Higgs Condensate Research Articles

Custodial and SUSY 2HDM breaking under interfering condensates’ Goldstone bosons

The Higgs condensates are proven along with the minimal versions of the hyper-symmetric 2HDM extensions when containing Supersymmetry that can play the role of oscillators for the CPC and CPV interferences, up to via [Formula: see text]. With the uncharged Higgs inclusion (considering the uncharged Goldstone Bosons compared to the spontaneously broken SM-like Higgs), the symmetric [Formula: see text] and anti-symmetric [Formula: see text] linear combinations of an ‘[Formula: see text]’ and a rescaled [Formula: see text], where masses of [Formula: see text]GeV and [Formula: see text][Formula: see text]GeV, such as under the condensate’s boundary impacts. The range of the [Formula: see text]s would be up to where the composed singlet and triplet can interchange, then, they approach the Custodial SUSY at a Triple point transition with a Goldstone-type order mass [Formula: see text][Formula: see text]GeV, as well into their Dark Matter sectors’ cut-off [Formula: see text], (including [Formula: see text]) up to order 1.7[Formula: see text]TeV. That will lead to opening the way to measure the existence of Supersymmetry, indirectly at the least, through any dominance of [Formula: see text]-violating Higgs decays.

The Higgs condensate as a quantum liquid: A critical comparison with observations

The triviality of four-dimensional scalar quantum field theories poses challenging problems to the usually adopted perturbative implementation of the Higgs mechanism. In the first part of the paper, we compare the triviality scenario and the renormalized two-loop perturbation theory to precise and extensive results from nonperturbative numerical simulations of the real scalar field theory on the lattice. The proposal of triviality and spontaneous symmetry breaking turns out to be in good agreement with numerical simulations, while the renormalized perturbative approach seems to suffer significant deviations from the numerical simulation results. In the second part of the paper, we try to illustrate how the triviality of four-dimensional scalar field theory leads, nevertheless, to the spontaneous symmetry breaking in the scalar sector of the Standard Model. We show how triviality allows us to develop a physical picture of the Higgs mechanism in the Standard Model. We suggest that the Higgs condensate behaves like a relativistic quantum liquid leading to the prevision of two Higgs bosons. The light Higgs boson resembles closely the new LHC narrow resonance at 125 GeV. The heavy Higgs boson is a rather broad resonance with mass of about 730 GeV. We critically compare our proposal to the complete LHC Run 2 data collected by the ATLAS and CMS Collaborations. We do not find convincingly evidences of the heavy Higgs boson in the ATLAS datasets. On the other hand, the CMS full Run 2 data display evidences of a heavy Higgs boson in the main decay modes [Formula: see text], while in the preliminary Run 2 data there are hints of the decays [Formula: see text] in the golden channel. We also critically discuss plausible reasons for the discrepancies between the two LHC experiments.

A model of d-wave superconductivity, antiferromagnetism, and charge order on the square lattice

We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of Nf = 2 massless Dirac fermions carrying fundamental gauge charges-this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π-flux per plaquette in the ℤ2 center of SU(2). This theory has an emergent SO(5)f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ2-flux. At half-filling, the low-energy theory of the Higgs sector has Nb = 2 relativistic bosons with a possible emergent SO(5)b global symmetry describing rotations between a d-wave superconductor, period-2 charge stripes, and the time-reversal breaking "d-density wave" state. We propose a conformal SU(2) gauge theory with Nf = 2 fundamental fermions, Nb = 2 fundamental bosons, and a SO(5)f×SO(5)b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)f and a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d-wave superconductivity. A similar theory applies at nonzero doping and large U, with longer-range couplings of the chargons leading to charge order with longer periods.

Generation of neutrino dark matter, baryon asymmetry, and radiation after quintessential inflation

We construct a model explaining dark matter, baryon asymmetry, and reheating in a quintessential inflation model. Three generations of right-handed neutrinos having hierarchical masses and the light scalar field leading to the self-interaction of active neutrinos are introduced. The lightest sterile neutrino is a dark matter candidate produced by a Dodelson-Widrow mechanism in the presence of a new light scalar field, while the heaviest and next-heaviest sterile neutrinos produced by gravitational particle production are responsible for the generation of the baryon asymmetry. Reheating is realized by spinodal instabilities of the Standard Model Higgs field induced by the nonminimal coupling to the scalar curvature, which can solve the overproduction of gravitons and curvature perturbation created by the Higgs condensation.

