Nonzero Vacuum Expectation Value Research Articles

Baryogenesis of the universe in cSMCS model plus iso-doublet vector quark

CP violation of the SM is insufficient to explain the baryon asymmetry in the universe and therefore an additional source of CP violation is needed. Here the extension of the SM by a neutral complex scalar singlet with a nonzero vacuum expectation value (cSMCS) plus a heavy vector quark pair is considered. This model offers the spontaneous CP violation and proper description in the baryogenesis, it leads strong enough first-order electro-weak phase transition to suppress the baryon-violating sphaleron process.

Radiative symmetry breaking in supersymmetricB−Lmodels with an inverse seesaw mechanism

We study the radiative symmetry breaking of $B\ensuremath{-}L$ in supersymmetric models with an inverse seesaw mechanism. We show that for a wide region of parameter space, the radiative corrections can drive the squared mass of the extra Higgs boson from positive initial values at the GUT scale to negative values at the TeV scale, leading to the spontaneous breaking of the $B\ensuremath{-}L$ symmetry. We also emphasize that in this class of models, unlike the supersymmetric $B\ensuremath{-}L$ models with a type-I seesaw, the right-handed sneutrino cannot get a nonzero vacuum expectation value. Therefore, $B\ensuremath{-}L$ can be radiatively broken, while $R$ parity remains an exact symmetry.

Confinement/deconfinement transition from symmetry breaking in gauge/gravity duality

We study the confinement/deconfinement transition in a strongly coupled system triggered by an independent symmetry-breaking quantum phase transition in gauge/gravity duality. The gravity dual is an Einstein-scalar-dilaton system with AdS near-boundary behavior and soft wall interior at zero scalar condensate. We study the cases of neutral and charged condensate separately. In the former case the condensation breaks the discrete $\mathbb{Z}_2$ symmetry while a charged condensate breaks the continuous $U(1)$ symmetry. After the condensation of the order parameter, the non-zero vacuum expectation value of the scalar couples to the dilaton, changing the soft wall geometry into a non-confining and anisotropically scale-invariant infrared metric. In other words, the formation of long-range order is immediately followed by the deconfinement transition and the two critical points coincide. The confined phase has a scale -- the confinement scale (energy gap) which vanishes in the deconfined case. Therefore, the breaking of the symmetry of the scalar ($\mathbb{Z}_2$ or $U(1)$) in turn restores the scaling symmetry in the system and neither phase has a higher overall symmetry than the other. When the scalar is charged the phase transition is continuous which goes against the Ginzburg-Landau theory where such transitions generically only occur discontinuously. This phenomenon has some commonalities with the scenario of deconfined criticality. The mechanism we have found has applications mainly in effective field theories such as quantum magnetic systems. We briefly discuss these applications and the relation to real-world systems.

How thermal inflation can saveminimal hybrid inflation in supergravity

Minimal hybrid inflation in supergravity has been ruled out by the 2015 Planck observations because the spectral index of the produced curvature perturbation falls outside observational bounds. To resurrect the model, a number of modifications have been put forward but many of them spoil the accidental cancellation that resolves the η-problem and require complicated Kähler constructions to counterbalance the lost cancellation. In contrast, in this paper the model is rendered viable by supplementing the scenario with a brief period of thermal inflation, which follows the reheating of primordial inflation. The scalar field responsible for thermal inflation requires a large non-zero vacuum expectation value (VEV) and a flat potential. We investigate the VEV of such a flaton field and its subsequent effect on the inflationary observables. We find that, for large VEV, minimal hybrid inflation in supergravity produces a spectral index within the 1-σ Planck bound and a tensor-to-scalar ratio which may be observable in the near future. The mechanism is applicable to other inflationary models.

Neutrino catalyzed diphoton excess

In this paper we explain the 750 GeV diphoton resonance observed at the run-2 LHC as a scalar singlet S, that plays a key role in generating tiny but nonzero Majorana neutrino masses. The model contains four electroweak singlets: two leptoquarks, a singly charged scalar and a neutral scalar S. Majorana neutrino masses might be generated at the two-loop level as S gets nonzero vacuum expectation value. S can be produced at the LHC through the gluon fusion and decays into diphoton with charged scalars running in the loop. The model fits perfectly with a narrow width of the resonance. Constraints on the model are investigated, which shows a negligible mixing between the resonance and the standard model Higgs boson.

