We study Coleman-De Luccia tunneling of the Standard Model Higgs field during inflation in the case when the electroweak vacuum is metastable. We verify that the tunneling rate is exponentially suppressed. The main contribution to the suppression is the same as in flat space-time. We analytically estimate the corrections due to the expansion of the universe and an effective mass term in the Higgs potential that can be present at inflation.
We propose a modification to the standard hybrid inflation model \cite{Linde:1993cn}, that connects a successful hybrid inflation scenario to the standard model Higgs sector, via the electroweak vacuum stability. The proposed model results in an effective inflation potential of a hilltop-type, with both the trans-Planckian and sub-Planckian inflation regimes consistent with the recent Planck/BICEP combined results. Reheating via the inflation sector decays to right-handed neutrinos is considered. An upper bound on the reheating temperature $T_{\rm R} \lsim 2\times 10^{11}~(1\times 10^{13})$ Ge…
We study inflation and cosmological electroweak phase transitions utilizing the Standard model augmented by $N$ scalars respecting a global $O(N)$ symmetry. We observe that the representation of the global symmetry is restricted by the inflationary observables and the condition of a strongly first order electroweak phase transition. Theoretical constraints including the stability, perturbativity and unitarity are used to bound the model parameter space. The Electroweak precision observables and Higgs precisions limit the representation of the symmetry. We evaluate the possibility to simultaneo…
Within the Standard Model, the current Higgs and top quark data favor metastability of the electroweak vacuum, although the uncertainties are still significant. The true vacuum is many orders of magnitude deeper than ours and the barrier separating the two is tiny compared to the depth of the well. This raises a cosmological question: how did the Higgs field get trapped in the shallow minimum and why did it stay there during inflation? The Higgs initial conditions before inflation must be fine--tuned to about one part in 10^8 in order for the Higgs field to end up in the right vacuum. In this …
The Next-to-Minimal Supersymmetric Standard Model (NMSSM) can incorporate inflation, where a combination of the Higgs-doublet fields plays the role of the inflaton. At the high scale, the Higgs doublets are non-minimally coupled to supergravity; this coupling appears as an additional contribution to the $μ$ term in the low-energy effective superpotential and potentially changes physics at the electroweak scale. In a recent publication, we investigate the extended parameter space of this model with respect to collider phenomenology at the electroweak scale, and discuss scenarios which are poten…
We show that, for all values of $Tan β$ and the light right-handed stop mass for which the electroweak phase transition is strong enough to avoid washout following electroweak baryogenesis, the electroweak vacuum is stable over the lifetime of the observed Universe. Cosmological stability of the electroweak vacuum is violated only if the light right-handed stop is lighter than 100-115GeV.
We make a change of variable in the standard model Higgs field by a fermion operator and show that the latter is responsible for the electroweak vacuum. By computing the vacuum expectation value of this fermion operator in the path integral formalism we determine a relation among the quark vacuum condensates, the quark masses and the intrinsic scale of the theory. We show that the heavy quark vacuum condensates do not justify the hypothesis of dynamical electroweak symmetry breaking with only standard model fermions.
We reveal a new source of CP-violation in the electroweak sector that is free of any experimental bounds, and we highlight the possible implications for baryogenesis.
In a previous paper, the standard model was generalized to include an electroweak axion which carries baryon plus lepton number, $B+L$. It was shown that such a model naturally gives the observed value of the dark energy, if the scale of explicit baryon number violation was chosen to be of the order of the Planck mass. In this paper, we consider the effect of the modulus of the axion field. Such a field must condense in order to generate the standard Goldstone boson associated with the phase of the axion field. This condensation breaks baryon number. We argue that this modulus might be associa…
We study the stability of the electroweak vacuum in low-scale inflation models whose Hubble parameter is much smaller than the instability scale of the Higgs potential. In general, couplings between the inflaton and Higgs are present, and hence we study effects of these couplings during and after inflation. We derive constraints on the couplings between the inflaton and Higgs by requiring that they do not lead to catastrophic electroweak vacuum decay, in particular, via resonant production of the Higgs particles.
