Top Quark Condensation Research Articles

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.

Top-Quark Condensate at Finite Temperature and Electroweak Symmetry Restoration**The project supported partially by National Natural Science Foundation of China and by Grant No. LWTZ-1298 of the Chinese Academy of Sciences

The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proven to have the identical form in both the imaginary and real time formalisms of thermal field theory. By means of the gap equation, combined with the basic relation to define the vacuum expectation value of the effective Higgs field, we analyze the dependence on temperature and chemical potential of the dynamical top-quark mass as the order parameter characteristic of symmetry breaking, and obtain the criticality curve for symmetry restoration. We find out that the critical temperature for and the critical chemical potential for When , the top-quark mass near has the leading behavior with an extra factor dependent on temperature and the momentum cutoff . However, it is generally argued that the symmetry restoration at is still a second-order phase transition.

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.

Electroweak Symmetry Breaking via a Top Condensation Seesaw Mechanism

We propose a new mechanism in which all of the electroweak symmetry breaking is driven by a natural top quark condensate, produced by ``top-color'' interactions at a multi-TeV scale. The scheme allows the observed top quark mass, and acceptable $T$ and $S$ parameters, by invoking a seesaw mechanism involving mixing of the top with an additional isosinglet quark.

Large-Nand vacuum alignment in top-color models

Top-color and top-color-assisted technicolor provide examples of dynamical electroweak symmetry breaking which include top-quark condensation, thereby naturally incorporating a heavy top quark. In this paper we discuss the roles of the Nambu--Jona-Lasinio (NJL) and large-$N$ approximations often used in phenomenological analyses of these models. We show that, in order to provide for top-quark condensation but not bottom-quark condensation, the top-color coupling must be adjusted to equal the critical value for chiral symmetry breaking up to $\mathcal{O}(1/N)$ in any theory in which the isospin-violating ``tilting'' interaction is a U(1) gauge interaction. A consequence of these considerations is that the potentially dangerous ``bottom pions'' are naturally light. We also show that the contributions to $\ensuremath{\rho}\ensuremath{-}1$ previously estimated are of leading order in $N,$ are not included in the usual NJL analysis, and are the result of ``vacuum alignment.''

Higher dimensional operators in top quark condensation from a renormalization group point of view

The predictive power of top-condensation models strongly depends on the behaviour of higher dimensional operators. These are analyzed in this paper by an extension of the standard renormalization group (RG) arguments which turns out to be a surprisingly powerful tool. Top-condensation models intermediated by underlying scalar exchange can be shown to be mere reparametrizations of the standard model. Further on, RG-arguments show that dynamical vector states cannot be lowered in top-condensation models. Finally we give a general argument concerning the size of higher dimensional operators of heavy vector exchange.

Higgs bosons strongly coupled to the top quark

Several extensions of the Standard Model require the burden of electroweak symmetry breaking to be shared by multiple states or sectors. This leads to the possibility of the top quark interacting with a scalar more strongly than it does with the Standard Model Higgs boson. In top-quark condensation this possibility is natural. We also discuss how this might be realized in supersymmetric theories. The properties of a strongly coupled Higgs boson in top-quark condensation and supersymmetry are described. We comment on the difficulties of seeing such a state at the Tevatron and LEPII, and study the dramatic signatures it could produce at the LHC. The four top quark signature is especially useful in the search for a strongly coupled Higgs boson. We also calculate the rates of the more conventional Higgs boson signatures at the LHC, including the two photon and four lepton signals, and compare them to expectations in the Standard Model.

Mirror families in electro-weak symmetry breaking

We study symmetry breaking in a left-right symmetric extension of the Standard Model with mirror fermions, one for each Standard-Model fermion. The new particles assist a top-quark condensate in breaking electro-weak symmetry. Half of the fermions acquire electro-weak-invariant masses at around 500 GeV and would be probably accessible at future high-energy experiments like LHC or NLC. The contributions to the S and T parameters are small and negative in accordance with electro-weak precision data.

Electroweak symmetry-breaking Higgs boson in models with top-quark condensation

The top quark may get its large mass not from a fundamental scalar but a Nambu--Jona-Lasinio mechanism involving a strongly coupled gauge sector that triggers top-quark condensation. Forbidding a large hierarchy in the gap equation implies that top-quark condensation is a spectator to electroweak symmetry breaking, which must be accomplished mainly by another sector. The properties of the electroweak symmetry-breaking scalars are identified. Production mechanisms and decay modes are studied. Unlike the standard model, the scalar degree of freedom most relevant to electroweak symmetry breaking can only be produced by its gauge interactions. An ${e}^{\ifmmode\pm\else\textpm\fi{}}{e}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}}+{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}{e}^{\ensuremath{\mp}}$ signal is proposed to help unambiguously detect the presence of such a gauge-coupled Higgs boson if it is light. Other useful modes of detection are also presented, and a summary is made of the search capabilities at CERN LEP II, Fermilab Tevatron, and CERN LHC.

