Heavy mesons in the Nambu-Jona-Lasinio model

We propose an extended Nambu-Jona-Lasinio model to include heavy mesons with heavy quark symmetry.The quark current-current interaction is generalized to include the heavy quark currents. In order to comply with the heavy quark spin symmetry at the heavy quark limit,the dependence of the quark mass on the interaction strength is introduced. The light and heavy pseudo-scalar and vector mesons,their masses and the weak decay constants are calculated in the unified frame.     

Nonstandard magnetic oscillations in the Nambu-Jona-Lasinio model

The Nambu-Jona-Lasinio model at nonzero values of an external magnetic field H and of the chemical potential is considered in the strong-coupling region G>G _c. The phase portrait of the model exhibits an infinitely large number of massless chiral-invariant phases and massive phases resulting from a spontaneous breakdown of chiral invariance. This phase structure is responsible for aperiodic oscillations of some thermodynamic parameters of the system, including the dynamical fermion mass, as functions of H ^?1.     

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.     

Diquarks in nucleons

Under the assumption that a scalar diquark coexists in part of the time with a single quark within a nucleon, which is favored to describe the higher twist effects of both γ and ν induced nucleon structure functions consistently, we consider how its presence affects nucleon properties. It is shown that the sum rule and the magnetic moment constrain its contribution strongly and the asymmetry is quite sensitive to it. In particular, theR=σ _L /σ _T ratio can be explained in terms of the large transverse momentum of the diquark which arises from the consideration on the neutron charge radius value.     

Strange-quark matter within the Nambu-Jona-Lasinio model

The equation of state of baryon-rich quark matter is studied within the SU(3) Nambu-Jona-Lasinio model with flavor-mixing interaction. Possible bound states (strangelets) and chiral phase transitions in this matter are investigated at various values of the strangeness fraction r _s. Model predictions are very sensitive to the ratio of the vector and scalar coupling constants, ξ=G _V/G _S. At ξ=0.5 and zero temperature, the binding energy takes a maximum value of about 15 MeV per baryon at r _s?0.4. Such strangelets are negatively charged and have typical lifetimes of about 10^?7s. Calculations are performed at finite temperatures as well. According to these calculations, bound states exist up to temperatures of about 15 MeV. The model predicts a first-order chiral phase transition at finite baryon densities. The parameters of this phase transition are calculated as functions of r _s.     

The axial form factor in the Nambu-Jona-Lasinio model

We give a general expression for the expectation value of the axial vector currentA _µ ^a in a system with baryon numberB=1, which arises as solution of theSU(2)—flavour Nambu-Jona-Lasinio model in the fermion-1-loop approximation. States with good spin and isospin quantum numbers are constructed by using the lowest order cranking approximation. Taking the self consistent solutions for such a system we calculate the axial form factorg _A(q ²) and the axial coupling constantg _A . The results can be checked by comparing the value of g_A with the one obtained from the radial integral or the asymptotic tail of the self consistent pion field by means of the PCAC relation.     

Terent'ev low-energy theorem in the Extended Nambu-Jona-Lasinio model

The low-energy theorem, derived by Terent'ev within the framework of current algebra, is proved at the quark level within the framework of the Extended Nambu-Jona-Lasinio model.One of the authors (A.N.I.) is pleased to thank Dr. A. Nogová and Dr. J. Boháik for a very kind hospitality during the stay at the Institute of Physics in Bratislava, where this work was finished.     

Chiral symmetry and supersymmetry in the Nambu-Jona-Lasinio model

The connection between chiral symmetry and supersymmetry is investigated in the context of a supersymmetric extension of the Nambu-Jona-Lasinio model. A supersymmetric gap equation is found and it is shown that no solution exists which breaks chiral symmetry. A simple physical argument for this phenomenon is given and possible implications for the dynamics of composite models are discussed.     

Crust-core properties of neutron stars in the Nambu–Jona-Lasinio model

We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the slope of the symmetry energy gives rise to an increase in the crust-core transition density and transition pressure.Given the slope of the symmetry energy at saturation density, the transition density and corresponding transition pressure increase with increasing symmetry energy. The increasing trend between the fraction of the crustal moment of inertia and the slope of symmetry energy at saturation density indicates that a relatively large momentum cutoff of the NJL model is preferred. For a momentum cutoff of 500 Me V, the fraction of the crustal moment of inertia clearly increases with the slope of symmetry energy at saturation density. Thus, at the required fraction(7%) of the crustal moment of inertia, the NJL model with momentum cutoff of 500 Me V and a large slope of the symmetry energy of saturation density can give the upper limit of the mass of the Vela pulsar to be above 1.40 M_⊙.