We present a simple model for slow-rollover inflation where the vacuum energy that drives inflation is of the order of $G_F^{-2}$; unlike most models, the conversion of vacuum energy to radiation (``reheating'') is moderately efficient. The scalar field responsible for inflation is a standard-model singlet, develops a vacuum expectation value of the order of $4\times 10^6\GeV$, has a mass of order $1\GeV$, and can play a role in electroweak phenomena.
The concept of Higgs inflation can be elegantly incorporated in the Next-to-Minimal Supersymmetric Standard Model (NMSSM). A linear combination of the two Higgs-doublet fields plays the role of the inflaton which is non-minimally coupled to gravity. This non-minimal coupling appears in the low-energy effective superpotential and changes the phenomenology at the electroweak scale. While the field content of the inflation-inspired model is the same as in the NMSSM, there is another contribution to the $μ$ term in addition to the vacuum expectation value of the singlet. We explore this extended p…
In the Standard Model (SM), the Higgs mass around 125 GeV implies that the electroweak vacuum is metastable since the quartic Higgs coupling turns negative at high energies. I point out that a tiny mixing of the Higgs with a heavy singlet can make the electroweak vacuum completely stable. This is due to a tree level correction to the Higgs mass-coupling relation, which survives in the zero-mixing/heavy-singlet limit. Such a situation is experimentally indistinguishable from the SM, unless the Higgs self-coupling can be measured. As a result, Higgs inflation and its variants can still be viable…
We consider an inflationary scenario where the energy scale of inflation stems from gauge theory dynamics. We point out its generic implications on vacuum selection of our universe, in particular, on determination of spacetime symmetries including its dimensions.
We extend the so-called singlet doublet dark matter model, where the dark matter is an admixture of a Standard Model singlet and a pair of electroweak doublet fermions, by a singlet scalar field. The new portal coupling of it with the dark sector not only contributes to the dark matter phenomenology (involving relic density and direct detection limits), but also becomes important for generation of dark matter mass through its vacuum expectation value. While the presence of dark sector fermions affects the stability of the electroweak vacuum adversely, we find this additional singlet is capable…
In many inflationary models, a large amount of energy is transferred rapidly to the long-wavelength matter fields during a period of preheating after inflation. We study how this changes the dynamics of the electroweak phase transition if inflation ends at the electroweak scale. We simulate a classical SU(2)xU(1)+Higgs model with initial conditions in which the energy is concentrated in the long-wavelength Higgs modes. With a suitable initial energy density, the electroweak symmetry is restored non-thermally but broken again when the fields thermalize. During this symmetry restoration, baryon …
Whether the Standard Model electroweak vacuum is stable, metastable or unstable depends crucially on the top mass (and, to a lesser extent, on other measurable quantities). These topics are reviewed and updated by taking into account the most recent determination of the top and Higgs masses. Moreover, the correction to the vacuum decay due to Einstein gravity is described. This process is also discussed in a scenario, called softened gravity, which has been proposed as a solution of the Higgs mass hierarchy problem.
We analyse effective potential around the electroweak (EW) scale in the Standard Model extended with a heavy scalar doublet. We show that the additional scalars can have a strong impact on vacuum stability. Although the additional heavy scalars may improve the behaviour of running Higgs self-coupling at large field values, we prove that they can destabilise the vacuum due to EW-scale effects. A new EW symmetry conserving minimum of the effective potential can appear rendering the electroweak symmetry breaking minimum meta- or unstable. However, for the case of the inert doublet model (IDM) wit…
We construct a phenomenological model of electroweak-scale inflation that is in accordance with recent cosmic microwave background observations by WMAP, while setting the stage for a zero-temperature electroweak transition as assumed in recent models of baryogenesis. We find that the scalar spectral index especially poses tight constraints for low-scale inflation models. The inflaton-Higgs coupling leads to substantial mixing of the scalar degrees of freedom. Two types of scalar particles emerge with decay widths similar to that of the Standard Model Higgs particle.