Top quark soliton and its anomalous chromomagnetic moment.

We show that under the assumption of dynamical symmetry breaking of electro weak interactions by a top quark condensate, motivated by the Top Mode Standard Model, the top quark in this effective theory can be considered then as chiral color soliton (qualiton). This is realized in an effective four-fermion interaction with chiral $SU(3)_c$ as well as $SU(2)_L\otimes U_Y(1)$ symmetry. In the pure top sector the qualiton consists of a top valence quark and a Dirac sea of top and anti-top quark coupled to a color octet of Goldstone pions. The mass spectra, isoscalar quadratic radii and the anomalous chromomagnetic moment due to a non-trivial color form factor are calculated with zero and finite current top masses and effects at the Hadron Colliders are discussed. The anomalous chromomagnetic moment turns out to have a value consistent with the top production rates of the D0- and CDF-measurements.

Condensation effects beyond one loop in the top-mode standard model without gauge bosons.

We study dynamical symmetry breaking in the Standard Model including the next-to-leading order terms. We introduce at a high, but finite, energy scale Lambda a top quark condensate H={t {bar t}} and derive, using path integral methods, the effective potential including quadratic fluctuations in the scalar field H. We neglect the contributions of all components of the massive electroweak gauge bosons. The existence of a non-trivial minimum in the effective potential leads to the condition that the cut-off Lambda is limited from above: Lambda < Lambda_{crit} approx 4.7 m_t^{phys.} (for N_c = 3), and to a new lower bound for the 4-fermion coupling a = (G N_c Lambda^2)/(8 pi^2) > 1.60. Similar results are obtained if we demand, instead, that the next-to-leading order contributions not shift the location z=(m_t^{bare}/Lambda)^2 of the minimum drastically, e.g.~by not more than a factor of 2. The results are reproduced diagrammatically, where the leading plus all the next-to-leading order diagrams in the (1/N_c)-expansion are included. Dominant QCD effects are also included, but their impact on the numerical results is shown to be small.

Top Quark Condensate Revisited

In the light of recent discovery of a very heavy top quark, we reexamine the top quark condensate model proposed by Miransky, Tanabashi and Yamawaki (MTY) and by Nambu. We first review the original MTY formulation based on the ladder Schwinger-Dyson equation and the Pagels-Stokar formula. It is particularly emphasized that the critical phenomenon gives a simple reason why the top quark can have an extremely large mass compared with other quarks and leptons. Then we discuss the Bardeen-Hill-Lindner (BHL) formulation based on the renormalization-group equation and the compositeness condition, which successfully picks up 1/N_c-sub-leading effects disregarded by MTY. In fact BHL is equivalent to MTY at the 1/N_c-leading order. Such a simplest version of the model predicts the top quark mass, m_t \simeq 250 GeV (MTY) and m_t \simeq 220 GeV (BHL), for the cutoff on the Planck scale. In this version we cannot take the cutoff beyond the Landau pole of U(1)_Y gauge coupling, which yields a minimum value of the top mass prediction m_t \simeq 200 GeV. We then propose a ``top mode walking GUT'' : The standard gauge groups are unified into a (``walking'') GUT so that the cutoff can be taken to infinity thanks to the renormalizability of the four-fermion theory coupled to ``walking'' gauge theory. The top and Higgs mass prediction is then controlled by the Pendleton-Ross infrared fixed point at GUT scale and can naturally lead to m_t \simeq m_H \simeq 180 GeV.

Dynamical fermion mass generation by strong gauge interaction shielded by a scalar field.

The strongly coupled lattice gauge models with confined fermion and scalar matter fields, which in a certain phase break dynamically a global chiral symmetry, are reconsidered from the point of view of the existence of heavy fermions. In these models heavy fermions can arise as neutral bound states of the fundamental fermion and scalar. We call this mechanism of dynamical fermion mass generation the shielded gauge mechanism. The scalar field induces at strong gauge coupling a second order phase transition which is necessary for a continuum limit. Therefore the mechanism might well exist also in continuum. In this case, assuming that strongly coupled chiral gauge theories with scalars have similar dynamical properties at strong coupling as the vectorlike models investigated on the lattice, the discussed mechanism could be considered as an alternative to the Higgs mechanism. In particular, if the broken global chiral symmetry is SU(2) and the heavy fermion interpreted as a top quark, the mechanism is analogous to some gauge models for the top quark condensate. We present some numerical data obtained in the quenched approximation of a model with vectorlike U(1) gauge symmetry. The observed scaling behavior of the chiral condensate and of the fermion mass and also the properties of Goldstone bosons are the first encouraging steps in a study of the continuum limit of the mechanism.

Z-->bb-bar versus dynamical electroweak symmetry breaking involving the top quark.