Z ′, Higgses and heavy neutrinos in U(1)′ models: from the LHC to the GUT scale

We study a class of non-exotic minimal $U(1) '$ extensions of the Standard Model, which includes all scenarios that are anomaly-free with the ordinary fermion content augmented by one Right-Handed neutrino per generation, wherein the new Abelian gauge group is spontaneously broken by the non-zero Vacuum Expectation Value of an additional Higgs singlet field, in turn providing mass to a $Z'$ state. By adopting the $B-L$ example, whose results can be recast into those pertaining to the whole aforementioned class, and allowing for both scalar and gauge mixing, we first extract the surviving parameter space in presence of up-to-date theoretical and experimental constraints. Over the corresponding parameter configurations, we then delineate the high energy behaviour of such constructs in terms of their stability and perturbativity. Finally, we highlight key production and decay channels of the new states entering the spectra of this class of models, i.e., heavy neutrinos, a second Higgs state and the $Z'$, which are amenable to experimental investigation at the Large Hadron Collider. We therefore set the stage to establish a direct link between measurements obtainable at the Electro-Weak scale and the dynamics of the underlying model up to those where a Grand Unification Theory embedding a $U(1)'$ can be realised.

Symmetry breaking patterns of the 3-3-1 model at finite temperature

We consider the minimal version of an extension of the standard electroweak model based on the $SU(3)_c \times SU(3)_L \times U(1)_X$ gauge symmetry (the 3-3-1 model). We analyze the most general potential constructed from three scalars in the triplet representation of $SU(3)_L$, whose neutral components develop nonzero vacuum expectation values, giving mass for all the model's massive particles. {}For different choices of parameters, we obtain the particle spectrum for the two symmetry breaking scales: one where the $SU(3)_L \times U(1)_X$ group is broken down to $SU(2)_L\times U(1)_Y$ and a lower scale similar to the standard model one. Within the considerations used, we show that the model encodes two first-order phase transitions, respecting the pattern of symmetry restoration. The last transition, corresponding to the standard electroweak one, is found to be very weak first-order, most likely turning second-order or a crossover in practice. However, the first transition in this model can be strongly first-order, which might happen at a temperature not too high above the second one. We determine the respective critical temperatures for symmetry restoration for the model.

IDMS: inert dark matter model with a complex singlet

We study an extension of the inert doublet model (IDM) that includes an extra complex singlet of the scalars fields, which we call the IDMS. In this model there are three Higgs particles, among them a SM-like Higgs particle, and the lightest neutral scalar, from the inert sector, remains a viable dark matter (DM) candidate. We assume a non-zero complex vacuum expectation value for the singlet, so that the visible sector can introduce extra sources of CP violation. We construct the scalar potential of IDMS, assuming an exact Z2 symmetry, with the new singlet being Z2-even, as well as a softly broken U(1) symmetry, which allows a reduced number of free parameters in the potential. In this paper we explore the foundations of the model, in particular the masses and interactions of scalar particles for a few benchmark scenarios. Constraints from collider physics, in particular from the Higgs signal observed at the Large Hadron Collider with , as well as constraints from the DM experiments, such as relic density measurements and direct detection limits, are included in the analysis. We observe significant differences with respect to the IDM in relic density values from additional annihilation channels, interference and resonance effects due to the extended Higgs sector.