It is known that the present electroweak vacuum is likely to be metastable and it may lead to a serious instability during/after inflation. We propose a simple solution to the problem of vacuum instability during/after inflation. If there is a moduli field which has Planck-suppressed interactions with the standard model fields, the Higgs quartic coupling in the early universe naturally takes a different value from the present one. A slight change of the quartic coupling in the early universe makes the Higgs potential absolutely stable and hence we are free from the vacuum instability during/af…
We investigate the electroweak vacuum stability in an extended version of the Standard Model which incorporates two additional singlet scalar fields and three right handed neutrinos. One of these extra scalars plays the role of dark matter while the other scalar not only helps in making the electroweak vacuum stable but also opens up the low mass window of the scalar singlet dark matter (< 500 GeV). We consider the effect of large neutrino Yukawa coupling on the running of Higgs quartic coupling. We have analyzed the constraints on the model and identify the range of parameter space which is c…
In this paper we investigate the consequences of imposing an SO(4) symmetry both on the scalar field and on spacetime prior to any spontaneous symmetry breakdown in the electroweak model. First we argue that the local electroweak gauge symmetry is implied by the initial SO(4) symmetry of the scalar field. Then we parameterize the vacuum, in a slightly different way with respect to the conventional assignment in the electroweak model, around the ground state mainly in two different ways: Once over the local electroweak gauge transformations and once over the local $γ$ basis which generates the …
The dynamics of false vacuum decay at the end of inflation is studied. It is shown that the creation of a new phase is mainly stimulated by temperature fluctuations. Moving walls of O(3)-symmetric bubbles weakly interact with their surroundings at the inflation stage. Large field fluctuations might arise as a result of wall collisions.
We consider singlet extensions of the standard model, both in the fermion and the scalar sector, to account for the generation of neutrino mass at the TeV scale and the existence of dark matter respectively. For the neutrino sector we consider models with extra singlet fermions which can generate neutrino mass via the so called inverse or linear seesaw mechanism whereas a singlet scalar is introduced as the candidate for dark matter. We show that although these two sectors are disconnected at low energy, the coupling constants of both the sectors get correlated at high energy scale by the cons…
We argue that fields responsible for inflation and supersymmetry breaking are connected by gravitational couplings. In view of the recent progress in studying supersymmetry breaking in a metastable vacuum, we have shown that in models of supersymmetric hybrid inflation, where R-symmetry plays an important role, the scale of supersymmetry breaking is generated dynamically at the end of inflation and turns out to be consistent with gravity mediation.
In strongly magnetized backgrounds, electrically charged vector bosons can condense. When considering the rho-meson sector of QCD, this results in the existence of a superconducting state with Abrikosov vortices. As a next order effect, also the neutral mesons condense and one expects the resulting lattice to be a mix of neutral and charged condensates, opening a possibility to the existence of a superfluid property. We will show how the detailed structure of the vacuum can be calculated and which implications it has on the nature of the exotic superconducting state.
We investigate the effect of fermionic electroweak multiplet dark matter models on the stability of the electroweak vacuum using two-loop renormalization group equations (RGEs) and one-loop matching conditions. Such a treatment is crucial to obtain reliable conclusions, compared with one-loop RGEs and tree-level matching conditions. In addition, we find that the requirement of perturbativity up to the Planck scale would give strong and almost mass-independent constraints on the Yukawa couplings in the dark sector. We also evaluate these models via the idea of finite naturalness for the Higgs m…
We examine the gauge dependence of lower bounds on the Higgs mass obtained from the requirement that the electroweak vacuum be the global minimum of the effective potential. We study a simple model, the spontaneously-broken Abelian Higgs model coupled to a chiral quark doublet in a two-parameter gauge and demonstrate that the lower bounds on the Higgs mass obtained in this model are dependent on the choice of gauge parameters. We discuss the significance of this result for calculations in the Standard Model.
