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We explore the features of the UA(1) and chiral symmetry breaking of the Nambu–Jona-Lasinio model without the Kobayashi–Maskawa–'t Hooft determinant term in the presence of a parallel electromagnetic field. We show that the electromagnetic chiral anomaly can induce both finite neutral pion condensate and isospin-singlet pseudo-scalar η condensate and thus modifies the chiral symmetry breaking pattern. In order to characterize the strength of the UA(1) symmetry breaking, we evaluate the susceptibility associated with the UA(1) charge. The result shows that the susceptibility contributed from the chiral anomaly is consistent with the behavior of the corresponding η condensate. The spectra of the mesonic excitations are also studied.

In this study, we investigate the Nambu--Jona-Lasinio (NJL) model at finite temperature and finite density in an external magnetic field using the functional renormalization group. We investigate the dependence of the position of the ultraviolet fixed point (UVFP) of the four-Fermi coupling constant on the temperature, density, and external magnetic field, and we obtain the chiral phase structure. The UVFP at low temperature and finite chemical potential oscillates in a small external magnetic field, which can be interpreted as the de Haas--van Alphen effect. We also obtain phase diagrams with complex structures, where the phase boundary moves back and forth as the external magnetic field increases in the low temperature and high density region., Comment: 6 pages, 6 figures, published version

We discuss a minimal holographic model for the description of heavy-light and light mesons with chiral symmetry, defined in a slab of AdS space. The model consists of a pair of chiral Yang-Mills and tachyon fields with specific boundary conditions that break spontaneously chiral symmetry in the infrared. The heavy-light spectrum and decay constants are evaluated explicitly. In the heavy mass limit the model exhibits both heavy-quark and chiral symmetry and allows for the explicit derivation of the one-pion axial couplings to the heavy-light mesons., Comment: 9 pages

The pseudoscalar projection of the pion's Poincare'-covariant Bethe-Salpeter amplitude onto the light-front may be understood to provide the probability distribution of the chiral condensate within the pion. Unlike the parton distribution amplitudes usually considered and as befitting a collective effect, this condensate distribution receives contributions from all Fock space components of the pion's light-front wave-function. We compute this condensate distribution using the Dyson-Schwinger equation (DSE) framework and show the result to be a model-independent feature of quantum chromodynamics (QCD). Our analysis establishes that this condensate is concentrated in the neighbourhood of the boundaries of the distribution's domain of support. It thereby confirms the dominant role played by many-particle Fock states within the pion's light-front wave function in generating the chiral condensate on the light-front and verifies that light-front longitudinal zero modes do not play a material role in that process., Comment: 5 pages, 1 figure. To appear in Phys. Lett. B

The NJL model for the octet baryons, using proper time regularization to simulate some of the features of confinement, is solved self-consistently in nuclear matter. This provides an alternative framework to the MIT bag model which has been used in the quark-meson coupling model. After fitting the parameters of the model to the saturation properties of symmetric nuclear matter the model is used to explore the equation of state of pure neutron matter as well as nuclear matter at densities relevant to heavy ion collisions. With a view to future studies of high mass neutron stars, the binding of hyperons is also explored., 7 pages and 4 figures

Recently, it was found in QED that the generation of a dynamical electron mass in a strong magnetic field is significantly enhanced by the perturbative electron mass. In the present paper, the related question of a possible enhancement of the dynamical quark mass in an external magnetic field and with a bare mass term is investigated in the Nambu--Jona-Lasinio model., 4 pages; Revtex4; new references added; version accepted for publication in Phys. Lett. B

The critical endpoint (CEP) and the phase structure are studied in the Polyakov-loop extended Nambu--Jona-Lasinio model in which the scalar type eight-quark (\sigma^4) interaction and the vector type four-quark interaction are newly added. The \sigma^4 interaction largely shifts the CEP toward higher temperature and lower chemical potential, while the vector type interaction does oppositely. At zero chemical potential, the \sigma^4 interaction moves the pseudo-critical temperature of the chiral phase transition to the vicinity of that of the deconfinement phase transition., Comment: 13 pages, 6 figures embedded, accepted for publication in Phys. Lett. B

We study the chiral phase transition at finite temperature T and baryonic chemical potential μ B within the framework of the SU(3) Nambu–Jona-Lasinio (NJL) model. The QCD critical end point (CEP) and the critical line at finite T and μ B are investigated: the study of physical quantities, such as the baryon number susceptibility and the specific heat in the vicinity the CEP, will provide relevant information concerning the order of the phase transition. The class of the CEP is determined by calculating the critical exponents of those quantities.

