Top Condensation Research Articles

Ladder top-quark condensation imprints in supercooled electroweak phase transition

The electroweak (EW) phase transition in the early Universe might be supercooled due to the presence of the classical scale invariance involving Beyond the Standard Model (BSM) sectors and the supercooling could persist down till a later epoch around which the QCD chiral phase transition is supposed to take place. Since this supercooling period keeps masslessness for all the six SM quarks, it has simply been argued that the QCD phase transition is the first order, and so is the EW one. However, not only the QCD coupling but also the top Yukawa and the Higgs quartic couplings get strong at around the QCD scale due to the renormalization group running, hence this scenario is potentially subject to a rigorous nonperturbative analysis. In this work, we employ the ladder Schwinger-Dyson (LSD) analysis based on the Cornwall-Jackiw-Tomboulis formalism at the two-loop level in such a gauge-Higgs-Yukawa system. We show that the chiral broken QCD vacuum emerges with the nonperturbative top condensate and the lightness of all six quarks is guaranteed due to the accidental U(1) axial symmetry presented in the top-Higgs sector. We employ a quark-meson model-like description in the mean field approximation to address the impact on the EW phase transition arising due to the top quark condensation at the QCD phase transition epoch. In the model, the LSD results are encoded to constrain the model parameter space. We then observe the cosmological phase transition of the first-order type and discuss the induced gravitational wave (GW) productions. We find that in addition to the conventional GW signals sourced from an expected BSM at around or over the TeV scale, the dynamical topponium-Higgs system can yield another power spectrum sensitive to the BBO, LISA, and DECIGO, etc.

Subaqueous felsic volcanic sequence and its contribution to the ancient alkaline lacustrine deposits in the Mahu Sag, Junggar Basin, NW China

Subaqueous eruptions alter the chemical conditions of the lake by intensifying the interaction between hot volcanic rocks and water, resulting in the exchange of alkalis. The lower part of the Fengcheng Formation in the Mahu Sag, NW China, has abundant rhyolitic welded tuff and related pyroclastic deposits, which were deposited under ancient alkaline lacustrine deposits of the Fengcheng Formation. Despite this, the effect of the eruption process on the formation of the alkali lake remains unclear. To gain a better understanding of the eruptive behaviour and emplacement processes, detailed drilling core descriptions, microscopic observations, and interpretations of textural characteristics of rhyolitic welded tuff units and adjacent volcano‐sedimentary associations have been conducted. The rhyolitic welded tuff can be categorized into seven lithofacies units based on the degree of welding, devitrification characteristics, pore development, and filling characteristics. The age of eruption was determined through zircon U–Pb dating of the rhyolitic welded tuff, revealing it to be approximately 300 Ma, thereby providing constraints on the deposition time of alkaline lacustrine deposits. Mudstones that encase the welded tuff unit and quenched structures such as perlitic fractures, quench cracks of spherulite and lithophysae, and chalcedony spherules indicate that the welded tuff unit was formed through subaqueous eruption. Alkali fractionation (sodium and potassium) occurs in the spherulite and lithophysae zone and at the top condensation boundary, demonstrating that the subaqueous eruption process significantly enhanced devitrification and hydration, causing sodium to escape from the welded tuff and released into the lake water as sodium ions. The rhyolitic welded tuff provides evidence of the evolution of a subaqueous felsic eruption where the water‐rock reaction played a fundamental role in alkalizing the lake by providing the lake with sodium ions in Mahu Sag.

Remarks on the QCD-electroweak phase transition in a supercooled universe

In extensions of the Standard Model with no dimensionful parameters the electroweak phase transition can be delayed to temperatures of order 100 MeV. Then the chiral phase transition of QCD can proceed with 6 massless quarks. The top-quark condensate destabilizes the Higgs potential through the Yukawa interaction, triggering the electroweak transition. Based on the symmetries of massless QCD, it has been argued that the chiral phase transition is first order. We point out that the top-Higgs Yukawa interaction is nonperturbatively large at the QCD scale, and that its effect on the chiral phase transition may not be negligible, violating some of the symmetries of massless QCD. The remaining symmetries indicate that top quarks condense in a second-order phase transition, but top condensation might also be triggered by a first-order symmetry-breaking transition in the light-quark sector.