We study the dynamics of $SU(2)_L$ times $U(1)_Y$ electroweak gauge fields during and after Higgs inflation. In particular, we investigate configurations of the gauge fields during inflation and find the gauge fields remain topologically non-trivial. We also find that the gauge fields grow due to parametric resonances caused by oscillations of a Higgs field after inflation. We show that the Chern-Simons number also grows significantly. Interestingly, the parametric amplification gives rise to sizable magnetic fields after the inflation whose final amplitudes depend on the anisotropy survived d…
The complex field $Φ$ containing the QCD axion has a natural portal coupling to the Higgs doublet of the form $λ_{h ϕ}|Φ|^2 |H|^2$. Here we consider the possibility that $λ_{h ϕ}$ has a natural magnitude for a dimensionless coupling, $λ_{h ϕ} \sim 0.1-1$. This is possible if the total mass squared parameter of the Higgs in the vacuum, including quadratic divergent and the $Φ$ vacuum expectation value contributions, is renormalized to reproduce the observed Higgs boson mass. It is then possible for the axion sector to stabilize the electroweak vacuum. We show the requirement of electroweak vacu…
The existence of a second Higgs doublet in Nature could lead to a cosmological first order electroweak phase transition and explain the origin of the matter-antimatter asymmetry in the Universe. We explore the parameter space of such a two-Higgs-doublet-model and show that a first order electroweak phase transition strongly correlates with a significant uplifting of the Higgs vacuum w.r.t. its Standard Model value. We then obtain the spectrum and properties of the new scalars $H_0$, $A_0$ and $H^{\pm}$ that signal such a phase transition, showing that the decay $A_0 \rightarrow H_0 Z$ at the L…
To avoid possible electroweak vacuum instability in the vector-like fermion model, we introduce a new singlet scalar to the model, which couples to the vector-like fermion, and also mixes with the Higgs boson after spontaneous symmetry breaking. We investigate the vector-like fermion predominantly coupled to the third generation quarks, and its mass is generated from the vacuum expectation value of the new scalar field in the model. In this setup, as running towards high energies, the new scalar provides positive contribution to the running of the higgs quartic coupling, and the matching on th…
We derive the QCD corrections to the electroweak gauge bosons vacuum polarization functions at high and zero--momentum transfer in the case of arbitrary internal quark masses. We then discuss in this general case (i) the connection between the $O(αα_S)$ calculations of the vector bosons self--energies using dimensional regularization and the one performed via a dispersive approach and (ii) the QCD corrections to the $ρ$ parameter for a heavy quark isodoublet.
We study the stability of the electroweak vacuum during and after the Starobinsky inflation, assuming the existence of the non-minimal Higgs coupling to the Ricci scalar. In the Starobinsky inflation, there exists $R^2$ term (with $R$ being the Ricci scalar), which modifies the evolution equation of the Higgs field. We consider the case that the non-minimal coupling is sizable so that the quantum fluctuation of the Higgs field is suppressed and that the Higgs amplitude is settled near the origin during the inflation. In such a case, the Higgs amplitude may be amplified in the preheating epoch …
Particle phase transitions in the early universe including electroweak and grand unification ones are well-studied subjects. We point out that there are new possible particle phase transitions around inflation. Those new inflationary particle phase transitions, if of the first order, may yield low-frequency gravitational waves (GWs) due to bubble dynamics, leaving imprints on the cosmic microwave background (CMB). In contrast to the nearly scale-invariant primordial GWs caused by vacuum fluctuation, these bubble-generated GWs are classical and have scale dependent B-mode spectra. If decoupled …
Recently it has been found that introducing a triplet Higgs to the standard model could provide a feasible leptogenesis to generate the baryon asymmetry of our universe, providing that the inflation is driven by the mixing state of the triplet Higgs and SM Higgs. In this work, we survey the viable parameter space satisfying the vacuum stability and perturbativity in this model. We find that the introduction of the triplet Higgs would also ameliorate the problem of the Higgs vacuum instability. We present two representative parameter regions where the origin of neutrino masses, baryon asymmetry…