High-scale validity of a model with three Higgs doublets

We consider a three-Higgs doublet scenario in this paper, invariant under the discrete group S3 , and probe its high-scale validity by allowing the model parameters to evolve under a renormalization group. We choose two particular alignments of vacuum expectation values (vev) for our study, out of a set of several such possible ones. All three doublets receive nonzero vacuum expectation values in the first case, and in the second case, two of the doublets remain without vev. The constraints on the parameter space at low energy, including the measured value of the Higgs mass and the signal strengths, oblique corrections and also measurements of relic density and direct detection rates are juxtaposed with the conditions of vacuum stability, perturbativity and unitarity at various scales. We find that the scenario with three nonzero vevs is not valid beyond 107 GeV, assuming no additional physics participates at the intermediate scales. On the contrary, the scenario with only one nonzero vev turns out to be a successful model for cold dark matter phenomenology, which also turns out to be valid up to the Planck scale at the same time. Stringent restrictions are obtained on the model parameter space in each case. Thus, the S3 symmetric scalar sector emerges as an ultraviolet complete theory.

Diphoton excess at 750 GeV in leptophobic U(1)′ model inspired by E 6 GUT

We discuss the 750 GeV diphoton excess at the LHC@13TeV in the framework of leptophobic U(1)$^\prime$ model inspired by $E_6$ grand unified theory (GUT). In this model, the Standard Model (SM) chiral fermions carry charges under extra U(1)$^\prime$ gauge symmetry which is spontaneously broken by a U(1)$^\prime$-charged singlet scalar ($\Phi$). In addition, extra quarks and leptons are introduced to achieve the anomaly-free conditions, which is a natural consequence of the assumed $E_6$ GUT. These new fermions are vectorlike under the SM gauge group but chiral under new U(1)$^\prime$, and their masses come entirely from the nonzero vacuum expectation value of $\Phi$ through the Yukawa interactions. Then, the CP-even scalar $h_\Phi$ from $\Phi$ can be produced at the LHC by the gluon fusion and decay to the diphoton via the one-loop diagram involving the extra quarks and leptons, and can be identified as the origin of diphoton excess at 750 GeV. In this model, $h_\Phi$ can decay into a pair of dark matter particles as well as a pair of scalar bosons, thereby a few tens of the decay width may be possible.

Entropic manifestations of topological order in three dimensions

We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by non-zero vacuum expectation value of contractible loop operators a new topological invariant appears that increases the entropy if the model consists of non-trivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.

Radiative breaking of the minimal supersymmetric left–right model

We study a variation to the SUSY Left-Right symmetric model based on the gauge group $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)_{BL}$. Beyond the quark and lepton superfields we only introduce a second Higgs bidoublet to produce realistic fermion mass matrices. This model does not include any $SU(2)_R$ triplets. We calculate renormalization group evolutions of soft SUSY parameters at the one-loop level down to low energy. We find that an $SU(2)_R$ slepton doublet acquires a negative mass squared at low energies, so that the breaking of $SU(2)_R\times U(1)_{BL}\rightarrow U(1)_Y$ is realized by a non-zero vacuum expectation value of a right-handed sneutrino. Small neutrino masses are produced through neutrino mixings with gauginos. Mass limits on the $SU(2)_R\times U(1)_{BL}$ sector are obtained by direct search results at the LHC as well as lepton-gaugino mixing bounds from the LEP precision data.

$${B_s^0}$$ B s 0 – $${\bar{B}}_s^0$$ B ¯ s 0 mixing within minimal flavor-violating two-Higgs-doublet models

In the "Higgs basis" for a generic 2HDM, only one scalar doublet gets a nonzero vacuum expectation value and, under the criterion of minimal flavor violation, the other one is fixed to be either color-singlet or color-octet, which are named as the type-III and type-C models, respectively. In this paper, the charged-Higgs effects of these two models on $B_s^0-\bar{B}_s^0$ mixing are studied. Firstly, we perform a complete one-loop computation of the electro-weak corrections to the amplitudes of $B_s^0-\bar{B}_s^0$ mixing. Together with the up-to-date experimental measurements, a detailed phenomenological analysis is then performed in the cases of both real and complex Yukawa couplings of charged scalars to quarks. The spaces of model parameters allowed by the current experimental data on $B_s^0-\bar{B}_s^0$ mixing are obtained and the differences between type-III and type-C models are investigated, which is helpful to distinguish between these two models.

