Theories of quark confinement

It is conjectured that a non-Abelian gauge theory based on the color SU(3) group will confine quarks. Various techniques that have been applied to this question are reviewed. These include approximate methods based on strong coupling expansions of Hamiltonian and Euclidian lattice theories, instanton improvements on perturbation theory, and solutions of truncated Dyson-Schwinger equations for the gauge field propagator. Formal results based on electric-magnetic duality arguments and on the study of loop field theories are presented. Deconfinement at high temperatures, the inclusion of light quarks, and a possible reconciliation with a hypothetical discovery of free quarks are discussed.     

Minimal subtraction and the decoupling of heavy quarks for arbitrary values of the gauge parameter

The decoupling of a heavy quark is investigated to two loops for QCD renormalized by minimal subtraction. It is shown that the heavy quark effects can be absorbed into an effective coupling constant, an effective gauge parameter and effective masses for the light quarks. The relations between these effective parameters and the parameters of the full theory are gauge invariant. In terms of the effective parameters the theory satisfies renormalization group equations which refer only to the light degrees of freedom.     

Dynamical Model of QCD Vacuum and Color Thaw at Finite Temperatures

In terms of the Nambu Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple local gauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalar fields is derived by solving the Euler equation for the gauge fields. Based on this relation the SU(3) gauge potential is given which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinement behavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can be melted away under high temperatures.     

Dynamical Model of QCD Vacuum and Quark Confinement

The phase transition of a simple local gauge model is investigated in terms of the Nambu-Jona-Lasinio mechanism and it is pointed out that the physical vacuum of QCD is bound state of quark-antiquark pairs which can be viewed, generally, as a nearly perfect color dia-electric medium. An important relation between the vacuum expectation value of gauge fields and scalar fields is also derived by solving the Euler equation for the gauge fields. Based on this relation the SU_C(3) gauge potential is given which can be used to explain the asymptotic behavior and confinement of quarks in a hadron, and at the same time the Yukawa potential of strong interaction can be given too.     

Dynamical Model of QCD Vacuum and Color Thaw at Finite Temperatures

In terms of the Nambu-Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple localgauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalarfields is derived by solving the Euler equation for the gauge fields. Based on this relation the SU(3) gauge potential isgiven which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinementbehavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can bemelted away under high temperatures.     

Exact solutions of the equations of motions of quarks in a non-Abelian field of a flat color wave

Exact solutions of the equations of motion of quarks in a non-Abelian field of a flat color wave of a spectral configuration are obtained. The gauge field of the wave takes values from the SU(2) group and is an exact solution of the Yang-Mills equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 76–78, December, 1986.     

Supersymmetric standard model from the heterotic string

We present a [FORMULA: SEE TEXT] orbifold compactification of the E8xE8 heterotic string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), whereas the Higgs fields do not form complete SO(10) multiplets. The model has large vacuum degeneracy. For generic vacua, no exotic states appear at low energies and the model is consistent with gauge coupling unification. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings, whereas the other Yukawa couplings are suppressed.     

Black hole evaporation with separated fermions

In models with a low quantum gravity scale, fast proton decay can be avoided by localizing quarks and leptons to separated positions in an extra 1/TeV sized dimension with gauge and Higgs fields living throughout. Black holes with masses of the order of the quantum gravity scale are therefore expected to evaporate nonuniversally, preferentially radiating directly into quarks or leptons but not both. Should black holes be copiously produced at a future hadron collider, we find the ratio of final state jets to charged leptons to photons is 113:8:1, which differs from previous analyses that assumed all standard model fields live at the same point in the extra dimensional space.     