We study the phase diagram of the strongly interacting matter at finite temperatures and densities including 2SC, uniform chiral and non-uniform chiral phases within the Nambu - Jona-Lasinio model in the mean field approximation., Comment: 11 pages, 4 figures, to appear in Phys. Lett. B

We present results of numerical simulations of the 2+1d Nambu -- Jona-Lasinio model with non-zero baryon chemical potential mu and spatially-varying complex diquark source strength j. By choosing arg(j) to vary smoothly through 2 pi across the spatial extent of the lattice, a baryon number current is induced which in the high density phase remains non-vanishing as |j|->0; we are hence able to extract a quantity characteristic of a superfluid known as the helicity modulus. We also study supercurrent flow at non-zero temperature and estimate the critical temperature at which the normal phase is restored, which is consistent with the conventional picture for thin-film superfluids in which the transition is viewed in terms of vortex -- anti-vortex unbinding., 10 pages, 5 figures

We study the stability of the highest symmetric solution (Wigner-solution) of Dyson-Schwinger equations in chiral limit and at zero temperature. Our results confirm that if the chemical potential is not very large, the QCD vacuum is in the chiral symmetry breaking phase and the quantum phase-transition of the chiral symmetry restoration is in first order. Meanwhile it seems that there is not competition between chiral symmetry breaking phase and color superconductivity phase since the color superconductivity phase appears only if the chemical potential is very large. Moreover, we propose that chiral symmetry breaking arises from the positive feedback with respect to the mass perturbation., 12 pages, 6 figures

Based on the Hawking-Unruh thermalization theorem, we investigate the phenomenon of the dynamical chiral symmetry breaking and its restoration for a uniformly accelerated observer. We employ the Nambu$-$Jona-Lasinio model in Rindler coordinates, and calculate the effective potential and the gap equation. The critical coupling and the critical acceleration for symmetry restoration are obtained., 7 pages. Phys. Lett. B (2004), in press

We investigate the renormalization group flow of the Yukawa model with a fixed momentum cutoff at the leading order in 1/N, where N is the number of the fermion species. We demonstrate the scale invariance of coupling constants of the Nambu-Jona-Lasinio model., 11 pages, 4 figures

Non-perturbative proof is presented of a generalized version of Goldstone theorem, where the Lagrangian conserves an approximate SU(3) chiral symmetry, that both quark masses and electromagnetism make contributions to the masses of spinless particles of pseudoscalar octet. We show that apart from what comes in the form of some projections of a two-body Bethe–Salpeter amplitude for which the photon lines like the gluon ones are all internal in the case of neutral pseudo-Goldstone bosons, the charged pseudoscalar mesons receive additional contributions that may be expressed in terms of the axial–vectorial projection of a three-body Bethe–Salpeter amplitude with an extra external photon line. Keywords: Spontaneously broken approximate chiral symmetry, Pseudo-Goldstone bosons, Pseudoscalar meson masses, Electromagnetic corrections, Non-perturbative methods

We estimate the slope of the topological susceptibility in the three flavour Nambu-Jona-Lasinio model with the 't Hooft interaction. The results are consistent with the evaluation from the QCD sum rule in favour of the full topological susceptibility. We apply it to the Shore-Veneziano formula to find that it shows satisfactory agreement with the anomalous suppression of the flavour-singlet axial charge. The behaviour at finite temperature is also discussed., Comment: 8 pages, 3 figures, submitted to Phys. Lett. B

We show that, as a consequence of fixing f_\pi = 93 MeV: (1) a bound state pole in the J^P = 1^- scattering amplitude of the ENJL model exists for arbitrarily weak (positive) vector coupling G_2 so long as the constituent quark mass is sufficiently large; (2) there is a bound state for any quark mass when G_2 \geq 0.6/(8 f_\pi^2); (3) this bound state becomes massless at G_2 = 1/(8 f_\pi^2) and a tachyon for G_2 exceeding it. We show by way of an example that the model has no trouble fitting the \rho meson mass simultaneously with other observables., Comment: 9 pages, 2 (eps) figures, to appear in PLB