We consider the introduction of a complex scalar field carrying a global lepton number charge to the Standard Model and the Higgs inflation framework. The conditions are investigated under which this model can simultaneously ensure Higgs vacuum stability up to the Planck scale, successful inflation, non-thermal Leptogenesis via the pendulum mechanism, and light neutrino masses. These can be simultaneously achieved when the scalar lepton is minimally coupled to gravity, that is, when standard Higgs inflation and reheating proceed without the interference of the additional scalar degrees of free…
In this work, we revisit the non-minimally coupled Higgs Inflation scenario and investigate its observational viability in light of the current Cosmic Microwave Background, Baryon Acoustic Oscillation and type Ia Supernovae data. We explore the effects of the Coleman-Weinberg approximation to the Higgs potential in the primordial universe, connecting the predictions for the Lagrangian parameters at inflationary scales to the electroweak observables through Renormalization Group methods at two-loop order. As the main result, we find that observations on the electroweak scale are in disagreement…
Recently, both ATLAS and CMS collaborations at the CERN Large Hadron Collider (LHC) have announced their observations of an excess of diphoton events around the invariant mass of $750~{\rm GeV}$ with a local significance of $3.6σ$ and $2.6σ$, respectively. In this paper, we interpret the diphoton excess as the on-shell production of a real singlet scalar in the $pp \to S \to γγ$ channel. To accommodate the observed production rate, we further introduce a vector-like fermion $F$, which is carrying both color and electric charges. The viable regions of model parameters are explored for this simp…
We perform a precise calculation of the decay rate of the electroweak vacuum in the standard model as well as in models beyond the standard model. We use a recently-developed technique to calculate the decay rate of a false vacuum, which provides a gauge invariant calculation of the decay rate at the one-loop level. We give a prescription to take into account the zero modes in association with translational, dilatational, and gauge symmetries. We calculate the decay rate per unit volume, $γ$, by using an analytic formula. The decay rate of the electroweak vacuum in the standard model is estima…
We explore the connection between tree-level Dirac neutrino masses and axion physics in a scenario where the PQ symmetry enforces lepton number conservation perturbatively. Requiring that the PQ scale $f_a$ is the only heavy scale to play a role in neutrino mass generation, we are led to the construction of a KSVZ-type model where Dirac neutrino masses are inversely proportional to $f_a$, provided a real scalar triplet (zero hypercharge) is added to the SM scalar sector. We analyse this extended scalar sector, focusing on the stabilisation of the electroweak vacuum. The contribution of the tri…
We study F-term hybrid inflation in a novel supersymmetric extension of the SM with a subdominant Fayet-Iliopoulos D-term. We call this particular form of inflation, in short, F_D-term hybrid inflation. The proposed model ties the mu-parameter of the MSSM to an SO(3)-symmetric Majorana mass m_N, through the vacuum expectation value of the inflaton field. The late decays of the ultraheavy particles associated with the extra U(1) gauge group, which are abundantly produced during the preheating epoch, could lower the reheat temperature even up to 1 TeV, thereby avoiding the gravitino overproducti…
We study the stability of neutral electroweak vacua in two Higgs doublet models, and calculate the lifetime of these states when the parameters are such that they are false vacua. As the two Higgs doublet model is invariant under a sign change of both doublets, degenerate true vacua exist. It is shown that this degeneracy, despite the fact that each of these minima locally describes the same physics, can immensely affect their lifetime. We apply these calculations to the parameter space of the models which is allowed by recent LHC searches, and infer combinations of parameters which should be …
It is shown that dark energy can be obtained from the interplay of the Higgs boson and the inflaton. A key element is the realization that electroweak symmetry breaking can trigger a second phase of rolling of the inflaton, which, when provided with the appropriate couplings between the fields, can be sufficiently slow to source accelerated expansion in the late time Universe. The observed dark energy density is obtained without fine-tuning of parameters or initial conditions due to an intricate conspiracy of numbers related to inflation, gravity and electroweak physics.
