Nonlocal NJL Model Research Articles

Bayesian analysis of multimessenger M-R data with interpolated hybrid EoS

We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a set of stiff quark matter EoS at high densities within a finite region of chemical potentials mu _H< mu < mu _Q. Fixing the hadronic EoS as the APR one and choosing the color-superconducting, nonlocal NJL model with two free parameters for the quark phase, we perform Bayesian analyses with this two-parameter family of hybrid EoS. Using three different sets of observational constraints that include the mass of PSR J0740+6620, the tidal deformability for GW170817, and the mass-radius relation for PSR J0030+0451 from NICER as obligatory (set 1), while set 2 uses the possible upper limit on the maximum mass from GW170817 as an additional constraint and set 3 instead of the possibility that the lighter object in the asymmetric binary merger GW190814 is a neutron star. We confirm that in any case, the quark matter phase has to be color superconducting with the dimensionless diquark coupling approximately fulfilling the Fierz relation eta _D=0.75 and the most probable solutions exhibiting a proportionality between eta _D and eta _V, the coupling of the repulsive vector interaction that is required for a sufficiently large maximum mass. We used the Bayesian analysis to investigate with the method of fictitious measurements the consequences of anticipating different radii for the massive 2~M_odot PSR J0740+6220 for the most likely equation of state. With the actual outcome of the NICER radius measurement on PSR J0740+6220 we could conclude that for the most likely hybrid star EoS would not support a maximum mass as large as 2.5~M_odot so that the event GW190814 was a binary black hole merger.

Critical end point in a thermomagnetic nonlocal NJL model

In this paper, we explore the critical end point in the [Formula: see text] phase diagram of a thermomagnetic nonlocal Nambu–Jona-Lasinio model in the weak field limit. We work with the Gaussian regulator, and find that a crossover takes place at [Formula: see text], [Formula: see text]. The crossover turns to a first-order phase transition as the chemical potential or the magnetic field increases. The critical end point of the phase diagram occurs at a higher temperature and lower chemical potential as the magnetic field increases. This result is in accordance to similar findings in other effective models. We also find that there is a critical magnetic field, for which a first-order phase transition takes place even at [Formula: see text].

η−γ and η′−γ transition form factors in a nonlocal NJL model

We study the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ distribution amplitudes (DAs) in the context of a nonlocal ${\mathrm{SU}(3)}_{L}\ensuremath{\bigotimes}{\mathrm{SU}(3)}_{R}$ chiral quark model. The corresponding Lagrangian allows us to reproduce the phenomenological values of pseudoscalar meson masses and decay constants, as well as the momentum dependence of the quark propagator arising from lattice calculations. It is found that the obtained DAs have two symmetric maxima, which arise from new contributions generated by the nonlocal character of the interactions. These DAs are then applied to the calculation of the $\ensuremath{\eta}\text{\ensuremath{-}}\ensuremath{\gamma}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\text{\ensuremath{-}}\ensuremath{\gamma}$ transition form factors. Implications of our results regarding higher twist corrections and/or contributions to the transition form factors originated by gluon-gluon components in the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons are discussed.

Thermo-magnetic nonlocal NJL model in the real and imaginary time formalisms

In this paper, we study a nonlocal Nambu–Jona-Lasinio (nNJL) model with a Gaussian regulator in presence of a uniform magnetic field. We take a mixed approach to the incorporation of temperature in the model, and consider aspects of both real and imaginary time formalisms. We include confinement in the model through the quasiparticle interpretation of the poles of the propagator. By working in the real time formalism and computing the spectral density function, we find that the effect of the magnetic field on the poles of the propagator can be entirely absorbed within the mean field value of the scalar field. The analytic structure of our propagator is then preserved in the weak magnetic field limit. The effect of the magnetic field in the deconfinement phase transition is then studied. It is found that, like with chiral symmetry restoration, magnetic catalysis occurs for the deconfinement phase transition. It is also found that the magnetic field enhances the thermodynamical instability of the system. We work in the weak field limit, i.e. [Formula: see text]. At this level there is no splitting of the critical temperatures for chiral and deconfinement phase transitions.

Quark-hadron Phase Transition in Proto-Neutron Stars Cores Based on a Non-local NJL Model

We study the QCD phase diagram using a non-local SU(3) NJL model with vector interactions among quarks. We analyze several thermodynamic quantities such as entropy and specific heat, and study the influence of vector interactions on the thermodynamic properties of quark matter. Upon imposing electric charge neutrality and baryon number conservation on the field equations, we compute models for the equation of state of the inner cores of proto-neutron stars by providing a non-local treatment of quark matter for astrophysics.

Pion light cone wave function in the nonlocal NJL model

We use the simple instanton motivated NJL-type model to calculate the leading twist pion light cone wave function. The model consists in employing the momentum dependent quark mass in the quark loop entering the definition of the wave function. The result is analytical up to a solution of a certain algebraic equation. Various properties including the ${k}_{T}$ dependence of the pion wave function are discussed. The resulting ${k}_{T}$ integrated wave function is not asymptotic and is in agreement with recent analysis of the CLEO data.

Chiral phase transition in a covariant nonlocal NJL model

The properties of the chiral phase transition at finite temperature and chemical potential are investigated within a nonlocal covariant extension of the Nambu–Jona-Lasinio model based on a separable quark–quark interaction. We consider both the situation in which the Minkowski quark propagator has poles at real energies and the case where only complex poles appear. In the literature, the latter has been proposed as a realization of confinement. In both cases, the behaviour of the physical quantities as functions of T and μ is found to be quite similar. In particular, for low values of T the chiral transition is always of first order and, for finite quark masses, at certain “end point” the transition turns into a smooth crossover. In the chiral limit, this “end point” becomes a “tricritical” point. Our predictions for the position of these points are similar, although somewhat smaller, than previous estimates. Finally, the relation between the deconfining transition and chiral restoration is also discussed.

Meson properties in an extended non-local NJL model

We consider a non-local version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The non-locality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes γγ* → π0 and ω → π0γ*. The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.