We investigate the effect of composite pions on the behaviour of the chiral condensate at finite temperature within the Polyakov-loop improved NJL model. To this end we treat quark-antiquark correlations in the pion channel (bound states and scattering continuum) within a Beth-Uhlenbeck approach that uses medium-dependent phase shifts. A striking medium effect is the Mott transition which occurs when the binding energy vanishes and the discrete pion bound state merges the continuum. This transition is triggered by the lowering of the continuum edge due to the chiral restoration transition. This in turn also entails a modification of the Polyakov-loop so that the SU(3) center symmetry gets broken at finite temperature and dynamical quarks (and gluons) appear in the system, taking over the role of the dominant degrees of freedom from the pions. At low temperatures our model reproduces the chiral perturbation theory result for the chiral condensate while at high temperatures the PNJL model result is recovered. The new aspect of the current work is a consistent treatment of the chiral restoration transition region within the Beth-Uhlenbeck approach on the basis of mesonic phase shifts for the treatment of the correlations.

Based on the relativistic Logunov–Tavkhelidze equation, we obtain the mass spectra and probabilities of radiative decays of heavy quarkonia in the framework of the constituent quark model of hadrons.

For the investigation of back-reactions of composite mesons in the NJL model, a variational path-integral treatment is formulated which yields an effective action Aeff[Dσ,Dπ;S], depending on the propagators Dσ, Dπ of σ− and π−mesons and on the full quark propagator S. The stationarity conditions δAeff/δS=0, δAeff/δDσ=0, δAeff/δDπ=0, then lead to coupled Schwinger–Dyson (SD) equations for the quark self-energy and the meson polarization functions. These results reproduce and extend results of the so-called “Φ−derivable” approach and provide a functional formulation for diagrammatic resummations of 1/Nc−corrections in the NJL model. Finally, we perform a low-momentum estimate of the quark and meson loop contributions to the polarization function of the pion and on this basis discuss the Goldstone theorem.

In this paper we investigate the phase structure of a (1 +/- 1)-dimensional schematic quark model with four-quark interaction and in the presence of baryon (mu(B)), isospin (mu(I)) and chiral isospin (mu(I5)) chemical potentials. It is established that in the large-N-c limit (N-c is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential mu(I5) promotes the appearance of the charged PC phase with nonzero baryon density.

In this paper we consider a class of (2+1)D schematic models with four-fermion interactions that are effectively used in studying condensed-matter systems with planar crystal structure, and especially graphene. Symmetry breaking in these models occurs due to a possible appearance of condensates. Special attention is paid to the symmetry properties of the appearing condensates in the framework of discrete chiral and C, P and T transformations. Moreover, boundary conditions corresponding to carbon nanotubes are considered and their relations with the effect of an applied external magnetic field are studied. To this end we calculated the effective potential for the nanotube model including effects of finite temperature, density and an external magnetic field. As an illustration we made numerical calculations of the chiral symmetry properties in a simpler Gross–Neveu model with only one condensate taken into account. We also investigated the phase structure of the nanotube model under the influence of the Aharonov–Bohm effect and demonstrated that there is a nontrivial relation between the magnitude of the Aharonov–Bohm phase, compactification of the spatial dimension and thermal restoration of the originally broken chiral symmetry.

In this paper the duality correspondence between fermion-antifermion and difermion interaction channels is established in two (2 + 1)-dimensional Gross-Neveu-type models with a fermion number chemical potential mu and a chiral chemical potential mu(5). The role and influence of this property on the phase structure of the models are investigated. In particular, it is shown that the chemical potential mu(5) promotes the appearance of dynamical chiral symmetry breaking, whereas the chemical potential mu contributes to the emergence of superconductivity.