Axigluon couplings in the presence of extra color-octet spin-one fields

In this paper, we study how the interaction of the axigluon with quarks is modified when we introduce new color-octet spin-one fields in a chiral color model. We show that in this case the strength of this interaction is not completely determined by the gauge symmetry anymore and may be significantly weaker than the one predicted in the original chiral color model. In this way, we reinterpret the non-observability of the axigluon at the Tevatron, not as a limit on the axigluon mass, but as a limit on the strength of the axigluon coupling to quarks. Nevertheless, it must be remarked that, because the experimental limits on colored resonances production depend on the mass of the resonance, the limits we find still depend on the mass of the axigluon.     

Action principle and equations of motion for nonabelian monopoles

Monopoles in gauge theories have an intrinsic interaction with the gauge field. The definition of a monopole as a topological charge implies a certain constraint coupling the gauge field to the coordinates of a particle carrying that charge. Hence, even starting with the free action, the constraint will give equations of motion in which field and particle interact. Applied to electromagnetism, this procedure gives the Maxwell and Lorentz equations. In this paper, we apply the same idea to nonabelian monopoles to deduce their equations of motion which are otherwise unknown. To surmount certain technical difficulties connected with patching, loop space techniques are developed to solve the variational problem. A closed set of equations are obtained, which are analogous to the Maxwell and Lorentz equations, and bear also a formal resemblance to the Wong equations for a “classical” point source of Yang-Mills fields.     

Electroweak symmetry breaking with hierarchical feature

Electroweak symmetry breaking is attributed to dynamical generation of quark masses. Our study is made in those models in which preons are confined by hypercolor gauge interactions to form massless quarks and leptons as well as heavy hyperhadrons or postons. The hierarchical nature of the breaking can be understood by assuming the necessity of infinite-range color interactions in addition to short-range postonic ones. Self-consistent mass equations forN families of quarks are given in an ideal limit in which left-right asymmetric effects and quark-lepton couplings are neglected.     

Non-minimal pp-wave Einstein–Yang–Mills–Higgs model: color cross-effects induced by curvature

Non-minimal interactions in the pp-wave Einstein–Yang–Mills–Higgs (EYMH) model are shown to give rise to color cross-effects analogous to the magneto-electricity in the Maxwell theory. In order to illustrate the significance of these color cross-effects, we reconstruct the effective (associated, color, and color-acoustic) metrics for the pp-wave non-minimal seven-parameter EYMH model with parallel gauge and scalar background fields. Then these metrics are used as hints for obtaining explicit exact solutions of the non-minimally extended Yang–Mills and Higgs equations for the test fields propagating in the vacuum interacting with curvature. The influence of the non-minimal coupling on the test particle motion is interpreted in terms of the so-called trapped surfaces, introduced in the Analog Gravity theory.     

Hedgehog structures in general quark-meson Lagrangians

We investigate stationarity properties of hedgehog configurations in effective quarkmeson Lagrangians involving scalar and vector boson fields with arbitrary self-couplings. The Lagrangians are assumed to be in theSU(2)-sector and to be invariant under Lorentz-transformations, isorotations and time reversal. Restricting ourselves to the mean field solution based on valence quarks in sphericals-orbits and bilinear couplings the quark-hedgehog is shown to generate simply structured meson fields and to correspond to a stationary solution of the equations of motion. In most practical cases this is even of minimal energy.     

Quark pair creation in color electric fields and effects of magnetic fields

The time evolution of a system where a uniform and classical SU(3) color electric field and quantum fields of quarks interact with each other is studied focusing on non-perturbative pair creation and its back reaction. We characterize a color direction of an electric field in a gauge invariant way, and investigate its dependence. Momentum distributions of created quarks show plasma oscillation as well as quantum effects such as the Pauli blocking and interference. Pressure of the system is also calculated, and we show that pair creation moderates degree of anisotropy of pressure. Furthermore, enhancement of pair creation and induction of chiral charge under a color magnetic field which is parallel to an electric field are discussed.     