Top condensation model: a step towards the correct prediction of the Higgs mass

A realization of the composite Higgs scenario in the context of the effective model with the SU(2)_Ltimes U(1)_R symmetric four-Fermi interactions proposed by Miransky, Tanabashi and Yamawaki is studied. The model implements Nambu’s mechanism of dynamical electroweak symmetry breaking leading to the formation of {{bar{t}}}t and {{bar{b}}}b quark condensates. We explore the vacuum structure and spectrum of the model by using the Schwinger proper-time method. As a direct consequence of this mechanism, the Higgs acquires a mass in accord with its experimental value. The present prediction essentially differs from the known overestimated value, m_chi = 2m_t, making more favourable the top condensation scenario presented here. The mass formulas for the members of the second Higgs doublet are also obtained. The Nambu sum rule is discussed. It is shown that the anomalous U(1)_A symmetry breaking modifies this rule at next to leading order in 1/N_c.

Dynamical symmetry breaking and negative cosmological constant

In the context of Clifford functional integral formalism, we revisit the Nambu–Jona-Lasinio-type dynamical symmetry breaking model and examine the properties of the dynamically generated composite bosons. Given that the model with 4-fermion interactions is nonrenormalizable in the traditional sense, the aim is to gain insight into the divergent integrals without resorting to explicit regularization. We impose a restriction on the linearly divergent primitive integrals, thus resolving the long-standing issue of momentum routing ambiguity associated with fermion–antifermion condensations. The removal of the ambiguity paves the way for the possible calculation of the true ratio of Higgs boson mass to top quark mass in the top condensation model. In this paper, we also investigate the negative vacuum energy resulted from dynamical symmetry breaking and its cosmological implications. In the framework of modified Einstein–Cartan gravity, it is demonstrated that the late-time acceleration is driven by a novel way of embedding the Hubble parameter into the Friedmann equation via an interpolation function, whereas the dynamically generated negative cosmological constant only plays a minor role for the current epoch. Two cosmic scenarios are proposed, with one of which suggesting that the universe may have been evolving from an everlasting coasting state towards the accelerating era characterized by the deceleration parameter approaching −0.5 at low redshift. One inevitable outcome of the modified Friedmannian cosmology is that the directly measured local Hubble parameter should in general be larger than the Hubble parameter calibrated from the conventional Friedmann equation. This Hubble tension becomes more pronounced when the Hubble parameter is comparable or less than a characteristic Hubble scale.

Desalination of Seawater by Liquid Columns and Decompression Boiling (Recovery of Condensation Latent Heat)

In this study, the concept of a new seawater desalination method and equipment using liquid columns of seawater and desalinated fresh water, decompression boiling and evaporation, condensation, and recovery of condensation latent heat are proposed. The equipment consists of seawater and freshwater columns approximately 10 m high with top spaces. The pressure of the top space, the evaporation and condensation area, of the seawater column, for example, is reduced approximately 30 mmHg (abs.) using the seawater column, after which it is heated from the general seawater temperature of 25°C to 30°C to boil and evaporate the seawater. The vapor is cooled by the seawater at approximately 25°C in a heat exchanger, and then, it is condensed and sent to the fresh water column. At this time, the condensation latent heat is recovered to preheat the newly flowing seawater. The evaporation or condensation rate, namely, the production rate of freshwater, by the new desalination equipment is also estimated by the results of the existing quadruplex effect vacuum evaporator used in the salt production industry. This new desalination method and its associated equipment also can be used to purify polluted water and waste water.