In this paper a (2 + 1)-dimensional model with four-fermion interactions is investigated in the case when one spatial coordinate is compactified and the space topology takes the form of an infinite cylinder, R-1 circle times S-1. It is supposed that the system is embedded in real three-dimensional space and that a magnetic flux Phi crosses the transverse section of the cylinder. The model includes four-fermion interactions both in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting) channels. We then study phase transitions that depend on the chemical potential mu and the flux Phi in the leading order of the large-N expansion technique, where N is the number of fermion fields. It is demonstrated that for arbitrary relations between coupling constants in the chiral and superconducting channels, superconductivity appears in the system at rather high values of mu (the length L of the circumference S-1 is fixed). Moreover, it is shown that at sufficiently small values of mu the growth of the magnetic flux Phi leads to a periodical reentrance of the chiral symmetry breaking or superconducting phase, depending on the values of mu and the coupling constants.

We consider electron transport in a planar fermion model containing various types of line defects modeled by δ-function pseudopotentials with different matrix coefficients. After determining the necessary boundary conditions, the transmission probability for electron transport through the defect line is obtained for various types of pseudopotentials. For the schematic model considered, which may describe a graphene structure with different types of linear defects, the valley polarization is obtained.

We investigate the possibility of spatially homogeneous and inhomogeneous chiral fermion-antifermion condensation and superconducting fermion-fermion pairing in the (1 + 1)-dimensional model by Chodos et al. [Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature T, electric charge chemical potential and chiral charge chemical potential mu(5). It is shown that at G(1) < G(2), where G(1) and G(2) are the coupling constants in the fermion-antifermion and fermion-fermion channels, the (mu,mu(5))-phase structure of the model is in a one-to-one correspondence with the phase structure at G(1) > G(2) (called duality correspondence). Under the duality transformation the (inhomogeneous) chiral symmetry breaking (CSB) phase is mapped into the (inhomogeneous) superconducting (SC) phase and vice versa. If G(1) = G(2), then the phase structure of the model is self-dual. Nevertheless, the degeneracy between the CSB and SC phases is possible in this case only when there is a spatial inhomogeneity of condensates.

We investigate the possibility of spatially inhomogeneous chiral and Cooper, or superconducting, pairing in the (1 + 1)-dimensional model by Chodos et al. [Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature T and quark number chemical potential mu. In the framework of the Fulde-Ferrel inhomogeneity ansatz for chiral and Cooper condensates, we show that if G(1) > G(2), where G(1) and G(2) are the coupling constants in the quark-antiquark and diquark channels, then in the (mu, T)-phase diagram the superconducting phase is suppressed by spatially inhomogeneous chiral spiral phase with broken chiral symmetry. In contrast, in the above mentioned original Chodos et al. model, where only the opportunity for homogeneous condensates is taken into account, the superconducting phase is realized at sufficiently high values of mu at arbitrary values of G(2) > 0, including the interval 0 < G(2) < G(1).

The properties of the (1 + 1)-dimensional massless Gross-Neveu model were studied for a compactified space S 1, as well as with allowance for nonzero values of the baryon (µ) and isospin (µ I ) chemical potentials. Our investigation was performed in the limit of a large number of fermion colors, N c . It is shown that, for L→∞(case of an unbounded volume), the pion-condensation phase characterized by zero quark density is formed at any nonzero value of µ I and a small value of µ. For any finite value of L (case of a bounded volume), the phase portrait of the model contains a pion-condensation phase where the quark density is nonzero. Thus, finite dimensions of the system being considered may serve as a factor that facilitates the formation of a pion-condensation phase in quark matter with a nonzero baryon density. At the same time, the phase where chiral symmetry is broken may exist only at very large values of L.

We investigate the phase portrait of the (1+1)-dimensional massless two-flavored NJL(2) model containing a quark number chemical potential mu and an isospin chemical potential mu(I) in the limit of a large number of colors N-c -> infinity.

The properties of two-flavored massless Nambu–Jona-Lasinio (NJL) model in (1+1)-dimensional R1 × S1 space–time with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials μI, μ. The consideration is performed in the large Nc limit, where Nc is the number of colored quarks. It is shown that at L = ∞ (L is the length of the circumference S1) the charged pion condensation (PC) phase with zero quark number density is realized at arbitrary nonzero μI and for rather small values of μ. However, at arbitrary finite values of L the phase portrait of the model contains the charged PC phase with nonzero quark number density (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the charged PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of L.