Leptogenesis via neutrino production during Higgs condensate relaxation

During inflation, scalar fields, including the Higgs boson, may acquire a nonzero vacuum expectation value, which must later relax to the equilibrium value during reheating. In the presence of the time-dependent condensate, the vacuum state can evolve into a state with a nonzero particle number. We show that, in the presence of lepton number violation in the neutrino sector, the particle production can explain the observed matter-antimatter asymmetry of the universe. We find that this form of leptogenesis is particularly effective when the Higgs condensate decays rapidly and at low reheat scale. As part of the calculation, we present some exact results for the Bogoliubov transformations for Majorana fermions with a nonzero time-dependent chemical potential, in addition to a time-dependent mass.

Interacting topological insulator and emergent grand unified theory

Motivated by the Pati-Salam Grand Unified Theory, we study $(4+1)d$ topological insulators with $SU(4) \times SU(2)_1 \times SU(2)_2$ symmetry, whose $(3+1)d$ boundary has 16 flavors of left-chiral fermions, which form representations $(\mathbf{4}, \mathbf{2}, \mathbf{1})$ and $(\bar{\mathbf{4}}, \mathbf{1}, \mathbf{2})$. The key result we obtain is that, without any interaction, this topological insulator has a $\mathbb{Z}$ classification, namely any quadratic fermion mass operator at the $(3+1)d $ boundary is prohibited by the symmetries listed above; while under interaction this system becomes trivial, namely its $(3+1)d$ boundary can be gapped out by a properly designed short range interaction without generating nonzero vacuum expectation value of any fermion bilinear mass, or in other words, its $(3+1)d$ boundary can be driven into a "strongly coupled symmetric gapped (SCSG) phase". Based on this observation, we propose that after coupling the system to a dynamical $SU(4) \times SU(2)_1 \times SU(2)_2$ lattice gauge field, the Pati-Salam GUT can be fully regularized as the boundary states of a $(4+1)d$ topological insulator with a {\it thin} fourth spatial dimension, the thin fourth dimension makes the entire system generically a $(3+1)d$ system. The mirror sector on the opposite boundary will {\it not} interfere with the desired GUT, because the mirror sector is driven to the SCSG phase by a carefully designed interaction and is hence decoupled from the GUT.

Naturalness and dimensional transmutation in classically scale-invariant gravity

We discuss the nature of quantum field theories involving gravity that are classically scale-invariant. We show that gravitational radiative corrections are crucial in the determination of the nature of the vacuum state in such theories, which are renormalisable, technically natural, and can be asymptotically free in all dimensionless couplings. In the pure gravity case, we discuss the role of the Gauss-Bonnet term, and we find that Dimensional Transmutation (DT) \`a la Coleman-Weinberg leads to extrema of the effective action corresponding to nonzero values of the curvature, but such that these extrema are local maxima. In even the simplest extension of the theory to include scalar fields, we show that the same phenomenon can lead to extrema that are local minima of the effective action, with both non-zero curvature and non-zero scalar vacuum expectation values, leading to spontaneous generation of the Planck mass. Although we find an asymptotically free (AF) fixed point exists, unfortunately, no running of the couplings connect the region of DT to the basin of attraction of the AF fixed point. We also find there remains a flat direction for one of the conformal modes. We suggest that in more realistic models AF and DT could be compatible, and that the same scalar vacuum expectation values could be responsible both for DT and for spontaneous breaking of a Grand Unified gauge group.

The Explanation for the Origin of the Higgs Scalar and for the Yukawa Couplings by the <i>Spin-Charge-Family</i> Theory