Ferrara University（费拉拉大学）；INFN Sez. Ferrara, Dept. of Physics and Earth Science（意大利国家核物理研究所费拉拉分部，地球科学与物理系）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；The Barcelona Institute of Science and Technology (BIST)（巴塞罗那科学技术研究所）
We demonstrate that the dispersive computation of the threshold enhancements to heavy quark vacuum polarizations is unstable. Because of the slow convergence of the dispersion relations the result critically depends on the intermediate energy region where the non-relativistic approximation, intrinsic to threshold calculations, is invalid. We discuss other ambiguities precluding a reliable calculation of the threshold contribution to the vacuum polarizations. In the absence of a solution prudence should force one to assign an error to the radiative corrections not far below the level of the per…
[Talk presented at the International Seminar Quarks `92, Zvenigorod, Russia, May 11-17, 1992.] The electroweak vacuum need not be absolutely stable. For certain top and Higgs masses in the Minimal Standard Model, it is instead metastable with a lifetime exceeding the present age of the Universe. The decay of our vacuum may be nucleated at low temperature by quantum tunneling or at high temperature in the early Universe by thermal excitation. I briefly review the constraints on top and Higgs masses from requiring that the electroweak vacuum be sufficiently stable to have survived to the present…
We study a scalar singlet dark matter (DM) having mass in sub-TeV regime by extending the minimal scalar singlet DM setup by additional vector like fermions. While the minimal scalar singlet DM satisfies the relic and direct detection constraints for mass beyond TeV only, presence of its portal coupling with vector like fermions opens up additional co-annihilation channels. These vector like fermions also help in achieving electroweak vacuum stability all the way up to Planck scale. We find that for one generation of vector like quarks consisting of a $SU(2)_L$ doublet and a singlet, scalar si…
We consider the most minimal scale invariant extension of the standard model that allows for successful radiative electroweak symmetry breaking and inflation. The framework involves an extra scalar singlet, that plays the rôle of the inflaton, and is compatibile with current experimental bounds owing to the non-minimal coupling of the latter to gravity. This inflationary scenario predicts a very low tensor-to-scalar ratio $r \approx 10^{-3}$, typical of Higgs-inflation models, but in contrast yields a scalar spectral index $n_s \simeq 0.97$ which departs from the Starobinsky limit. We briefly …
Formation of a vacuum like domain of the strong-interaction chiral condensate misaligned with respect to the electroweak symmetry breaking arguably modifies the mass spectrum of electroweak gauge bosons and their interactions in that domain in an observable manner. In particular,photon acquires the mass $m_γ\sim{1/2}f_π\sin2θ_{W}$.
A two-component scalar DM scenario comprising an additional scalar doublet and a $Y$ = 0 scalar triplet is proposed. Key features of the ensuing dark matter phenomenology are highlighted with emphasis on inter-conversion between the two dark matter components. For suitable choices of the model parameters, we show that such inter-conversion can explain the observed relic abundance when the doublet dark matter component has mass in the \emph{desert} region while the triplet component has sub-TeV mass. This finding is important in the context of such mass regions known to predict under-abundant r…
We study the minimal type-III seesaw model in which we extend the SM by adding two $SU(2)_L$ triplet fermions with zero hypercharge to explain the origin of the non-zero neutrino masses. We show that the naturalness conditions and the limits from lepton flavor violating decays provide very stringent bounds on the model parameters along with the constraints from the stability/metastability of the electroweak vacuum. We perform a detailed analysis of the model parameter space including all the constraints for both normal as well as inverted hierarchies of the light neutrino masses. We find that …
Electroweak vacuum transition processes (sphalerons) in the early Universe provide a possible explanation of the baryon asymmetry. Combining this physics with the anomalous commutators of Adler and Boulware and renormalization group invariance, we argue that electroweak baryon number violation also induces a ``topological condensate'' in the vacuum. QCD sphaleron processes act to distribute the baryon number violation between both left and right handed quarks and induce a spin independent component in this ``condensate''.
We propose a two component dark matter set-up by extending the Standard Model with a singlet and a hypercharge-less triplet scalars, each of them being odd under different $Z_2$ symmetries. We observe that the inter-conversion between the two dark matter components allow a viable parameter space where masses of both the dark matter candidates can be below TeV, even though their individual contribution to single component dark matter rules out any such sub-TeV dark matter. We find that a lighter mass of the neutral component of the scalar triplet, playing the role of one dark matter component, …
Recent analysis shows that if the 125-126 GeV LHC resonance turns out to be the Standard Model Higgs boson, the electroweak vacuum would be a metastable state at 98% C.L. In this paper we argue that, during inflation, the electroweak vacuum can actually be very short-lived, contrary to the conclusion that follows from the flat spacetime analysis. Namely, in the case of a pure Higgs potential the electroweak vacuum decays via the Hawking-Moss transition, which has no flat spacetime analogue. As a result, the Higgs vacuum is unstable, unless the rate of inflation is low enough: $H_{\rm inf}\less…
We study the electroweak vacuum stability in Type I seesaw models for 3 generations of neutrinos in scenarios where the right-handed neutrinos have explicit bare mass terms in the Lagrangian and where these are dynamically generated through the mechanism of spontaneous symmetry breaking. To best highlight the difference of the two cases we concentrate on the absolute stability of the scalar potential. We observe that for the first scenario, the scale at which the scalar potential becomes unstable is lower from that within the Standard Model. In addition the Yukawa couplings $\mathbf{Y}_ν$ are …
