Chiral Invariant Model Research Articles

QCD string tension curve, the ferromagnetic magnetization, and the quark-antiquark confining potential at finite temperature

We study the string tension as a function of temperature, fitting the SU(3) lattice QCD finite temperature free energy potentials computed by the Bielefeld group. We compare the string tension points with order parameter curves of ferromagnets, superconductors, or string models, all related to confinement. We also compare the SU(3) string tension with the one of SU(2) lattice QCD. With the curve providing the best fit to the finite temperature string tensions, the spontaneous magnetization curve, we then show how to include finite temperature, in the state of the art confining and chiral invariant quark models.

Gluon excitations and quark chiral symmetry in the meson spectrum: An einbein solution to the large degeneracy problem of light mesons

A large approximate degeneracy of the excited hadron spectra, appears in the light meson spectra measured at LEAR, suggesting a novel principal quantum number n+j in QCD spectra. We recently showed that the large degeneracy could not be understood with state of the art confining and chiral invariant quark models, derived in a truncated Coulomb gauge. To search for a solution to this problem, here we add the gluon or string degrees of freedom. Although independently the quarks or the gluons would lead to a 2 n +j or 2 n +l spectrum, adding them may lead to the desired n+j pattern.

Microscopic 8-quark study of the antikaon-nucleon-nucleon systems

We study the possibility of binding eight quarks in a molecular hadronic system composed of two nucleons and an antikaon, with the quantum numbers of a hexaquark flavor, in particular, with strangeness $\ensuremath{-}1$, isospin $1/2$, parity -, baryonic number 2, and two possible spins, 0 or 1. We discuss the possible production of this hadron in the experiments which are presently investigating hot topics like the ${\ensuremath{\Theta}}^{+}$ pentaquark or the ${K}^{\ensuremath{-}}$ deeply bound in nuclei. The ${K}^{\ensuremath{-}}\ifmmode\bullet\else\textbullet\fi{}N$ interactions and the coupling to other channels are computed microscopically from a confining and chiral invariant quark model resulting in local plus separable Gaussian potentials. The $N\ifmmode\bullet\else\textbullet\fi{}N$ interactions used here are the state of the art Nijmegen potentials. The binding energy and the decay rate of the ${K}^{\ensuremath{-}}\ifmmode\bullet\else\textbullet\fi{}N$ and ${K}^{\ensuremath{-}}\ifmmode\bullet\else\textbullet\fi{}N\ifmmode\bullet\else\textbullet\fi{}N$ systems are computed with configuration space variational methods.

Painlevé test for integrability for a combination of Yang’s self-dual equations for SU (2) gauge fields and Charap’s equations for chiral invariant model of pion dynamics and a comparative discussion among the three

Painleve test for integrability for the combined equations generated from Yang’s self-dual equations for SU (2) gauge fields and Charap’s equations for chiral invariant model of pion dynamics faces some peculiar situations that allow none of the stages (leading order analysis, resonance calculation and checking of the existence of the requisite number of arbitrary functions) to be conclusive. It is also revealed from a comparative study with the previous results that the existence of abnormal behaviour at any of the stated stages may have a correlation with the existence of chaotic property or some other properties that do not correspond to solitonic behaviour.

Painlevé test for integrability and exact solutions for the field equations for Charap’s chiral invariant model of the pion dynamics

It has been shown that the field equations for Charap’s chiral invariant model of the pion dynamics pass the Painleve test for complete integrability in the sense of Weisset al. The truncation procedure of the same analysis leads to auto-Backlund transformation between two pairs of solutions. With the help of this transformation non-trivial exact solutions have been rediscovered

Two-scale scalar mesons in nuclei

We generalize the linear σ model in order to develop a chiral-invariant model of the nuclear structure. The model is natural, and contains not only the usual σ-meson which is the chiral partner of the pion but also a new chiral singlet that is responsible for the medium-range nucleon-nucleon attraction. This approach provides significant advantages in terms of its description of nuclear matter and finite nuclei in comparison with conventional models based on the linear σ model.

Quark distribution functions in nuclear matter

The convolution formalism is applied to calculate thedistribution function for valence quarks in the nuclearmedium. A manifestly covariant expression for the quarkdistribution function is obtained and applied to studythe case of nuclear matter. A covariant and chiralinvariant model of the nucleon is used to producenumerical results.

A combination of Yang’s equations forSU(2) gauge fields and Charap’s equations for pion dynamics with exact solutions

Two sets of nonlinear partial differential equations originating from two different physical situations have been combined and a new set of nonlinear partial differential equations has been formed wherefrom the previous two sets can be obtained as particular cases. One of the two sets of equations was obtained by Yang [1] while discussing the condition of self-duality ofSU(2) gauge fields on Euclidean four-dimensional space. The second one was reported by Charap [2] for the chiral invariant model of pion dynamics under tangential parametrization. Using the same type of ansatz in each case De and Ray [16] and Ray [7] obtained physical solutions of the two sets of equations. Here exact solutions of the combined set of equations with particular values of the coupling constants have been obtained for a similar ansatz. These solutions too are physical in nature.

Screening in supersymmetric gauge theories in two dimensions

We show that the string tension in N=1 two-dimensional super Yang-Mills theory vanishes independently of the representation of the quark anti-quark external source. We argue that this result persists in SQCD 2 and in two-dimensional gauge theories with extended supersymmetry or in chiral invariant models with at least one massless dynamical fermion. We also compute the string tension for the massive Schwinger model, as a demonstration of the method of the calculation.