Holograms of a dynamical top quark

We present holographic descriptions of dynamical electroweak symmetry breaking models that incorporate the top mass generation mechanism. The models allow computation of the spectrum in the presence of large anomalous dimensions due to walking and strong Nambu--Jona-Lasinio interactions. Technicolor and QCD dynamics are described by the bottom-up Dynamic AdS/QCD model for arbitrary gauge groups and numbers of quark flavors. An assumption about the running of the anomalous dimension of the quark bilinear operator is input, and the model then predicts the spectrum and decay constants for the mesons. We add Nambu--Jona-Lasinio interactions responsible for flavor physics from extended technicolor, top-color, etc., using Witten's multitrace prescription. We show the key behaviors of a top condensation model can be reproduced. We study generation of the top mass in (walking) one doublet and one family technicolor models and with strong extended technicolor interactions. The models clearly reveal the tensions between the large top mass and precision data for $\ensuremath{\delta}\ensuremath{\rho}$. The necessary tunings needed to generate a model compatible with precision constraints are simply demonstrated.

Nucleate boiling inside small evaporating droplets: An experimental and numerical study

Evaporating and boiling of droplets on heated surfaces are widely involved in many industrial applications. In this work, the phase change characteristics inside the small droplets in the nucleate boiling regime are studied experimentally and numerically. Confined by the free surface of the droplet, the bubble dynamics in the small evaporating droplet is found experimentally to be greatly different from those observed in pool boiling. After the droplet is deposited on the heated surface, nucleate bubbles generate immediately on the droplet bottom, and then they grow fast and coalesce into large bubbles. However, unlike pool boiling, once the bubbles grow to a specific size, they stop growing and always attach to the heated surface until the droplet evaporates to a thin liquid film, subsequently the bubbles start shrinking, collapsing and finally disappearing due to the confined effects induced by the thin film free surface. With such bubble dynamics, the heat transfer rates of the fast initial bubble nucleation stage and the last thin film evaporation stage are almost four times as large as the middle stable bubble stage. A numerical model is proposed to understand the confined boiling mechanisms with flow and temperature details. The results show that the confined boiling can be attributed to either the evaporation-condensation competition, or the jetting flows induced by the Marangoni convection inside the droplet. The bubble bottom evaporates while the top condensate when its top enters the droplet subcooled region; thus, the bubble seems to stop growing. The jetting flow due to the Marangoni flows further inhibits the bubble growing by pumping the cooled liquids from the top of the droplet onto the bubble surface. For hydrophobic surfaces, the Marangoni effect dominates the bubble dynamics within the evaporating droplet. For hydrophilic surface, the evaporation-condensation competition dominates the bubble dynamics inside the evaporating droplet.

Tree level relations in a composite electroweak theory

We work out simple tree level relations in a top condensate model with dynamical electroweak symmetry breaking. We find that in this picture the mass of the composite Higgs boson at tree level is given by [Formula: see text] where mt is the mass of the top quark.

A hierarchy of the quark masses in a top condensate model with multiple Higgses

We discuss the quark masses in a top condensate model where not only two quark but also four quark composite states may exist. We show that the presence of the top color group SU (3)1× SU (3)2 with the correct quark representations can justify even in the absence of the additional technicolor interactions a hierarchy of the quark masses where the light quarks masses have the same size, the charm and bottom masses are higher and similar and the top is the heaviest.

Top condensate model with a Higgs doublet and a Higgs triplet

We reconsider top condensate models from the perspective that not only two-quark composite states can form but also four-quark ones. We obtain a model which contains a Higgs doublet and a Higgs triplet, where one of the neutral components of the Higgs triplet identifies with the Higgs boson found at the LHC. We discuss some of the phenomenological consequences.

Top condensation as a motivated explanation of the top forward-backward asymmetry

Models of top condensation can provide both a compelling solution to the hierarchy problem as well as an explanation of why the top-quark mass is large. The spectrum of such models, in particular topcolor-assisted technicolor, includes top-pions, top-rhos and the top-Higgs, all of which can easily have large top-charm or top-up couplings. Large top-up couplings in particular would lead to a top forward-backward asymmetry through t-channel exchange, easily consistent with the Tevatron measurements. Intriguingly, there is destructive interference between the top-mesons and the standard model which conspire to make the overall top pair production rate consistent with the standard model. The rate for same-sign top production is also small due to destructive interference between the neutral top-pion and the top-Higgs. Flavor physics is under control because new physics is mostly confined to the top quark. In this way, top condensation can explain the asymmetry and be consistent with all experimental bounds. There are many additional signatures of topcolor with large tu mixing, such as top(s) + jet(s) events, in which a top and a jet reconstruct a resonance mass, which make these models easily testable at the LHC.

