The fermion dark matter particle interacts with the Standard Model sector via the Higgs portal through a dimension five interaction term as also through a pseudoscalar interaction term. The parameter space of the model is then constrained by using the vacuum stability and perturbativity condition as also with the LHC constraints. They are finally constrained by the PLANCK results for dark matter relic densities. The direct detection limits are then ensured to have satisfied by the model. We then explore within the framework of the model, the possible signatures of synchrotron radiation from the annihilations of dark matter in the Galactic Centre region when the end product is e+e−. We consider the observational data from the radio telescopes namely SKA, GMRT and Jodrell Bank telescopes and compare our calculated synchrotron flux density with them and also with the results predicted by these experiments. We predict that if the low frequency radio telescopes like GMRT, SKA operate at the peak frequencies obtained from our calculations should get a better r.m.s sensitivity.

Vacuum stability conditions of the economical 3-3-1 model from copositivity

By applying copositivity criterion to the scalar potential of the economical 3-3-1 model, we derive necessary and sufficient bounded-from-below conditions at tree level. Although these are a large number of intricate inequalities for the dimensionless parameters of the scalar potential, we present general enlightening relations in this work. Additionally, we use constraints coming from the minimization of the scalar potential by means of the orbit space method, the positivity of the squared masses of the extra scalars, the Higgs boson mass, the Z' gauge boson mass and its mixing angle with the SM Z boson in order to further restrict the parameter space of this model.

Gluino-mediated electroweak penguin with flavor-violating trilinear couplings

In light of a discrepancy of the direct CP violation in K → ππ decays, ε′/εK , we investigate gluino contributions to the electroweak penguin, where flavor violations are induced by squark trilinear couplings. Top-Yukawa contributions to ΔS = 2 observables are taken into account, and vacuum stability conditions are evaluated in detail. It is found that this scenario can explain the discrepancy of ε′/εK for the squark mass smaller than 5.6 TeV. We also show that the gluino contributions can amplify mathrm{mathcal{B}}left(Kto pi nu overline{nu}right) , ℬ(KS → μ+μ−)eff and ΔACP(b → sγ). Such large effects could be measured in future experiments.

Explaining dark matter and neutrino mass in the light of TYPE-II seesaw model

With the motivation of simultaneously explaining dark matter and neutrino masses, mixing angles, we have invoked the Type-II seesaw model extended by an extra SU(2) doublet Φ. Moreover, we have imposed a Z2 parity on Φ which remains unbroken as the vacuum expectation value of Φ is zero. Consequently, the lightest neutral component of Φ becomes naturally stable and can be a viable dark matter candidate. On the other hand, light Majorana masses for neutrinos have been generated following usual Type-II seesaw mechanism. Further in this framework, for the first time we have derived the full set of vacuum stability and unitarity conditions, which must be satisfied to obtain a stable vacuum as well as to preserve the unitarity of the model respectively. Thereafter, we have performed extensive phenomenological studies of both dark matter and neutrino sectors considering all possible theoretical and current experimental constraints. Finally, we have also discussed a qualitative collider signatures of dark matter and associated odd particles at the 13 TeV Large Hadron Collider.

Right-handed neutrino dark matter in the classically conformal U(1)′ extended standard model

We consider the dark matter (DM) scenario in the context of the classically conformal ${\mathrm{U}(1)}^{\ensuremath{'}}$ extended standard model (SM), with three right-handed neutrinos (RHNs) and the ${\mathrm{U}(1)}^{\ensuremath{'}}$ Higgs field. The model is free from all of the ${\mathrm{U}(1)}^{\ensuremath{'}}$ gauge and gravitational anomalies in the presence of the three RHNs. We introduce a ${Z}_{2}$ parity in the model, under which an odd parity is assigned to one RHN, while all of the other particles are assigned to be ${Z}_{2}$ even, and hence the ${Z}_{2}$-odd RHN serves as a DM candidate. In this model, the ${\mathrm{U}(1)}^{\ensuremath{'}}$ gauge symmetry is radiatively broken through the Coleman-Weinberg mechanism, by which the electroweak symmetry breaking is triggered. There are three free parameters in our model---the ${\mathrm{U}(1)}^{\ensuremath{'}}$ charge of the SM Higgs doublet (${x}_{H}$), the new ${\mathrm{U}(1)}^{\ensuremath{'}}$ gauge coupling (${g}_{X}$), and the ${\mathrm{U}(1)}^{\ensuremath{'}}$ gauge boson (${Z}^{\ensuremath{'}}$) mass (${m}_{{Z}^{\ensuremath{'}}}$)---which are severely constrained in order to solve the electroweak vacuum instability problem, and satisfy the LHC Run-2 bounds from the search for the ${Z}^{\ensuremath{'}}$ boson resonance. In addition to these constraints, we investigate the RHN DM physics. Because of the nature of classical conformality, we find that a RHN DM pair mainly annihilates into the SM particles through ${Z}^{\ensuremath{'}}$ boson exchange. This is the so-called ${Z}^{\ensuremath{'}}$-portal DM scenario. Combining the electroweak vacuum stability condition, the LHC Run-2 bounds, and the cosmological constraint from the observed DM relic density, we find that all constraints work together to narrow the allowed parameter regions and, in particular, exclude ${m}_{{Z}^{\ensuremath{'}}}\ensuremath{\lesssim}3.5\text{ }\text{ }\mathrm{TeV}$. For the obtained allowed regions, we calculate the spin-independent cross section of the RHN DM with nucleons. We find that the resultant cross section is well below the current experimental upper bounds.

Vacuum stability and perturbativity of SU(3) scalars

We calculate the vacuum stability conditions and renormalisation group equations for the extensions of standard model with a higher colour multiplet scalar up to the representation 15′ that leaves the strong interaction asymptotically free. In order to find the vacuum stability conditions, we calculate the orbit spaces for the self-couplings of the higher multiplets, which for the representations 15 and 15′ of SU(3)c are highly complicated. However, if the scalar potential is linear in orbit space variables, it is sufficient to know the convex hull of the orbit space. Knowledge of the orbit spaces also facilitates the minimisation of the potentials. In contrast to the self-couplings of other multiplets, we find that the scalar quartic couplings of the representations 3 and 8walk rather than run, remaining nearly constant and perturbative over a vast energy range. We describe the conditions for walking couplings using a schematic model. With these technical results at hand we revise earlier results of generation of new scales with large SU(3)c scalar multiplets. Our results are easily extendable to models of new physics with additional SU(3) or SU(N) gauge symmetries.

Stability and UV completion of the Standard Model

The knowledge of the electroweak vacuum stability condition is of the greatest importance for our understanding of beyond Standard Model physics. It is widely believed that new physics that lives at very high-energy scales should have no impact on the stability analysis. This expectation has been recently challenged, but the results were controversial as new physics was given in terms of non-renormalizable higher-order operators. Here we consider for the first time new physics at extremely high-energy scales (say close to the Planck scale) in terms of renormalizable operators, in other words we consider a sort of toy UV completion of the Standard Model, and definitely show that its presence can be crucial in determining the vacuum stability condition. This result has important phenomenological consequences, as it provides useful guidance in studying beyond Standard Model theories. Moreover, it suggests that very popular speculations based on the so-called “criticality” of the Standard Model do not appear to be well founded.