Exact solutions of the field equations for Charap’s chiral invariant model of the pion dynamics

The field equations for the chiral invariant model of pion dynamics developed by Charap have been revisited. Two new types of solutions of these equations have been obtained. Each type allows infinite number of solutions. It has also been shown that the chiral invariant field equations admit invariance for a transformation of the dependent variables.

Repulsive core ofNNS-wave scattering in a quark model with a condensed vacuum

We work in a chiral invariant quark model, with a condensed vacuum, characterized by only one parameter. Bound state equations for the nucleon and {Delta} are solved in order to obtain an updated value of their radii and masses. Nucleon-nucleon S-wave scattering is studied in the resonating group method framework both for isospin T=1 and T=0. The phase shifts are calculated and an equivalent local potential, which is consistent with K-N scattering, is derived. The result is a reasonable microscopic short range repulsion in the nucleon-nucleon interaction. {copyright} {ital 1997} {ital The American Physical Society}

Investigation of a chiral model in a relativistic Hartree - Fock approximation to asymmetric nuclear matter

A relativistic HF approximation is developed for a globally chiral invariant model including mesons and the axial meson a. Some bulk properties of asymmetric nuclear matter are investigated in this framework and compared with the approximate version of the model where the axial meson is omitted and the meson is taken into account in a conventional way.

The Chiral Quark Soliton Model for the Nucleon

We study the chiral invariant quark model lagrangians under the Hartree approximation for construction of a hedgehog solution with the baryon number B=1. We take into account the Dirac sea contributions to the energy and various densities in terms of the heat-kernel method. With the parameters of the Nambu-Jona-Lasinio model lagrangian fixed by the meson properties, we do not find any B=1 hedgehog solutions except for one case, even which is, however, unstable against small perturbation. We study then the Diakonov-Petrov model lagrangian, which is introduced by investigating the properties of the quark field in the instanton background in QCD

Comments on chiral invariant and non-hermitian lattice fermion actions

Abstract Discussions are made on the structure of chiral-invariant and non-hermitian actions of lattice fermions. With the help of the Ward-Takahashi identity a general conclusion can be derived that there must be species doublers in any chiral invariant models provided that the model is well-regularized, that is, there is no singularity in the propagator after introducing a fermion mass on the lattice. A better model has been found in two dimensions in the sense that the number of species doublers is smaller than that of the naive Dirac action.

The spin content of the proton in the chiral bag

We analyze the sum-rules of the nucleon spin structure functions using a two-phase chiral invariant quark model. Due to the axial anomaly, the flavor SU (3) singlet component outside the quark confinement cavity is suppressed. This singlet is also reduced inside the cavity due to (non-strange) intermediate qqqq q states gluon exchange current corrections. Chiral symmetry requires Goldstone pions outside which generate part of the proton spin.

Integrable fermion chiral models connected with the classical Lie algebras

A chiral-invariant model of quantum field theory with four-fermion interaction andO(2k+1)-symmetry is studied. The thermodynamical equations and the equation describing the ground state of the system are derived. TheS-matrices of the fundamental fermions are calculated.

Some exact solutions of nonlinear chiral field equations

Some new exact solutions of the nonlinear field equations for the chiral invariant model of pion dynamics are presented here. These solutions are a further generalization of some previous works presented by one of the authors (Ray). It is interesting to note that equations in (3.2) obtained by Ray (1978) are conformally invariant. Hence from any solution of these equations one can immediately generate infinitely many other solutions of these equations simply by replacing (x 1, x 2) by ( y, z), where y and z are any two mutually conjugate solutions of Laplace’s equations. Further, a striking similarity in form of these equations with one of the two generalized Lund–Regge equations makes the study of the solutions of these equations more worthwhile with the view that the study of the solutions of these equations will eventually lead to the study of the solution of a larger class of equations that will include these equations and generalized Lund–Regge equations as special cases.

Canonical charge algebras for integrable fermionic theories

The non-local charges for a class of chiral invariant fermionic models as well as for the Gross-Neveu models are shown to obey a quadratic Poisson bracket algebra. Both commuting and anticommuting spinors are considered. The classical r-matrices for these models are found. The Schwinger terms in the quantum current algebra are computed.

Scale-Dependent Analysis of Phase Structures in Two- and Four-Dimensional Fermion Models

The structure of vacuum is studied in twoand four-dimensional fermion models by means of a resolution-dependent analysis which is proposed by Ezawa and Iwazaki. We first make the resolution-dependent analysis of the Gross-Neveu model based on the mean field expansion technique. Then we generalize this method to four dimensional models. As fermion models in two and four dimensions, we analyze a discrete and a continuous chiral invariant model (the Nambu-Jona-Lasinio model). In these models, we find that the discrete or the continuous symmetry breakdown occurs dynamically only at a long distance scale. The vacuum undergoes a second order phase transition in resolution R; for R Rc it is in an ordered phase. In four dimensions resolution R has a lower limit Rp-1=A (a cutoff parameter) because the four-dimensional fermion models are cutoff dependent theories.

A chiral bag model with skin

A chiral invariant bag model is defined, in which the Wigner phase region does not coincide with the confinement region. It reconciles the two existing bag model philosophies.