QCD string and the Lorentz nature of confinement

We address the question of the Lorentz nature of the effective long-range interquark interaction generated by the QCD string with quarks at the ends. Studying the Dyson-Schwinger equation for a heavy-light quark-antiquark system, we demonstrate explicitly how a Lorentz scalar interaction appears in the Dirac-like equation for the light quark as a consequence of chiral symmetry breaking. We argue that the effective interquark interaction in the Hamiltonian of the QCD string with quarks at the ends stems from this effective scalar interaction.     

Problems with vector confinement in 4d QCD

It is shown that vector confinement does not support bound state spectrum in the 4d Dirac equation. The same property is confirmed in the heavy–light and light–light QCD systems. This situation is compared with the confinement in the 2d system, which is generated by the gluon exchange. Considering the existing theories of confinement, it is shown that both the field correlator approach and the dual superconductor model ensure the scalar confinement in contrast to the Gribov–Zwanziger model, where the confining Coulomb potential does not support bound states in the Dirac equation.     

Quark confinement and vortices in massive gauge-invariant QCD

Massive gauge-invariant QCD can support vortices (analogous to Nielsen-Olesen strings) of nearly finite classical action per unit area (there is a logarithmic short-distance singularity which is of little consequence). These vortices lead, in analogy to Abelian lattice-gauge theories, to confinement of fractionally charged quarks and color screening for gluons. In this paper, we make some qualitative remarks about the (Minkowski-space) dynamics which follows from this sort of confinement, studying not only $\text{q}\text{q}$ processes but also qqq processes. For the latter, the effective long-range vortex-induced interaction is approximately described as a sum of two-body potentials each of half the strength of the $\text{q}\text{q}$ potential (just as for the asymptotically free short-distance potentials), and linearly rising non-relativistically. There is an essential two-dimensionality about the confinement process which suppresses what would be the transverse degrees of freedom of strings joining quarks. A fully relativistic dynamics is given which is amenable to a simple phenomenological joining of long- and short-distance effects, with a running coupling constant such that g²(k) ～ k^?2 for small k. Spin-dependent potentials have no linearly-rising parts, and there are no strong Van der Waals forces. Little is said about gluon dynamics, except to point out the existence of rather massive hadronic glueballs and of (classically singular) instanton-like solutions which are screened at large distances.     

Color confinement and long-distance color fields in QCD

We use an effective lagrangian previously derived from a long-distance self-consistent solution of the Schwinger-Dyson equations of Yang-Mills theory to study some long-distance problems in QCD. In particular we show: (i) the long-distance contribution to the energy of a system containing a net color electric charge is infinite and hence there are no such states in the physical spectrum; (ii) the long-distance contribution to the energy of a system containing a net color magnetic charge is completely screened at distances r > 1/Λ_rmQCD.     

On confinement in a light-cone Hamiltonian for QCD

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fock-space amplitudes can be retrieved self-consistently from solutions in the -space. The approach is based on the novel method of iterated resolvents and on discretized light-cone quantization driven to the continuum limit. It is free of the usual perturbative Tamm-Dancoff truncations in particle number and coupling constant and respects all symmetries of the Lagrangian including covariance and gauge invariance. Approximations are done to the non-truncated formalism. Together with vertex as opposed to Fock-space regularization, the method allows to apply the renormalization programme non-perturbatively to a Hamiltonian. The conventional QCD scale is found arising from regulating the transversal momenta. It conspires with additional mass scales to produce possibly confinement. Received: 27 March 1998 / Revised version: 3 June 1998 / Published online: 16 September 1998     

Gauge-invariant formalism and quark confinement in QCD2

New gauge-invariant vector and spinor fields are introduced. Gauge-invariant quark propagator is defined in terms of these new fields. The equation for such a propagator, taken in 1/N approximation, does not require the introduction of an infrared regularization. As the regularization parameter in our approach there stands such a parameter which limit value corresponds to the gauge-invariant fields and translationally invariant quark propagator. It is shown that in this limit the pole of the gauge-invariant quark propagator shifts towards infinity what is usually treated as the confinement of a single quark.     

QCD confinement and the GlueX experiment at Jefferson Lab

An understanding of the confinement mechanism in QCD requires a detailed mapping of the spectrum of hybrid mesons.Understanding confinement means understanding the role of gluons and it is in hybrid mesons that the gluonic degrees of freedom are manifest.High statistics searches for such states with π and p beams have resulted in some tantalizing signals.There is good reason to expect beams of photons to yield hybrid mesons with J P C quantum numbers not possible within the conventional picture of mesons as qq bound states.Meager data currently exist on the photoproduction of light quark mesons.This talk represents an overview of the available data and what has been learned.In looking toward the future,the GlueX experiment at Jefferson Laboratory represents a new initiative that will perform detailed spectroscopy of the light-quark meson spectrum.This experiment and its capabilities will be reviewed.     

