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.     

On the Lorentz nature of confinement in heavy—light quarkonia

The Lorentz nature of the effective interquark interaction in a heavy—light quarkonium is studied using the vacuum correlators method and the generalized Nambu—Jona-Lasinio potential quark model. An effective scalar interaction is demonstrated to appear self-consistently owing to chiral-symmetry breaking and to dominate for low-lying states in the bound-state spectrum. The relation between such an effective interquark interaction and the QCD string approach is discussed. On the contrary, the upper part of this spectrum is found to be governed by the spatial Lorentz vector interaction which leads to a degeneracy for the states with opposite parity—the so-called restoration of chiral symmetry for excited hadrons. The text was submitted by the author in English.     

Nonperturbative dynamics in the color-magnetic QCD vacuum

In the deconfinement phase of QCD, quarks and gluons interact with the dense stochastic color-magnetic vacuum. We consider the dynamics of quarks in this deconfinement phase using the field correlators method and derive an effective nonperturbative interquark potential, in addition to the usual perturbative short-range interaction. We find the resulting angular-momentum-dependent interaction to be attractive enough to maintain bound states and, for light quarks (and gluons), to cause emission of quark and gluon pairs. Possible consequences for the strong-interacting quark-gluon plasma are briefly discussed. The text was submitted by the authors in English.     

Hadron-quark phase transition in dense stars

An equation of state is computed for a plasma of one flavour quarks interacting through some phenomenological potential, at zero temperature. Assuming that the confining potential is scalar and colour-independent, it is shown that the quarks undergo a first-order mass phase transition. In addition, due to the way screening is introduced, all the thermodynamic quantities computed are independent of the actual shape of the interquark potential. This equation of state is then generalized to a several quark flavour plasma and applied to the study of the hadron-quark phase transition inside a neutron star.     

The quark bag model with surface tension

A membranous closed surface is introduced to confine colored vector gluon fields in a Lorentz invariant manner. Since the colored pointlike quarks are always coupled to the gluon fields, they become confined inside the closed membrane. The Hamiltonian formulation of the model is presented, and the classical string limit is discussed.     

Nucleons in nuclei in the selfconsistent soliton model to QCD

In the scalar Soliton model of QCD the gluon field operators are replaced by a classical selfcoupling scalar field with solitontype interaction. The quark wave-functions and the soliton field are calculated for the free nucleon as compared to a nucleon inside nuclear matter approximated by averaged boundary conditions to simulate the surrounding nucleons. The mass of the nucleon as well as its mean effective radius are given in terms of the nuclear-matter density and the model parameters. For large quark-soliton coupling the EMC-effect is seen, and then at high densities a plasma of free quarks and free localized solitons is the lowest energy solution.     

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.     

Dynamical suppression of the spin-orbit interaction in hadrons

A spin-dependent interaction in hadrons is considered in the approach of the QCD string. The string moment of inertia, which ensures the correct (inverse) Regge slope 2πσ, is found to suppress the spin-orbit interaction. For light quarks and moderate angular momenta, the suppression constitutes around 25%, whereas for large angular momenta the spin-orbit interaction is suppressed by the factor L ^−2/5. For heavy quarks, the effect manifests itself as a string correction for the spin-dependent potential. The text was submitted by the authors in English.     

Quark interaction with an instanton liquid

The effect of quarks on an instanton liquid through the excitation of adiabatic phonon-like modes in it is considered. An effective Lagrangian that includes a scalar color-singlet field interacting with quarks is derived, and the relevant generating functional is estimated in the tadpole approximation. The nature of this dynamical field as a mediator of interaction at soft momenta and its possible relationship with unusual properties of the sigma meson are discussed.     

