Deconfinement transition: a three dimensional model

We present a three–dimensional model for quark matter with a density dependent quark–quark (confining) potential, which allows to describe a sort of deconfinement transition as the system evolves from a low density assembly of bound structures to a high density free Fermi gas of quarks. We consider different confining potentials, some of which successfully utilized in hadron spectroscopy. We find that a proper treatment of the many–body correlations induced by the medium is essential to disentangle the different nature of the two (hadronic and deconfined) phases of the system. For this purpose the ground state energy per particle and the pair correlation function are investigated. Received: 10 June 1998 / Revised version: 24 September 1998     

Non-relativistic quark cluster model of the isospin-violating two-nucleon interaction

The violations of isospin symmetry induced in the two-nucleon system at the quark level by the mass difference between up and down quarks are studied in a quark cluster model. Quark dynamics are treated by means of the standard non-relativistic quark model with a quark hamiltonian consisting of a confining harmonic potential, eventually corrected for anharmonicities, and a spin-dependent potential truncated to the contact-gluon-exchange hyperfine interaction. The resonating group method is adopted to treat the six-quark system and we restrict ourselves to configurations of two three-quark clusters with nucléon quantum numbers. π- and σ-meson-mediated quark interactions are tentatively considered in an attempt to achieve a good matching to the empirical strong NN potentials. We supply explicit formulas for the various kernels. Equivalent adiabatic potentials are calculated for the pp, np and nn systems in low partial waves. We also solve the resonating group scattering equations for these systems and give predictions for phase observables and low-energy parameters.     

On the confining potential in 4D SU(N_{\mathrm c}) gauge theory with dilaton

Using the formal analogy between the Dick superstring inspired model and the problem of the building of an Eguchi–Hanson metric in 4D N = 2 harmonic superspace (HS), we derive a general formula for the quark–quark interaction potential V(r) including the Dick confining potential. The interquark potential V(r) depends on the dilaton–gluon coupling and may be related to the parameterization of confinement by the quark and gluon vacuum condensates. It is also shown how the axion field may be incorporated in agreement with 10D type IIB superstring requirements. Others features are also discussed. Received: 23 December 1999 / Published online: 6 March 2000     

Is the universe homogeneous and isotropic in the time when quark-gluon plasma exists?

In this study, quark and strange quark matter which exist in the first seconds of the early Universe have been studied in the context of general relativity to be able to obtain space–time geometry of first seconds of the early Universe. For this purpose, Einstein’s field equations for quark and strange quark matter in the non static spherically symmetric space–time have been solved by using experimental result that anisotropy parameter of quark matter is very small. We have concluded from obtained solutions that the space–time structure of first seconds of the Early Universe is homogeneous and isotropic. Also we have concluded that the color interactions of the quarks may be origin of primordial magnetic field in the early universe.     

Doubly heavy-quark baryon spectroscopy and semileptonic decay

Working in the framework of a nonrelativistic quark model we evaluate the spectra and semileptonic decay widths for the ground state of doubly heavy Ξ and Ω baryons. We solve the three-body problem using a variational ansatz made possible by the constraints imposed by heavy-quark spin symmetry. In order to check the dependence of our results on the inter-quark interaction, we have used five different quark-quark potentials which include Coulomb and hyperfine terms coming from one-gluon exchange, plus a confining term. Our results for the spectra are in good agreement with a previous calculation done using a Faddeev approach. For the semileptonic decay our results for the total decay widths are in good agreement with the ones obtained within a relativistic quark model in the quark-diquark approximation.     

Improved effective action for light quarks beyond the chiral limit

We propose an improvement of the Diakonov–Petrov effective action on the basis of the Lee–Bardeen results for the quark determinant in the instanton field. This improved effective action provides a proper account of the current quark masses, which is particularly important for strange quarks. This action is successfully tested by calculations of the quark condensate, the masses of the pseudoscalar meson octet and axial-anomaly low-energy theorems. Received: 19 October 1998 / Revised version: 17 January 1999 / Published online: 20 May 1999     

From Euclidean to Minkowski space with the Cauchy–Riemann equations

We present an elementary method to obtain Green’s functions in non-perturbative quantum field theory in Minkowski space from Green’s functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy–Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson–Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy–Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation.     

On Gribov’s supercriticality picture of quark confinement

Some years ago Gribov developed the so-called supercritical light-quark confinement scenario. Based on physical arguments he conjectured a drastic change in the analytical properties of the quark propagator when the back reaction of Goldstone bosons (pions) is considered. We investigate this scenario and provide numerical solutions for the quark propagator in the complex plane with and without the pion back reaction. We find no evidence for the scenario Gribov advocated. As an aside we present a novel method to solve the quark Dyson–Schwinger equation in the complex plane and discuss new characteristics of dynamical chiral symmetry breaking in our truncation scheme.     

EMC and polarized EMC effects in nuclei

We determine nuclear structure functions and quark distributions for ⁷Li, ¹¹B, ¹⁵N and ²⁷Al. For the nucleon bound state we solve the covariant quark–diquark equations in a confining Nambu–Jona-Lasinio model, which yields excellent results for the free nucleon structure functions. The nucleus is described using a relativistic shell model, including mean scalar and vector fields that couple to the quarks in the nucleon. The nuclear structure functions are then obtained as a convolution of the structure function of the bound nucleon with the light-cone nucleon distributions. We find that we are readily able to reproduce the EMC effect in finite nuclei and confirm earlier nuclear matter studies that found a large polarized EMC effect.     