New order parameter for the Higgs transition in SU(2) -Higgs theory

We investigate the Higgs transition within the four-dimensional $SU(2)$-Higgs model in search for an order parameter as a function of the Higgs field hopping parameter, $\ensuremath{\kappa}$, using lattice technique. We measure the Higgs condensate after applying Landau gauge fixing and study the corresponding susceptibility, magnetization, and fourth order Binder cumulant using four different spatial volumes with ${N}_{\ensuremath{\tau}}=2$. The computation is carried out with gauge coupling, ${\ensuremath{\beta}}_{g}=8$, for a range of scalar self-coupling, $\ensuremath{\lambda}={0.00010,0.00350}$, with an emphasis near the critical end point. Finite size scaling analysis of the gauge fixed condensate and its cumulants agree with the standard 3D Ising values $\ensuremath{\nu}=0.62997$, $\ensuremath{\beta}/\ensuremath{\nu}=0.518$, $\ensuremath{\gamma}/\ensuremath{\nu}=1.964$ at $\ensuremath{\lambda}=0.00150$. These results are in agreement with previous studies suggesting 3D Ising universality class. The numerical results also indicate that, at the transition point, the gauge fixed condensate vanishes in the infinite volume limit.

Reheating and dark matter freeze-in in the Higgs-R2 inflation model

We study the post-inflationary dynamics for reheating and freeze-in dark matter in the Higgs-R2 inflation model. Taking the perturbative approach for reheating, we determine the evolution of the temperature for radiation bath produced during reheating and determine the maximum and reheating temperatures of the Universe. Adopting a singlet scalar dark matter with a conformal non-minimal coupling and a vanishing Higgs-portal coupling, we discuss the freeze-in production of dark matter both from the non-thermal scattering during reheating and the thermal scattering after reheating. We find that thermal scattering is dominant for dark matter production in our model due to the high reheating temperature. The reheating temperature in our model is determined dominantly by the Higgs condensate to be up to about 1014 GeV and dark matter with masses up to about 109 GeV can be produced with a correct relic density.

Gauge symmetry restoration by Higgs condensation in flux compactifications on coset spaces

Extra-dimensional components of gauge fields in higher-dimensional gauge theories will play a role of the Higgs field and become tachyonic after Kaluza-Klein compactifications on internal spaces with (topologically nontrivial) gauge field backgrounds. Its condensation is then expected to break gauge symmetries spontaneously. But, contrary to the expectation, some models exhibit restoration of gauge symmetries. In this paper, by considering all the massive Kaluza-Klein excitations of gauge fields, we explicitly show that some of them indeed become massless at the minimum of the Higgs potential and restore (a part of) the gauge symmetries which are broken by gauge field backgrounds. We particularly consider compactifications on ${S}^{2}$ with monopolelike fluxes and also on ${\mathbb{CP}}^{2}$ with instanton and monopolelike fluxes. In some cases, the gauge symmetry is fully restored, as argued in previous literatures. In other cases, there is a stable vacuum with a partial restoration of the gauge symmetry after Higgs condensation. Topological structure of the gauge field configurations prevent the gauge symmetries from being restored.

Achieving the highest temperature during reheating with the Higgs condensate

We study the role of the Standard Model Higgs condensate, formed during cosmological inflation, in the epoch of reheating that follows. We focus on the scenario where the inflaton decays slowly and perturbatively, so that there is a long period between the end of inflation and the beginning of radiation domination. The Higgs condensate decays nonperturbatively during this period, and we show that it heats the primordial plasma to much higher temperatures than would result from the slowly decaying inflaton alone. We discuss the effect of this hot plasma on the thermalization of the inflaton's decay products, and study its phenomenological implications for the formation of cosmological relics like dark matter, with associated isocurvature fluctuations, and the restoration of the electroweak and Peccei-Quinn symmetries.

Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

Effective field theory for fractional quantum Hall systems nearν=5/2

We propose an effective field theory (EFT) of fractional quantum Hall systems near the filling fraction $\nu=5/2$ that flows to pertinent IR candidate phases, including non-abelian Pfaffian, anti-Pfaffian, and particle-hole Pfaffian states (Pf, APf, and PHPf). Our EFT has a 2+1$d$ O(2)$_{2,L}$ Chern-Simons gauge theory coupled to four Majorana fermions by a discrete charge conjugation gauge field, with Gross-Neveu-Yukawa-Higgs terms. Including deformations via a Higgs condensate and fermion mass terms, we can map out a phase diagram with tunable parameters, reproducing the prediction of the recently-proposed percolation picture and its gapless topological quantum phase transitions. Our EFT captures known features of both gapless and gapped sectors of time-reversal-breaking domain walls between Pf and APf phases. Moreover, we find that Pf$\mid$APf domain walls have higher tension than domain walls in the PHPf phase. Then the former, if formed, may transition to the energetically-favored PHPf domain walls; this could, in turn, help further induce a bulk transition to PHPf.

Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions

For a zero-temperature Landau symmetry breaking transition in $n$-dimensional space that completely breaks a finite symmetry $G$, the critical point at the transition has the symmetry $G$. In this paper, we show that the critical point also has a dual symmetry - a $(n-1)$-symmetry described by a higher group when $G$ is Abelian or an algebraic $(n-1)$-symmetry beyond higher group when $G$ is non-Abelian. In fact, any $G$-symmetric system can be viewed as a boundary of $G$-gauge theory in one higher dimension. The conservation of gauge charge and gauge flux in the bulk $G$-gauge theory gives rise to the symmetry and the dual symmetry respectively. So any $G$-symmetric system actually has a larger symmetry called categorical symmetry, which is a combination of the symmetry and the dual symmetry. However, part (and only part) of the categorical symmetry must be spontaneously broken in any gapped phase of the system, but there exists a gapless state where the categorical symmetry is not spontaneously broken. Such a gapless state corresponds to the usual critical point of Landau symmetry breaking transition. The above results remain valid even if we expand the notion of symmetry to include higher symmetries and algebraic higher symmetries. Thus our result also applies to critical points for transitions between topological phases of matter. In particular, we show that there can be several critical points for the transition from the 3+1D $Z_2$ gauge theory to a trivial phase. The critical point from Higgs condensation has a categorical symmetry formed by a $Z_2$ 0-symmetry and its dual - a $Z_2$ 2-symmetry, while the critical point of the confinement transition has a categorical symmetry formed by a $Z_2$ 1-symmetry and its dual - another $Z_2$ 1-symmetry.

The Higgs Condensate as a Quantum Liquid

We model the Higgs condensate of the Standard Model as a relativistic quantum fluid analogous to superfluid helium. We find that the low-lying excitations of the Higgs condensate behave like two relativistic Higgs fields. The lighter Higgs boson has a mass of order $10^2$ GeV. We identify this light Higgs particle with the new LHC resonance at 125 GeV. The heavy Higgs boson has a mass around 750 GeV consistent with our recent phenomenological analysis of the preliminary LHC Run 2 data in the golden channel. We critical compare our theoretical scenario with two Higgs bosons to the available LHC Run 2 data.

The Added Mass Effect and the Higgs Mechanism

A rigid body accelerated through an inviscid, incompressible fluid appears to gain mass, which is encoded in an added mass tensor. Swimmers, air bubbles, submarines and airships are slowed down by the associated `added mass' force proportional to their acceleration, which is distinct from viscous drag and buoyancy. In particle physics, otherwise massless electrons, quarks, $W$ and $Z$ bosons, moving through the Higgs scalar field acquire masses encoded in a mass matrix. In this expository article we give an introduction to the fluid mechanical added mass effect through examples of potential flows in various dimensions and exploit a correspondence with the Higgs mechanism [introduced in Proc. R. Soc. A471: 20140803 (2015)] to relate this to how the $W$ and $Z$ bosons can get their masses, while leaving the photon massless. The correspondence relates the Higgs scalar field to the fluid, the vacuum expectation value of the Higgs field to a constant fluid density and quantum fluctuations around the Higgs condensate to compressional waves in the fluid. The shape of the rigid body encodes the pattern of gauge symmetry breaking through the eigenvalues of the corresponding mass matrices. Possible directions of acceleration of the rigid body are related to directions in the gauge Lie algebra with a `flat' direction in the body corresponding to a massless photon. Moreover, symmetries of the body are related to those of the scalar vacuum manifold. The Higgs boson may be viewed as the analog of a long wavelength fluid mode around an accelerated body.

Preheating after Higgs inflation: Self-resonance and gauge boson production

We perform an extensive analysis of linear fluctuations during preheating in Higgs inflation in the Einstein frame, where the fields are minimally coupled to gravity, but the field-space metric is nontrivial. The self-resonance of the Higgs and the Higgsed gauge bosons are governed by effective masses that scale differently with the nonminimal couplings and evolve differently in time. Coupled metric perturbations enhance Higgs self-resonance and make it possible for Higgs inflation to preheat solely through this channel. For $\xi\gtrsim 100$ the total energy of the Higgs-inflaton condensate can be transferred to Higgs particles within $3$ $e$-folds after the end of inflation. For smaller values of the nonminimal coupling preheating takes longer, completely shutting off at around $\xi\simeq 30$. The production of gauge bosons is dominated by the gauge boson mass and the field space curvature. For large values of the nonminimal coupling $\xi \gtrsim 1000$, it is possible for the Higgs condensate to transfer the entirety of its energy into gauge fields within one oscillation. For smaller values of the nonminimal coupling gauge bosons decay very quickly into fermions, thereby shutting off Bose enhancement. Estimates of non-Abelian interactions indicate that they will not suppress preheating into gauge bosons for $\xi \gtrsim 1000$.