In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking $Z_4 \to Z_2$ caused by gaugino condensation., latex, 12 pages, 1 figure with epsfig

A new formula for the composite Higgs boson mass is given, based on the Ward-Takahashi identity and the Schwinger-Dyson(SD) equation. In this formula the dominant asymptotic solution of the SD equation yields a correct answer, in sharp contrast to the Partially Conserved Dilatation Current(PCDC) approach where the sub- and sub-sub-dominant solutions should be taken into account carefully. In the gauged Nambu-Jona-Lasinio model we find M_H \simeq \sqrt{2}M for the composite Higgs boson mass M_H and the dynamical mass of the fermion M in the case of the constant gauge coupling(with large cut off), which is consistent with the PCDC approach and the renormalization-group approach. As to the case of the running gauge coupling, we find M_H \simeq 2 \sqrt{(A-1)/(2A-1)}M, where A \equiv 18 C_2 /(11N_c - 2N_f) with C_2 being the quadratic Casimir of the fermion representation. We also discuss a straightforward application of our formula to QCD(without 4-Fermi coupling), which yields M_{\sigma} \sim \sqrt{2}M_{dyn}, with M_{\sigma} and M_{dyn} being the light scalar(``\sigma-meson'') mass and mass of the constituent quark, respectively., Comment: LaTeX file, 10 pages and 2 eps figures, application to QCD is described in detail

Dynamical chiral symmetry breaking (D$\chi$SB) is studied in the Nambu-Jona-Lasinio model for an arbitrary combination of external constant electric and magnetic fields. In 3+1 dimensions it is shown that the critical coupling constant increases with increasing of the value of the second invariant of electromagentic field $\vec{E}\cdot\vec{B}$, i.e. the second invariant inhibits $D\chi SB$. The case of 2+1 dimensions is simpler because there is only one Lorentz invariant of electromagnetic field and any combination of constant fields can be reduced to cases either purely magnetic or purely electric field., Comment: final version which will appear in Physics Letters B, we show that the second invariant of electromagnetic field inhibits D$\chi$SB. 11 pages. LaTeX. 2 figures included

We propose a model of monopoles where a condensate of monopole-antimonopole pairs leads to confinement. We investigate the condensation of these monopole-antimonopole pairs around a dual Dirac string.

We study the spontaneous chiral symmetry breaking in discretized light-cone field theory using the Gross-Neveu model. With the help of the 1 N expansion, zero mode of the field operator is obtained nonperturbatively by solving the constraint relation involving the zero mode. The zero mode has c-number part at the lowest order, by which the discrete chiral symmetry is broken. Renormalization is done by use of the constraint relation of the zero mode, and we get explicitly the operator part of the zero mode which is O (1 N) .

The effective dimensional reduction of fermion-antifermion pairing dinamics in Nambu-Jona-Lasinio model in external chromomagnetic field is considered. It is shown that such a field causes the reduction of the space dimension by one unit in contrast to an ordinary magnetic field which reduces it by two units. The enhancement of the dynamical chiral symmetry breaking due to the reduction is discussed., Comment: 8 pages, LaTeX, no figures

We suggest a relativistic field theory model of the deuteron. We start from a local unphysical deuteron field, taken as a bound proton-neutron state at zero binding energy. Following the Nambu-Jona-Lasinio prescription we construct the physical deuteron field. We describe all parameters of the physical deuteron in the one-nucleon loop approximation and in leading order of the long-wavelength expansion. The one-pion exchange contribution to the binding energy calculated in the two-nucleon loop approximation is found small compared with that obtained in the one-nucleon loop one. The present model can be applied to the description of the decouplet of dibaryons 10 f where the deuteron is the component with Y = 2 and I = 0.

We study quantum electrodynamics in an external field of gaussian configuration varying in all four dimensions and find that for certain ranges of the widths there is a non-zero value for 〈 Ψ Ψ〉 ext . This indication of chiral symmetry breaking in QED via a varying external field configuration which is quite similar to those in the GSI experiments, provides further evidence that the peaks seen in those experiments may be explained by a “new” phase of QED.

The quark condensate is extracted from the singular (monopole-dominated) and the regular (photon-dominated) parts of a maximal abelian field in SU(2) lattice gauge theory at finite temperature. The results obtained give support to the possibility that monopole condensation can describe both chiral symmetry breaking and confinement.