Phenomenological description of relativistic-quark interaction on the basis of the Dirac equation with the Cornell potential

Relativistic-quark interaction is described phenomenologically on the basis of the Dirac equation with the Cornell potential. A general form of the initial equation involving the vector and scalar components of the Cornell potential is used for the case of an arbitrary relation between them. The Hamiltonian in the Foldy–Wouthuysen representation is derived in a general form with allowance for electromagnetic interaction. In contrast to earlier investigations, it is relativistic and exact for the zeroth- and first-order terms in the Planck constant and also for those second-order terms that describe contact interactions. General quantum-mechanical equations of motion for the momentum and spin are derived, and the classical limit of the Hamiltonian and for the equations of motion is found for the first time. A relation between the angular velocity of quark spin precession and the force acting on the quark is obtained. The energy of spin–orbit interaction is rather high (on the order of 100 MeV). Terms that describe spin–orbit and contact interactions have opposite signs for the vector and scalar components of the Cornell potential. The evolution of the quark helicity and the spin–spin interaction of the quarks are also calculated.     

Heavy quarkonia spectra and their decays in a relativistic quark model

Using the phenomenological relativistic harmonic model (RHM) for quarks, we have obtained the masses of S wave charmonium and bottomonium states. The full Hamiltonian used in the investigation has Lorentz scalar plus vector confinement potential, along with the confined one gluon exchange potential (COGEP). A good agreement with the experimental masses for the ground and the radially excited states is obtained both for the triplet and singlet S wave mesons. The decay properties of the ground state charmonium and bottomonium are investigated.     

Instanton induced chiral symmetry breaking in extended QCD model

A mechanism for instanton induced chiral symmetry breaking in an extended QCD model (QCD with fundamental scalars) is proposed to describe quarks and gluons inside a baryon. The model Lagrangian that we use has the same symmetry properties as QCD. The scalar fields are shown to develop vacuum expectation values in the instanton background and generate masses for the three generation of quarks. The minimization condition is also used to break the flavour symmetry to make the -quark heavier that the and quarks. Received: 16 August 1996 / Revised version: 15 October 1997 / Published online: 26 February 1998     

Hadronic spectrum of a holographic dual of QCD

We compute the spectrum of light hadrons in a holographic dual of QCD defined on AdS5 x S5 which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale Lambda(QCD), is used, the agreement with the pattern of physical states is remarkable. In particular, the ratio of delta to nucleon trajectories is determined by the ratio of zeros of Bessel functions.     

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.     

Solutions of a bethe-salpeter equation

We study systematically and exhibit the Lorentz symmetry of the Bethe-Salpeter equation in the light-like case for two scalar quarks of different masses interacting via the exchange of a scalar photon. We develop a new approach for solving the eigenvalue problem of the equation for the general case (not only the light-like). Our method permits accurate analytic expressions for the spectrum and the wave functions.     

Leading logarithmic approximation in QCD

The leading logarithmic approximation (LLA) for the scattering amplitudes in QCD is reviewed. The double-logarithmic asymptotics of scattering amplitudes is obtained as a solution to nonlinear evolution equations in the infrared cutoff. The DGLAP equation describes an evolution of parton distributions with increasing parton virtuality. The evolution of the amplitudes with respect to the scale in the longitudinal subspace is given by the BFKL equation. The gluon and quarks in QCD lie on the Regge trajectories calculable in perturbation theory. Mesons and baryons are composite states of Reggeized quarks. Similarly the Pomeron and Odderon are colorless ground states of Reggeized gluons. In the case of multicolor QCD, the Reggeon field theory in LLA is completely integrable. The Reggeon interactions in QCD are derived from a gauge-invariant effective action. In particular, next-to-leading corrections to the BFKL equation in QCD and in supersymmetric gauge models are obtained in this way.     

Exact Three-Dimensional Relativistic Equation for qq Bound states

Starting with the QCD generating functional, a new derivation and a new form of the Dirac-Schriidinger (D-S) equation,catisfied by the equal-time Bethe-Salpeter amplitude of quark-antiquark bound states have been given. In this equation, the effective interaction kernel has a compact expression and can be directly calculated by means of the conventional QCD Feynman rules. F'urthermore, an equivalent reduction of the above equation to a Pauli-Schriidinger equation has also been achieved and a closed form of the effective interaction Hamiltonian appearing in the latter equation has been explicitly written out.