We investigate the phase portrait of the (1 + 1)-dimensional massless two-flavored NJL(2) model containing a quark number chemical potential mu and an isospin chemical potential mu(I) in the limit of a large number of colors N-c -> infinity. Particular attention is paid to the question of to what extent the inclusion of an isospin asymmetry affects chiral condensates to have a spatial inhomogeneity in the form of the so-called chiral density waves (CDW) (chiral spirals). It is shown that, at zero temperature and comparatively small values of mu, i.e. at mu < mu(c) approximate to 0.68M(0) (M-0 is the dynamical quark mass in the vacuum), only the homogeneous charged pion condensation phase is realized for arbitrary nonzero values of mu(I). Contrary to this, for large values of mu > mu(c), two CDW phases appear in the (mu(I), mu)-phase diagram of the model. In the first phase, CDWs are clockwise twisted chiral spirals, and in the second phase they are counterclockwise. The influence of nonzero temperature on the formation of the CDW phases is also investigated.

The masses of the heavy tetraquarks with open charm and bottom are calculated within the diquark–antidiquark picture in the framework of the relativistic quark model. The dynamics of the light quarks and diquarks is treated completely relativistically. The diquark structure is taken into account by calculating the diquark–gluon form factor. New experimental data on charmed and charmed-strange mesons are discussed. Our results indicate that the anomalous scalar Ds0⁎(2317) and axial vector Ds1(2460) mesons could not be considered as diquark–antidiquark bound states. On the other hand, Ds(2632) and DsJ⁎(2860) could be interpreted as scalar and tensor tetraquarks, respectively. The predictions for masses of the corresponding bottom counterparts of the charmed tetraquarks are given.

We study the dynamical symmetry breaking in quark matter within two different models. First, we consider the effect of gravitational catalysis of chiral and color symmetries breaking in strong gravitational field of ultrastatic hyperbolic spacetime ℝ ⊗ H 3 in the framework of an extended Nambu-Jona-Lasinio model. Second, we discuss the dynamical fermion mass generation in the flat 4-dimensional brane situated in the 5D spacetime with one extra dimension compactified on a circle. In the model, bulk fermions interact with fermions on the brane in the presence of a constant abelian gauge field A 5 in the bulk. The influence of the A 5 -gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable.

The properties of light and heavy mesons, baryons and tetraquarks are discussed within a QCD-motivated relativistic quark model. The results for the mass spectra, electroweak properties and Regge trajectories of hadrons are presented.

Starting from a NJL-type model with $N$ fermion species, fermion and difermion condensates and their associated phase structures are considered at nonzero chemical potential $\ensuremath{\mu}$ and zero temperature in spaces with nontrivial topology of the form ${S}^{1}\ensuremath{\bigotimes}{S}^{1}\ensuremath{\bigotimes}{S}^{1}$ and ${R}^{2}\ensuremath{\bigotimes}{S}^{1}$. Special attention is devoted to the generation of the superconducting phase. In particular, for the cases of antiperiodic and periodic boundary conditions we have found that the critical curve of the phase transitions between the chiral symmetry breaking and superconducting phases as well as the corresponding condensates and particle densities strongly oscillate versus $\ensuremath{\lambda}\ensuremath{\sim}1/L$, where $L$ is the length of the circumference ${S}^{1}$. Moreover, it is shown that at some finite values of $L$ the superconducting phase transition is shifted to smaller values both of $\ensuremath{\mu}$ and particle density in comparison with the case of $L=\ensuremath{\infty}$.

The relativistic model of heavy tetraquarks is formulated within the diquark-antidiquark picture. The diquark structure is taken into account by the diquark-gluon form factor. New experimental data on charmonium-like states above open charm threshold are discussed. The obtained results indicate that X(3872), Y(4140), Y(4260), Y(4360), Z 2(4250), Z(4433) and Y(4660) could be tetraquark states with hidden charm. Predictions for the masses of bottom counterparts to the charm tetraquark candidates are given.