A Variational Approach for Hadronic Properties in NJL Model

We develop a variational approach for the Nambu-Jona-Lasinio (NJL) model with explicit chiral symmetry breaking and compute the constituent quark mass, the pion decay constant and the vacuum condensate. For a simple ansatz for the hadronic wavefunction, we also analyze the effects of the current quark mass and the ultraviolet cutoff on the static properties of hadrons.     

Properties of the nucleon in the nuclear medium within a chiral quark-meson theory

The modifications of the nucleon structure due to the presence of an external baryon medium are investigated in a chiral quark meson theory. To that end the Nambu-Jona-Lasinio (NJL) model is combined with the projected chiral soliton model. The medium effects are incorporated using the medium modified values of the pion decay constant and the pion and sigma masses at finite density. These values are evaluated within the NJL model. Using functional integral techniques the latter is solved in a quark continuum at finite density. The effective meson values serve to fix the parameters of the linear chiral sigma model which is solved in a variational projected mean field approach in order to obtain the nucleon properties. All nucleon properties show modifications in the medium except for the pion nucleon coupling constant. The proton radius shows an increase of 19% and the nucleon mass a decrease of 17% if the medium reaches nuclear matter density. The magnetic moments and axial vector coupling constant are less modified. All form factors show remarkable reduction at finite transfer momenta.     

Nonlocal quark model beyond mean field

The nonlocal chiral quark model is extended beyond mean field using a strict 1/N _c expansion scheme. The nonlocal interaction has the advantage that all diagrams are finite and leads to unique evaluation of the 1/N _c corrections. Parameters of the nonlocal model are refitted making use of the physical values of the pion mass and the weak pion decay constant. The size of the 1/N _c correction to the quark condensate is carefully studied in nonlocal and local Nambu-Jona-Lasinio models. It is found that even the sign of the corrections can be different.     

Electromagnetic form factors in the Nambu-Jona-Lasinio model

The original Nambu-Jona-Lasinio model is treated to leading order in 1/N. The electromagnetic form factors of the constituent quarks and the pion, and the anomalous π⁰ → 2γ decay amplitude are obtained. Their dependence on the cutoff of the model is made explicit. Two distinct limits (depending on the ratio of the cutoff to the constituent quark mass) in which the cutoff can be taken to infinity are also discussed. We find that to leading order of 1/N the model in one limit corresponds to the linear and in the other to the nonlinear sigma model.     

Pion and σ-meson Properties in a Strong Magnetic Field

With the Nambu-Jona-Lasinio (NJL) model we calculate the properties of pion and σ-meson at finite temperature and finite magnetic field. The obtained temperature and magnetic field strength dependence of the constituent quark mass M, the pion and σ-meson masses and the neutral pion decay constant indicates that, in the simple four fermion interaction model, there exists the magnetic catalysis effect. It also shows that the Gell-Mann-Oakes-Renner relation is violated obviously with the increasing of the temperature, and the effect of the magnetic field becomes pronounced only around the critical temperature. The deviation of the critical temperatures obtained with different criteria indicates that the chiral phase transition driven by the temperature in the magnetic field strength region we have considered is in fact a crossover.     

Pion radii in the nonlocal chiral quark model

The electromagnetic radius of a charged pion and the transition radius of a neutral pion are calculated in the framework of the nonlocal chiral quark model. It is shown in this model that the vector meson contributions to the pion radii are noticeably suppressed in comparison with a similar contribution in the local Nambu-Jona-Lasinio model. The form factor for the process is calculated for -1 GeV²< q ² < 1.6 GeV². Our results are in satisfactory agreement with experimental data.Received: 28 November 2003, Published online: 13 July 2004PACS: 14.40.-n Mesons - 11.10.Lm Nonlinear or nonlocal theories and models - 12.39.Ki Relativistic quark model     

Pion and chiral density waves in a (1 + 1)-dimensional Nambu-Jona-Lasinio model

A (1 + 1)-dimensional massless Nambu-Jona-Lasinio model is investigated in the limit of a large number of colors. The model describes a system with two quark flavors if μ baryon and μ _I isospin chemical potentials occur. The question of whether spatially inhomogeneous chiral and pion condensates can form in a dense quark environment is also examined.     

Mesons in the Low-Energy Limit of QCDh

Quark-antiquark bound states are described within the Bethe-Salpeter approach for a class of quark models with instantaneous 4-quark interaction. Thereby decompositions of the Bethe-Salpeter vertex and wave functions according to their Lorentz structures and the particle content are used. Normalization conditions for the bound state functions are given. As an application of the general scheme, we determine the mass spectrum of low-lying mesons without expanding in energy. This calculation is performed for a special Nambu-Jona-Lasinio model which follows from the so-called QCD for hadrons, QCD_h, by a localization of the potential. Furthermore the pion and kaon decay constants are determined. We receive good agreement with the experimental data.     

The fermion condensate of the Nambu-Jona-Lasinio model in Light Cone quantisation

We investigate the incorporation of condensates in Light Cone quantisation in the frame-work of the Nambu-Jona-Lasinio model. Although it is shown that the physical and perturbative vacua are identical, a gap equation for the dynamical quark mass is obtained and chiral symmetry is dynamically broken. The complete fermion condensate is found in the perturbative vacuum. The corresponding Goldstone mode is a zero mass bound state of the Weinberg equation.     