In models of dynamical electroweak symmetry breaking which sensitively involve the third generation, such as top quark condensation, the effects of the new dynamics can show up experimentally in Z->b\bar{b}. We compare the sensitivity of Z->b\bar{b} and top quark production at the Tevatron to models of the new physics. Z->b\bar{b} is a relatively more sensitive probe to new strongly coupled U(1) gauge bosons, while it is generally less sensitive a probe to new physics involving color octet gauge bosons as is top quark production itself. Nonetheless, to accomodate a significant excess in Z->b\bar{b} requires choosing model parameters that may be ruled out within run I(b) at the Tevatron.

Fermion mass predictions in a generalized extended technicolor scenario.

One family extended technicolor (ETC) models with technifermion mass spectra compatible with the experimental data for the precision parameters S, T, U, V, W, and X, and ETC interactions compatible with the CERN LEP measurements of the Z\ensuremath{\rightarrow}bb\ifmmode\bar\else\textasciimacron\fi{} vertex have recently been proposed. To investigate whether these scenarios are consistent with the third family fermion masses we develop a generalized ETC model in which ETC interactions are represented by four-Fermi interactions. We discuss the reliability of the gap equation approximation to the nonperturbative dynamics. Two generic scenarios of couplings fit the precision data and third family masses: one is an unpredictive existence proof, the other, which generates the large top mass by direct top quark condensation, has a minimal number of interactions that break the global symmetry of the light fermions in the observed manner. This latter scenario makes surprisingly good predictions of the charm, strange, and up quark masses.

Regularization in the gauged Nambu-Jona-Lasinio model.

Various prescriptions employed for regulating gauged Nambu--Jona-Lasinio type models such as the top-quark condensate model are discussed. The use of dimensional regularization maintains gauge invariance but destroys the quadratic divergence in the gap equation. If instead a simple ultraviolet momentum cutoff is used to regulate loop integrals, then gauge invariance is destroyed by a quadratically divergent term as well as by ambiguities associated with arbitrary routing of loop momenta. Finally it is shown that one can use dispersion relations to regulate the top-quark condensate model. This prescription maintains gauge invariance and does not depend on arbitrary shifts in loop momenta.

Phase Structure of the Gauged Yukawa Model

Based on the ladder Schwinger-Dyson equation, we investigate phase structure of the gauged Yukawa model possessing a global SU(2)L X SU(2)R symmetry and an unbroken (vector-like) gauge symmetry. We show that even when we tune the squared mass of the scalar boson in the Lagrangian to be positive, there still exists the dynamical chiral symmetry breaking due to fermion pair conden­ sate (VEV of the composite scalar) triggered by the strong Yukawa coupling larger than a certain critical value. We find a nontrivial ultraviolet fixed line and renormalized trajectories in the three-dimensional coupling space of the Yukawa coupling, the gauge coupling and the hopping parameter of the elementary scalar field. Presence of the gauge coupling is crucial to existence of the fixed line. Implications of the result for the lattice calculation and the top quark condensate model are also discussed.

Phase Structure of the Gauged Yukawa Model

Based on the ladder Schwinger-Dyson equation, we investigate phase struc- ture of the gauged Yukawa model possessing a global $SU(2)_L \times SU(2)_R$ symmetry and an unbroken (vector-like) gauge symmetry. We show that even when we tune the squared mass of the scalar boson in the Lagrangian to be positive, there still exists the dynamical chiral symmetry breaking due to fermion pair condensate (VEV of the composite scalar) triggered by the strong Yukawa coupling larger than a certain critical value. We find a "nontrivial ultraviolet fixed line" and "renormalized trajectories" in the three-dimensional coupling space of the Yukawa coupling, the gauge cou- pling and the "hopping parameter" of the elementary scalar field. Presence of the gauge coupling is crucial to existence of the fixed line. Implications of the result for the lattice calculation and the top quark condensate model are also discussed.

Top quark condensation from broken family symmetry

We investigate the vacuum alignment in a fully dynamical “moose” model which breaks electroweak symmetry with a top quark condensate and show how the prefered vacuum depends on the explicit masses of the fermions involved. Our results are also applicable to the cases in which electroweak symmetry is broken by a fourth family of quarks, or by a technicolour mechanism. Such moose models allow the scale of new physics, Λ, to be in the TeV range with the absence of flavour changing neutral currents ensured by a GIM mechanism.

TOP QUARK MASS IN THE CONDENSATE MODEL AND THE POSSIBILITY OF COLORED BOSONS

The dynamical electroweak symmetry breaking of the Standard Model triggered by a top quark condensate (induced by an effective strong interaction, associated with a highenergy scale, of the form [Formula: see text]) usually requires an embarrassingly large top quark mass. A suggestion that this problem could be avoided through the introduction of an additional interaction [Formula: see text] (where [Formula: see text] are SU(3)c generators á la Okubo) is analyzed using the renormalization group approach. The mass of the top quark and the concomitant emergence of colored composite bosons is discussed.