Magnetized quark and strange quark matter in the spherical symmetric space–time admitting conformal motion

In this paper, we have examined magnetized quark and strange quark matter in the spherical symmetric space–time admitting one-parameter group of conformal motions. For this purpose, we have solved Einstein’s field equations for spherical symmetric space–time via conformal motions. Also, we have discussed the features of the obtained solutions.     

String cloud and domain walls with quark matter in 5-D Kaluza–Klein cosmological model

In this study Kaluza–Klein Cosmological solutions are obtained for quark matter coupled to the string cloud and domain wall in the context of general relativity. For this purpose Einstein field equations are solved by using anisotropy feature of the universe in the five-dimensional Kaluza–Klein Cosmological model. Also, the features of obtained solutions are discussed.     

Quark Mass Functions and Pion Structure in Minkowski Space

We present a study of the dressed quark mass function and the pion structure in Minkowski space using the covariant spectator theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We use an interaction kernel in momentum space that is a relativistic generalization of the linear confining \({q\bar{q}}\) potential and a constant potential shift that defines the energy scale. The confining interaction has a Lorentz scalar part that is not chirally invariant by itself but decouples from the equations in the chiral limit and therefore allows the Nambu–Jona–Lasinio mechanism to work. We adjust the parameters of our quark mass function calculated in Minkowski-space to agree with LQCD data obtained in Euclidean space. Results of a calculation of the pion electromagnetic form factor in the relativistic impulse approximation using the same mass function are presented and compared with experimental data.     

The spin-symmetry of the quark model

Corrections to the exact heavy–quark symmetry results are expected to come from the inverse powers of the heavy-quark mass. We show, by an explicit calculation using the quark model, that the breaking of the spin symmetry is suppressed by other kinematic effects even when the quark masses are not heavy. Received: 21 January 1999 / Published online: 20 May 1999     

Effective quark Lagrangian in the instanton vacuum with nonzero modes included

A new approach to the effective theory of quarks in the instanton vacuum is presented. Exact equations for the quark propagator and Lagrangian are derived which contain contributions of all quark modes with known coefficients. The resulting effective Lagrangian differs from the standard one and resembles that of the Nambu-Jona-Lasinio model. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 128–132 (25 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Bosonization and Integral Representation of Solutions¶of the Knizhnik–Zamolodchikov–Bernard Equations

We construct an integral representation of solutions of the Knizhnik–Zamolodchikov–Bernard equations, using the Wakimoto modules. Received: 5 October 1998 / Accepted: 8 February 1999     

Filter for strangeness in J^{PC} exotic four-quark states

Symmetrization selection rules for the decay of four–quark states to two J=0 mesons are analysed in a non – field theoretic context with isospin symmetry. The OZI allowed decay of an isoscalar exotic state to or is only allowed for four–quark components of the state containing one pair, providing a filter for strangeness content in these states. Decays of four–quark states are narrower than otherwise expected. If the experimentally observed enhancement in is resonant, it is qualitatively in agreement with being a four–quark state. Received: 10 May 2001 / Revised version: 15 August 2001 / Published online: 21 September 2001     

Bulk viscosity of strange quark matter in density dependent quark mass model

We have studied the bulk viscosity of strange quark matter in the density dependent quark mass model (DDQM) and compared results with calculations done earlier in the MIT bag model where u, d masses were neglected and first order interactions were taken into account. We find that at low temperatures and high relative perturbations, the bulk viscosity is higher by 2 to 3 orders of magnitude while at low perturbations the enhancement is by 1–2 order of magnitude as compared to earlier results. Also the damping time is 2–3 orders of magnitude lower implying that the star reaches stability much earlier than in MIT bag model calculations.     

Parametrization of Fully Dressed Quark Propagator

Based on an extensive study of the Dyson-Schwinger equations for a fully dressed quark propagator in the “rainbow” approximation, a parametrized form of the quark propagator is suggested. The corresponding quark self-energy Σ_f and the structure of non-local quark vacuum condensate <0|:\bar{q}(x)q(0):|0> are investigated. The algebraic form of the quark propagator proposed in this work describes a confining quark propagation, and is quite convenient to be used in any numerical calculations.     

Propagators and Masses of Light Quarks

Based on Dyson-Schwinger equations in “rainbow“ approximation, fully dressed confining quark propagator is obtained, and then the masses of light quarks (mu, md, and ms) are derived from the fully dressed confining quark propagator. At the same time, the local and non-local quark vacuum condensates as well as the quark-gluon mixed condensate are also predicted. Furthermore, the quark masses are also deduced from the Gell-Mann-Oakes-Renner relation and chiral perturbative theory. The results from different methods are consistent with each other.     

Mass spectrum of diquarks and mesons in the color–flavor locked phase of dense quark matter

The spectrum of meson and diquark excitations of dense quark matter is considered in the framework of the Nambu–Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential μ. We investigate the effective action of meson and diquark fields both at sufficiently large values of μ>μ_c≈  330 MeV, where the color–flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter (μ<μ_c). In the latter case all nine pseudoscalar mesons are Nambu–Goldstone (NG) bosons, whereas the mass of the scalar meson nonet is twice the dynamical quark mass. In the chirally broken phase the pseudoscalar diquarks are not allowed to exist as stable particles, but the scalar diquarks might be stable only at a rather strong interaction in the diquark channel. In the case of the CFL phase, all NG bosons of the model are realized as scalar and pseudoscalar diquarks. Moreover, it turns out that massive diquark excitations are unstable for this phase. In particular, for the scalar and pseudoscalar octets of diquark resonances a mass value around 230 MeV was found numerically. In contrast, mesons are stable particles in the CFL phase. Their masses lie in the interval 400–500 MeV for not too large values of μ>μ_c. PACS 11.30.Qc; 12.38.-t; 12.39.-x