Spontaneous generation of Nambu-Jona-Lasinio interaction in QCD involving two light quarks

Within QCD involving two light quarks, the possibility of a spontaneous generation of effective interaction leading to Nambu-Jona-Lasinio model is studied by using the Bogolyubov quasiaverage approach. The compensation equation for the form factor of this interaction is shown to have a nontrivial solution that leads to a theory involving two parameters: the average value of the low-energy constant α _s and a dimensional parameter f _π. All of the remaining parameters, including the current and constituent quark masses, the quark condensate, the pion mass, and the sigma-meson mass and width, are expressed in terms of the input parameters in satisfactory agreement with experimental phenomenology. The results obtained here give sufficient grounds to conclude that the proposed approach is applicable in low-energy hadron physics and that it can be used in dealing with other problems.     

Generalized vector form factors of the pion in a chiral quark model

Generalized vector form factors of the pion, related to the moments of the generalized parton distribution functions, are evaluated in the Nambu-Jona-Lasinio model with the Pauli-Villars regularization. The lowest moments (the electromagnetic and the gravitational form factors) are compared to recent lattice data, with fair agreement. Predictions for higher-order moments are also made. Relevant features of the generalized form factors in the chiral quark models are highlighted and the role of the QCD evolution for the higher-order GFFs is stressed.     

Emergence of a nonuniform pion condensate in the (1 + 1)-dimensional Nambu-Jona-Lasinio model

The (1 + 1)-dimensional Nambu-Jona-Lasinio model describing the system of two-flavor quarks is studied in the limit of a large number of colors in the presence of a baryon chemical potential µ and an isospin chemical potential µ _I . The possible formation of a nonuniform pion condensate in dense quark matter is considered for the cases of both the massive and the massless model.     

Diquark confinement in an extended NJL model

In a Nambu-Jona-Lasinio model supplemented with an infrared cutoff in addition to the ultraviolet cutoff we study the issue whether diquarks are confined when the model is extended beyond the rainbow-ladder approximation. The gap equation, obtained in a truncation scheme motivated via a non-trivial quark-gluon vertex function, is solved to determine the constituent quark mass if chiral symmetry is spontaneously broken. In a second step, the Bethe-Salpeter equations for mesons and diquarks beyond the ladder approximation are derived, taking care to preserve Goldstone's theorem in the pion channel. While the obtained masses of pseudo-scalar and vector mesons are only moderately shifted compared to the values in the ladder approximation, we observe that scalar diquarks disappear from the physical spectrum and therefore are confined. For axial-vector diquarks we observe indications that the same mechanism may also work, but the NJL model allows no conclusive answer in this channel.     

Solution of a symmetry conserving chiral soliton model for nucleon and delta

The linear chiral soliton model is solved for nucleon and delta by constructing Fock states in the coherent pair approximation with correct spin and isospin properties. The quark configurations are those arising from theSU(2)×SU(2) coupling of three quarks in 1s-orbits. The overall Fock state is formed by the vector coupling of the quark configurations with the pion coherent state and thus avoids the use of the hedgehog ansatz. The sigma field is treated in the mean field approximation. Equations of motion for the quark, sigma and pion fields are solved in the static approximation. Soliton solutions are found with properties that are in reasonable agreement with those observed for the nucleon and delta including the axial vector coupling constant. With only components having zero and one unpaired pion in the coherent pair approximation the nucleon mass is found to be larger than that using the projected hedgehog approach.     

Regularization scheme dependence of vacuum observables in the Nambu-Jona-Lasinio model

We consider a bosonized version of the Nambu-Jona-Lasinio model consisting of classical scalar and pseudoscalar fields. Various regularization schemes (sharp covariant and non-covariant, proper-time and Pauli-Villars) are used in order to determine ultraviolet divergent vacuum observables such as the quark condensate 〈¯qq〉 and the current quark mass. Both quantities turn out to be very sensitive to the special choice of the scheme applied. Without further modification the proper-time and Pauli-Villars scheme appear to be unable to reproduce simultaneously the commonly used values of the quark condensate and the current quark mass.     

The Effect of Bare Quark Mass on the Pion Properties in BS Formalism Containing a Confining Term

Using the SD equation and the covariant BS equation, we investigate dynamical chiral symmetry breaking in the presence of a bare quark mass in a QCD motivated model containing a confining interaction. The bare quark mass m₀ corresponding to the physical mass of the pion and corrections to the dynamical quark mass and the pion decay constant due to mo are calculated. The results are consistent with the notion of chiral perturbatiyn and predictions of the current algebra.     

Mass splitting of the pseudoscalar and vector mesons induced by the homogeneous vacuum gluon field

Masses of the pseudoscalar and vector mesons are calculated within the generalized Nambu-Jona-Lasinio model taking into account homogeneous vacuum gluon field. This vacuum provides an analytical quark confinement. Colorless modes are determined by the confined gluons and are described by the nonlocal quark currents with appropriate radial and angular quantum numbers. An interaction of the quark spin with the vacuum gluon field arises naturally within the model under consideration. It is shown that this spin-field interaction leads to mass splitting between vector and pseudoscalar mesons with identical quark structure (ρ-π,K-K ^* and so on). This allows to use the four-fermion coupling constant being common for both nonets.