QCD confinement and the GlueX experiment at Jefferson Lab

An understanding of the confinement mechanism in QCD requires a detailed mapping of the spectrum of hybrid mesons.Understanding confinement means understanding the role of gluons and it is in hybrid mesons that the gluonic degrees of freedom are manifest.High statistics searches for such states with π and p beams have resulted in some tantalizing signals.There is good reason to expect beams of photons to yield hybrid mesons with J P C quantum numbers not possible within the conventional picture of mesons as qq bound states.Meager data currently exist on the photoproduction of light quark mesons.This talk represents an overview of the available data and what has been learned.In looking toward the future,the GlueX experiment at Jefferson Laboratory represents a new initiative that will perform detailed spectroscopy of the light-quark meson spectrum.This experiment and its capabilities will be reviewed.     

Implications of neutrino mass generation from QCD confinement

We consider the possibility that the quark condensate formed by QCD confinement generates Majorana neutrino masses mν$m_{\nu }$ via dimension seven operators. No degrees of freedom beyond the Standard Model are necessary, below the electroweak scale. Obtaining experimentally acceptable neutrino masses requires the new physics scale Λ∼TeV$\Lambda \sim \text{TeV}$, providing a new motivation for weak-scale discoveries at the LHC. We implement this mechanism using a Z₃$Z_3$ symmetry which leads to a massless up quark above the QCD chiral condensate scale. We use non-helicity-suppressed light meson rare decay data to constrain Λ. Experimental constraints place a mild hierarchy on the flavor structure of dimension seven operators and the resulting neutrino mass matrix.     

Kugo-Ojima confinement and QCD Green''s functions in covariant gauges

In Landau gauge QCD the Kugo-Ojima confinement criterion and its relations to the infrared behaviour of the gluon and ghost propagators are reviewed. It is demonstrated that the realization of this confinement criterion (which is closely related to the Gribov-Zwanziger horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, (0) = 8.915/N_c. Solutions for the coupled system of Dyson-Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry takes place. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the ones in quenched approximation. While the positivity violation of the gluon spectral function is manifest in the gluon propagator, there are no clear indications of analogous positivity violations for quarks so far.     

QCD Aspects of Exclusive B Decays

We review QCD approaches to exclusive B meson decays, concentrating on QCD-improved factorization and perturbative QCD. The ideas of soft-collinear effective theory and light-cone sum rules are briefly explained. We discuss the recently measured time-dependent CP asymmetry of the B⁰ _d^{+ –} modes, from which the unitarity angle can be extracted.     

Vacuum background fields in QCD as a source of confinement

Quarks and gluons in the vacuum background field with a finite correlation length d are shown to be linearly confined inside white states. The string tension for an arbitrary representation of SU(N) is obtained in terms of d and the gluon condensate and agrees with numerical data and large N behaviour. The QCD string picture is shown to emerge asymptotically at large euclidean distances.     

Structure of the exact effective action and quark confinement in MSSM QCD

An expression for the exact (beyond perturbation theory) effective action in N=1 supersymmetric gauge theories where all particles, with the exception of gauge bosons, are massive is proposed. By analyzing the form of this expression, it is shown that, in supersymmetric theories, instanton effects can lead to quark confinement. On the basis of first principles, the characteristic scale of confinement is calculated within MSSM QCD, and the result is found to be consistent with experimental data. The proposed explanation differs drastically with the dual Higgs mechanism.     

Phase transition over the gauge group center and quark confinement in QCD

A lattice gauge model with the phase transition corresponding to spontaneous breakdown of the group center symmetry is considered. The possible continuum limit in a phase with permanently confined quarks is discussed.     

Cylindrical gauge field configurations. A signal of confinement in QCD

An infrared approximation to the field equations of QCD is proposed which generates a mapping of configuration space into two dimensions (one time, one space dimension). The associated cylindrical gauge field configurations insure confinement whenever nontrivial interactions in two dimensions remain. This feature distinguishes abelian from nonabelian gauge theories.     

Non-perturbative Aspects of QCD and Parameterized Quark Propagator

Based on the Global Color Symmetry Model, the non-perturbative Q, CD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenologieal QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter ofμ in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.     

Quark-antiquark bound states and QCD running coupling within infrared confinement

Bound states of spin-half and spin-one particles are studied within a relativistic quantum-field model based on the infrared confinement. The spectra of quark-antiquark and two-gluon states are determined by master equations similar to the ladder Bethe-Salpeter equations. Masses of light, intermediate and heavy mesons are estimated in a wide range of scale (from hundreds MeV up to 10 GeV). A new, independent and specific infrared-finite behavior of QCD effective coupling is revealed in the low-energy domain.