We provide a compact approximation for the electron propagator in a strong magnetic field of the form B x = B y =0, B z = B z ( y ). The method developed in this work can be used to discuss some non-perturbative aspects of QED. As a simple application we consider the Nambu-Jona-Lasinio model minimally coupled to an external space-dependent magnetic field. As in the uniform case, the associated gap equation admits non-trivial solutions corresponding to a massive phase.

The off--shell electromagnetic vertex function of pions and kaons is studied in a bosonized Nambu--Jona-Lasinio model with a gauge--invariant proper--time cutoff. The slope of the pion form factor with respect to the pion 4--momentum is found to be equal to the on--shell pion charge radius in the chiral limit. The off--shell slope of the $K^0$ form factor is zero, that of the $K^\pm$ about 15\% smaller than that of the pion. We compare our results with those of a recent calculation in chiral perturbation theory., Comment: (9 p., standard LaTeX, 1 PostScript figure appended) UNITUE-THEP-7/94

We study the lattice \njl~model with two flavors of Wilson fermions in the large $N$ limit, where $N$ is the number of `colors'. For large values of the four-fermion coupling we find a phase in which both, flavor symmetry and parity, are spontaneously broken. In accordance with general expectations there are three massless pions on the phase boundary, but only two of them remain massless inside the broken phase. This is analogous to earlier results obtained in lattice QCD, indicating that this behavior is a very general feature of the Wilson term., Comment: 7 pages, 4 figures, LATEX, tared and uuencoded

In an effort to investigate some of the low energy properties of QCD, in particular those related to chiral symmetry breaking, as well as to obtain insights on the behavior of an interacting theory of fermions on the lattice, the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral symmetry is studied on the four--dimensional hypercubic lattice using large $N$ techniques and numerical simulations. Naive and Wilson fermions are considered and transparent results are obtained regarding the following: the scalar and pseudoscalar spectrum, the approach to the continuum and chiral limits, the size of the $1/N$ corrections, and the effects of the zero momentum fermionic modes on finite lattices. Also, some interesting observations are made by viewing the model as an embedding theory of the Higgs sector. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called NJL.ps (to get it type: get NJL.ps), 10 pages, LaTex file. FSU-SCRI-93-127

A toy model based on a πN multiple scattering approach consistent with most chiral properties in the nuclear medium is shown to depend crucially on the short-range correlations. Within the model the average σ-term is unrenormalized, as is the pion mass. The average quark condensate can also be made to vanish without restoration of chiral symmetry. The common statement that it is sufficient for restoration that the condensate vanishes is therefore manifestly non-trivial and it requires proof.

I study the chiral corrections to the O(p2) prediction of Chiral Perturbation Theory BK ⋍ 0.29. I point out that neglecting non-factorizable chiral corrections one obtains BK ⋍ 0.61; this result takes into account factorizable chiral corrections to all orders in the chiral expansion. Non-factorizable O(p4) chiral corrections are computed within the framework of the mean field approximation of the extended Nambu-Jona-Lasinio Model and appear to be negative. I find BK = 0.38−0.02+0.10.

We examine $O(1/\Ne)$ rotational corrections to axial couplings \gt~ and \go~ in the framework of the semibosonized SU(3) Nambu--Jona-Lasinio model. A novelty is due to the observation that the rotational (cranking) velocity and the rotation matrix itself do not commute within semiclassical quantization scheme. If time ordering in the quark loop is maintained new contributions, which have no analogue in the Skyrme model, appear. They substantially improve numerical results for the axial couplings which without the present corrections are badly underestimated., Comment: RUP-TPII-54/93, in LaTeX, 6pages, no figures, in revised version two references have been updated

A relativistic hadronic model that provides a realization of the broken chiral and scale invariance of quantum chromodynamics has recently been applied to nuclear matter at the mean-field level. Although the model can reproduce nuclear matter saturation, calculations of finite nuclei reveal serious deficiencies.

The extended SU(3) Nambu and Jona-Lasinio model is considered in the context of Chiral Perturbation Theory and in the anomalous sector. Vector, axial and scalar degrees of freedom are integrated out explicitly up to fourth order in the chiral expansion for field configurations with trivial topology. It is found that the anomalous structure of QCD is only reproduced if vector and axial couplings vanish. The result is illustrated for some particular processes.