A model of unified quantum chromodynamics and Yang-Mills gravity

Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging T (4) × [SU (3)] color in flat space-time, we have a unified model of chromo-gravity with a new tensor gauge field, which couples universally to all gluons, quarks and anti-quarks. The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same ’effective Riemann metric tensors’ in the geometric-optics (or classical) limit. The emergence of ef f ective metric tensors in the classical limit is essential for the unified model to agree with experiments. The unified model suggests that all gravitational, strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework.     

An alternate smearing method for Wilson loops in lattice QCD

We have constructed the bag model having a central constant color field. The motion of the quark is studied in this bag and the Dirac equation is solved for it. The energy spectrum found has a branching due to the interaction of the quarks with the color background. It is pointed out that this model can be applied for taking into account, in the mass spectrum of the hadrons, the coupling of the constituent quarks with the gluon condensation as the interaction with the color background.Received: 7 December 2003, Revised: 18 January 2004, Published online: 3 March 2004Sh. Mamedov: shahin@theory.ipm.ac.ir     

Generalizations of gravitational theory based on group covariance

The mathematical structure, the field equations, and fundamentals of the kinematics of generalizations of general relativity based on semisimple invariance groups are presented. The structure is that of a generalized Kaluza-Klein theory with a subgroup as the gauge group. The group manifold with its Cartan-Killing metric forms the source-free solution. The gauge fields do not vanish even in this case and give rise to additional modes of free motion. The case of the de Sitter groups is presented as an example where the gauge field is tentatively assumed to mediate a spin interaction and give rise to spin motion. Generalization to the conformal group and a theory yielding features of Dirac's large-number hypothesis are discussed. The possibility of further generalizations to include fermions are pointed out. The Kaluza-Klein theory is formulated in terms of principal fibre bundles which need not to be trivial.     

Axial gauge propagators for quarks and gluons on the Polyakov-Wilson lattice

We discuss problems encountered in defining gauge-dependent propagators in a confining theory. For precision we use a finite Polyakov-Wilson lattice to define the Yang-Mills theory and to provide the ultraviolet and infrared regularization. Gauge fixing in a class of superaxial gauges is natural in this framework. A variety of approaches for defining the propagators for quarks and gluons is discussed and the propagators are evaluated explicitly in the strong coupling limit. We speculate upon the infrared behavior of these propagators in the weak coupling limit and upon the utility and validity of the Schwinger-Dyson equations for these propagators. In conclusion we propose that the leading infrared behavior is strongly gauge dependent and governed by the masses of low-lying color singlet states in the hadron spectrum. In the ultraviolet limit, however, with a properly constructed propagator, we find no reason to question the conventional wisdom derived from perturbation theory. Our conclusions should not depend in any fundamental way on the lattice formulation of the gauge theory, except insofar as that formulation serves to give precision to the continuum functional integration.     

Heisenberg Equations of Motion in a Nonabelian Gauge Theory

Heisenberg type equations of motion are established in a nonabelian gauge theory with minimal and nonminimal couplings and various relativistic particle equations of motion are derived from them. These equations for pointlike particles possessing a nonabelian gauge interaction (chosen for definiteness to be of SO(4,1) type) ore obtained in classical limit, ħ → 0, or in a semiclassical limit in which contributions of first order in ħ are retained. As a byproduct of the formalism, which can be applied to an arbitrary gauge group, a simple derivation of the Lorentz equation and the Bargmann-Michel-Telegdi equation from spinor electrodynamics with anomalous (i.e. nonminimal) coupling is given starting from the associated quantum mechanical Heisenberg equations of motion and specializing the gauge group to the electromagnetic U(1) group.     

Covariant quantization of non-Abelian antisymmetric tensor gauge theories

The non-Abelian Freedman-Townsend gauge tensor model is quantized in large class of covariant gauges using the geometrical reinterpretation of the BRS equations. In addition to the now usual pyramid of gauge and ghost states, a pyramid of auxiliary fields is found in our construction. These fields enforce the consistency of equations of motion and the integrability of the BRS equations.