Planck scale from top condensation

We propose a scenario in which the Planck scale is dynamically linked to the electroweak scale induced by top condensation. The standard model field content, without the Higgs, is promoted to a 5D warped background. There is also an additional 5D fermion with the quantum numbers of the right-handed top. Localization of the zero-modes leads, at low energies, to a Nambu-Jona-Lasinio model that also stabilizes the radion field dynamically thus explaining the hierarchy between the Planck scale and v_EW = 174 GeV. The top mass arises dynamically from the electroweak breaking condensate. The other standard model fermion masses arise naturally from higher-dimension operators, and the fermion mass hierarchies and flavor structure can be explained from the localization of the zero-modes in the extra dimension. If any other contributions to the radion potential except those directly related with electroweak symmetry breaking are engineered to be suppressed, the KK scale is predicted to be about two orders of magnitude above the electroweak scale rendering the model easily consistent with electroweak precision data. The model predicts a heavy (composite) Higgs with a mass of about 500 GeV and standard-model-like properties, and a vector-like quark with non-negligible mixing with the top quark and mass in the 1.6 - 2.9 TeV range. Both can be within the reach of the LHC. It also predicts a radion with a mass of a few GeV that is very weakly coupled to standard model matter.

Top mode standard model in six dimensions

We construct a top-mode standard model where the third generation fermions and the SU(2)_L \times U(1)_Y gauge bosons are put on a 6-dimensional brane(5-brane) with the extra dimensions compactified on the TeV scale(R_5^{-1}=R_6^{-1} \equiv R^{-1}= 1-10 TeV), while only the gluons live in a compactified 8-dimensional bulk(R_7^{-1}=R_8^{-1} \equiv \Lambda \gg R^{-1}).On the 5-brane, Kaluza-Klein (KK) modes of the bulk gluons give rise to induced four-fermion interactions which, combined with the gauge interactions, are shown to be strong enough to trigger the top quark condensate, based on the dynamics of 6-dimensional gauged Nambu-Jona-Lasinio (NJL) model. Moreover, we can use a freedom of the brane positions to tune the four-fermion coupling close to the critical line of 6-dimensional gauged NJL model, so that the gap equation can ensure the top condensate on the weak scale while keeping other fermions massless. There actually exists a scale (``tMAC scale''), \Lambda_{\rm tM} = (7.8-11.0) R^{-1}, where the running gauge couplings combined with the induced four-fermion interactions trigger only the top condensate while no bottom and tau condensates. Furthermore, presence of such explicit four-fermion interactions enables us to formulate straightforwardly the compositeness conditions at \Lambda=\Lambda_{\rm tM}, which, through the renormalization-group analysis, yields a prediction of masses of the top quark and the Higgs boson, m_t = 177 - 187 GeV and m_H = 183 - 207 GeV.

Topcolor breaking through boundary conditions

The nontrivial boundary conditions (BC's) for the topcolor breaking are investigated in the context of the TeV-scale extra dimension scenario. In the gauge symmetry breaking mechanism via the BC's we do not need to incorporate a dynamical mechanism for the topcolor breaking into the model. Moreover, the topcolor breaking can be realized without introducing explicitly a (composite) scalar field. We present a six dimensional model where the top and bottom quarks in the bulk have the topcolor charge while the other quarks in the bulk do not. We also put the electroweak gauge interaction in the six dimensional bulk. The bottom quark condensation is naturally suppressed owing to the powerlike running of the bulk $\mathrm{U}(1{)}_{Y}$ interaction, so that only the top condensation is expected to take place. We explore such a possibility based on the ladder Schwinger-Dyson equation and show the cutoff to make the model viable.