Reheating through the Higgs amplified by spinodal instabilities and gravitational creation of gravitons

It is shown that a positive non-minimal coupling of the Higgs field to gravity can solve the two problems in inflation models in which postinflationary universe is dominated by an energy with stiff equation of state such as a kination, namely, overproduction of gravitons in gravitational reheating scenario, and overproduction of curvature perturbation from Higgs condensation. Furthermore, we argue that the non-minimal coupling parameter can be constrained more stringently with the progress in observations of large-scale structure and cosmic microwave background.

Revisiting the decoupling effects in the running of the Cosmological Constant

We revisit the decoupling effects associated with heavy particles in the renormalization group running of the vacuum energy in a mass-dependent renormalization scheme. We find the running of the vacuum energy stemming from the Higgs condensate in the entire energy range and show that it behaves as expected from the simple dimensional arguments, meaning that it exhibits the quadratic sensitivity to the mass of the heavy particles in the infrared regime. The consequence of such a running to the fine-tuning problem with the measured value of the Cosmological Constant is analyzed and the constraint on the mass spectrum of a given model is derived. We show that in the Standard Model (SM) this fine-tuning constraint is not satisfied while in the massless theories this constraint formally coincides with the well-known Veltman condition. We also provide a remarkably simple extension of the SM where saturation of this constraint enables us to predict the radiative Higgs mass correctly. Generalization to constant curvature spaces is also given.

Quantum spin superfluid from Bose-Einstein condensation of spinons in pyrochlore spin ice

Quantum spin ice in pyrochlore lattice exemplifies three-dimensional frustrated spin systems. In existing studies, Bose-Einstein condensation of bosonic spinons gives rise to magnetically ordered ground state. A truly liquid quantum spin superfluid state that manifests a deconfined Higgs condensate of spinons is demonstrated. This state is shown to occur in the fully antiferromagnetic case of the non-Kramers quantum spin ice with a fluctuation-induced first-order quantum phase transition from the U(1) spin liquid to the spin superfluid. The spin superfluid density jump is obtained analytically.

Localization of the Standard Model via the Higgs mechanism and a finite electroweak monopole from non-compact five dimensions

We propose a minimal and self-contained model in non-compact flat five dimensions which localizes the Standard Model (SM) on a domain wall. Localization of gauge fields is achieved by the condensation of Higgs field via a Higgs dependent gauge kinetic term in five-dimensional Lagrangian. The domain wall connecting vacua with unbroken gauge symmetry drives the Higgs condensation which provides both electroweak symmetry breaking and gauge field localization at the same time. Our model predicts higher-dimensional interactions $|H|^{2n}(F_{\mu\nu})^2$ in the low-energy effective theory. This leads to two expectations: The one is a new tree-level contribution to $H \to \gamma\gamma$ ($H \to gg$) decay whose signature is testable in future LHC experiment. The other is a finite electroweak monopole which may be accessible to the MoEDAL experiment. Interactions of translational Nambu-Goldstone boson is shown to satisfy a low-energy theorem.

Intersecting branes, Higgs sector, and chirality from mathcal{N} = 4 SYM with soft SUSY breaking

We consider SU(N ) mathcal{N} = 4 super Yang-Mills with cubic and quadratic soft SUSY breaking potential, such that the global SU(4)R is broken to SU(3) or further. As shown recently, this set-up supports a rich set of non-trivial vacua with the geometry of self-intersecting SU(3) branes in 6 extra dimensions. The zero modes on these branes can be interpreted as 3 generations of bosonic and chiral fermionic strings connecting the branes at their intersections. Here, we uncover a large class of exact solutions consisting of branes connected by Higgs condensates, leading to Yukawa couplings between the chiral fermionic zero modes. Under certain decoupling conditions, the backreaction of the Higgs on the branes vanishes exactly. The resulting physics is that of a spontaneously broken chiral gauge theory on branes with fluxes. In particular, we identify combined brane plus Higgs configurations which lead to gauge fields that couple to chiral fermions at low energy. This turns out to be quite close to the Standard Model and its constructions via branes in string theory. As a by-product, we construct a G2-brane solution corresponding to a squashed fuzzy coadjoint orbit of G2.

Revisiting the decoupling effects in the running of the Cosmological Constant

We revisit the decoupling effects associated with heavy particles in the renormalization group running of the vacuum energy in a mass-dependent renormalization scheme. We find the running of the vacuum energy stemming from the Higgs condensate in the entire energy range and show that it behaves as expected from the simple dimensional arguments meaning that it exhibits the quadratic sensitivity to the mass of the heavy particles in the infrared regime. The consequence of such a running to the fine-tuning problem with the measured value of the Cosmological Constant is analyzed and the constraint on the mass spectrum of a given model is derived. We show that in the Standard Model (SM) this fine-tuning constraint is not satisfied while in the massless theories this constraint formally coincides with the well known Veltman condition. We also provide a remarkably simple extension of the SM where saturation of this constraint enables us to predict the radiative Higgs mass correctly. Generalization to constant curvature spaces is also given.