The spin-charge-family theory is a kind of the Kaluza-Klein theories, but with two kinds of the spin connection fields, which are the gauge fields of the two kinds of spins. The SO(13,1) representation of one kind of spins manifests in d = (3 + 1) all the properties of family members as assumed by the standard model; the second kind of spins explains the appearance of families. The gauge fields of the first kind, carrying the space index m = (0,...,3), manifest in d = (3 + 1) all the vector gauge fields assumed by the standard model. The gauge fields of both kinds of spins, which carry the space index (7, 8) gaining at the electroweak break nonzero vacuum expectation values, manifest in d = (3 + 1) as scalar fields with the properties of the Higgs scalar of the standard model with respect to the weak and the hyper charge ( and , respectively), while they carry additional quantum numbers in adjoint representations, offering correspondingly the explanation for the scalar Higgs and the Yukawa couplings, predicting the fourth family and the existence of several scalar fields. The paper 1) explains why in this theory the gauge fields are with the scalar index s = (5,6,7,8) doublets with respect to the weak and the hyper charge, while they are with respect to all the other charges in the adjoint representations; 2) demonstrates that the spin connection fields manifest as the Kaluza-Klein vector gauge fields, which arise from the vielbeins; and 3) explains the role of the vielbeins and of both kinds of the spin connection fields.

Fermionic dark matter with pseudo-scalar Yukawa interaction

We consider a renormalizable extension of the standard model whose fermionic dark matter (DM) candidate interacts with a real singlet pseudo-scalar via a pseudo-scalar Yukawa term while we assume that the full Lagrangian is CP-conserved in the classical level. When the pseudo-scalar boson develops a non-zero vacuum expectation value, spontaneous CP-violation occurs and this provides a CP-violated interaction of the dark sector with the SM particles through mixing between the Higgs-like boson and the SM-like Higgs boson. This scenario suggests a minimal number of free parameters. Focusing mainly on the indirect detection observables, we calculate the dark matter annihilation cross section and then compute the DM relic density in the range up to mDM = 300 GeV.We then find viable regions in the parameter space constrained by the observed DM relic abundance as well as invisible Higgs decay width in the light of 125 GeV Higgs discovery at the LHC. We find that within the constrained region of the parameter space, there exists a model with dark matter mass mDM ∼ 38 GeV annihilating predominantly into b quarks, which can explain the Fermi-LAT galactic gamma-ray excess.

Vortex matter inU(1)×U(1)×Z2phase-separated superconducting condensates

We study the properties of vortex solutions and magnetic response of two-component $U(1)\ifmmode\times\else\texttimes\fi{}U(1)\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ superconductors, with phase separation driven by intercomponent density-density interaction. Such a theory can be viewed arising from the breakdown of $SU(2)$ symmetry by a biquadratic interaction between the components of the field. Depending on the symmetry-breaking term, there are two ground-state phases: one where both components of the doublet are equal (the miscible phase) and one where only one component assumes a nonzero vacuum expectation value (the immiscible state). In the latter phase, the spectrum of topological excitations contains both domain walls and vortices. We show the existence of another kind of excitation that has properties of both topological excitations at the same time. This kind of excitation combines vorticity together with a circular domain wall, interpolating between inequivalent broken states, that shows up as a ring of localized magnetic flux. Asymptotically, this resembles a vortex carrying multiple flux quanta, but because the magnetic field is localized at a given distance from the center this looks like a pipe. The isolated multiquanta pipelike vortices can be either stable or metastable, even if the system is not type 1. We discuss the response of such a system to an externally applied magnetic field. Also we discuss magnetic response of $\mathit{SU}$(2) superconductor.

Vacuum-induced symmetry breaking in a superconducting quantum circuit

The ultrastrong-coupling regime, where the atom-cavity coupling rate reaches a considerable fraction of the cavity or atom transition frequencies, has been reported in a flux qubit superconducting quantum circuit coupled to an on-chip coplanar resonator. In this regime situations may arise where the resonator field $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}=\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}+{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}}$ acquires a nonzero expectation value in the system ground state. We demonstrate that, in this case, the parity symmetry of an additional artificial atom with an even potential is broken by the interaction with the resonator. Such a mechanism is analogous to the Higgs mechanism where the gauge symmetry of the weak force's gauge bosons is broken by the nonzero vacuum expectation value of the Higgs field. The results presented here open the way to controllable experiments on symmetry-breaking mechanisms induced by nonzero vacuum expectation values. Moreover, the mechanism proposed here can be used as a probe of the ground-state macroscopic coherence emerging from quantum phase transitions with vacuum degeneracy.