Most attractive channel analysis in the top mode standard model with extra dimensions

We perform the most attractive channel (MAC) analysis in the top mode standard model with TeV-scale extra dimensions, where the standard model gauge bosons and the third generation of quarks and leptons are put in D(=6,8,10,...) dimensions. In such a model, bulk gauge couplings rapidly grow in the ultraviolet region. In order to make the scenario viable, only the attractive force of the top condensate should exceed the critical coupling, while other channels such as the bottom and tau condensates should not. We then find that the top condensate can be the MAC for D=8, whereas the tau condensation is favored for D=6. The analysis for D=10 strongly depends on the regularization scheme. We predict masses of the top (m_t) and the Higgs (m_H), m_t=172-175 GeV and m_H=176-188 GeV for D=8, based on the renormalization group for the top Yukawa and Higgs quartic couplings with the compositeness conditions at the scale where the bulk top condenses. The Higgs boson in such a characteristic mass range will be immediately discovered in H -> WW^(*)/ZZ^(*) once the LHC starts.

Top-quark mass in the minimal top-condensation model with extra dimensions

The minimal model of dynamical electroweak-symmetry breaking through top condensation in the presence of compact large extra dimensions is studied. It is shown that, owing to the power-law evolution of gauge and Yukawa couplings, the original predictions of Bardeen, Hill, and Lindner for the top-quark mass are significantly lowered and that, even for a small cutoff scale Λ of a few TeV, one can obtain experimentally allowed values.

Dynamical gauge symmetry breaking in anSU(3)L⊗U(1)Xextension of the standard model

We study the $\mathrm{SU}(3{)}_{L}\ensuremath{\bigotimes}\mathrm{U}(1{)}_{X}$ extension of the standard model with a strong U(1) coupling. We argue that current experiments limit this coupling to be relatively large. The model is dynamically broken to the standard $\mathrm{SU}(2{)}_{L}\ensuremath{\bigotimes}\mathrm{U}(1)$ model at the scale of a few TeV with all the extra gauge bosons and the exotic quarks acquiring masses much larger than the scale of electroweak symmetry breaking. Furthermore we find that the model naturally displays the top condensation mechanism for the dynamical breakdown of electroweak gauge symmetry. By adding an $\mathrm{SU}{(3)}_{L}$ singlet quark $\ensuremath{\chi},$ we find that the model can fit the experimental masses of the top quark and the $W,Z$ bosons. Based on the dynamical symmetry breaking mechanism we predict the masses of the exotic quarks in this model to be of the order of a few TeV.

Flavor universal dynamical electroweak symmetry breaking

The top condensate see-saw mechanism of Dobrescu and Hill allows electroweak symmetry to be broken while deferring the problem of flavour to an electroweak singlet, massive sector. We provide an extended version of the singlet sector that naturally accommodates realistic masses for all the standard model fermions, which play an equal role in breaking electroweak symmetry. The models result in a relatively light composite Higgs sector with masses typically in the range of (400-700)~GeV. In more complete models the dynamics will presumably be driven by a broken gauged family or flavour symmetry group. As an example of the higher scale dynamics a fully dynamical model of the quark sector with a GIM mechanism is presented, based on an earlier top condensation model of King using broken family gauge symmetry interactions (that model was itself based on a technicolour model of Georgi). The crucial extra ingredient is a reinterpretation of the condensates that form when several gauge groups become strong close to the same scale. A related technicolour model of Randall which naturally includes the leptons too may also be adapted to this scenario. We discuss the low energy constraints on the massive gauge bosons and scalars of these models as well as their phenomenology at the TeV scale.

Top-quark condensation

Top quark condensation, in particular the minimal framework where the neutral Higgs scalar is (predominantly) an effective ¯ tt condensate of the stan- dard model, is reviewed. Computational approaches are compared and sim- ilarities, differences and deficiencies pointed out. Extensions of the minimal framework, including scenarios with two composite Higgs doublets, additional neutrino condensates, andcondensation arising from four-fermion interac- tions with enlarged symmetries, are described. Possible renormalizable mod- els of underlying physics potentially responsible for the condensation, includ- ing topcolor assisted technicolor frameworks, are discussed. Phenomenological implications of top condensate models are outlined. Outstanding theoretical issues and problems for future investigation are pointed out. Progress in the field after this article was accepted has been briefly covered in a Note added at the end.