Nonlocal Nambu Jona-Lasinio Model Research Articles

Fulfilling modern astrophysical observations and lattice QCD constraints based on a nonlocal NJL model with 3D form factor

AbstractIn the present work, we employ a nonlocal Nambu–Jona–Lasinio (NJL) model with a Gaussian form factor that is dependent on the spatial components of the momentum (3D‐FF). Focusing on the temperature‐baryon chemical potential plane, we investigate some aspects of the phase diagram. Initially, we propose an assumption that the range of interactions in momentum space may be modified by temperature, allowing us to obtain the critical temperature values based on lattice QCD (LQCD) predictions. Subsequently, we consider this model within a hybrid framework to examine the effects of temperature, together with neutrino trapping, in compact object configurations.

The role of U(1) A symmetry breaking in the QCD corrections to the pion mass difference

The charged and neutral pion mass difference can be attributed to both the quantum electrodynamics and QCD contributions. The current quark mass difference (Δm) is the source of the QCD contribution. Here, in a two-flavour non-local Nambu–Jona-Lasinio model, we try to estimate the QCD contribution. Interestingly, we find that the strength of the symmetry-breaking parameter c plays a crucial role in obtaining the pion mass difference while intertwined with the current quark mass difference. To obtain the QCD contribution for the pion mass difference, we scan the parameter space in {Δm, c}, and by comparing this with the existing results, we constrained the parameter space. Further, using a fitted value of c, we determine the allowed range for the Δm in the model. The model estimated Δm ranges enable us to extract the chiral perturbation theory low energy constant, l 7 and verify the dependence of the pion mass difference on Δm. We also find out its dependence on c—it increases with the decreasing value of c, i.e. toward an axial anomaly restored phase.

Hybrid neutron stars with the Thomas-Fermi approximation and nonlocal Nambu–Jona-Lasinio model

We probe the outcomes of the baryon-quark phase transition in the hybrid neutron star (HNS) structure with the help of the Gibbs and Maxwell constructions, adopting a semiclassical mean-field (MF) model for the equation of state (EOS) of baryonic matter based on the Thomas-Fermi (TF) approximation and a nonlocal extension of the Nambu--Jona-Lasinio (NJL) model for the EOS of the deconfined quark phase. We find that the repulsive vector contribution of the nonlocal NJL (NNJL) EOS plays an inevitable role in modeling a stable $2{M}_{\ensuremath{\bigodot}}$ HNS. Our results exclude the emergence of the pure quark phase in the inner core of a stable HNS. Within the Gibbs construction, as the quark vector interaction becomes stronger, the contribution of the baryon-quark coexisting phase in the total HNS mass is reduced. On the other hand, a stable HNS is not predicted within the Maxwell construction because it does not include a pure quark core. A comparison is made to the corresponding results employing the local (standard) NJL (LNJL) model of quark matter. Fulfilling the observational constraints, our model indicates that a neutron star (NS) with canonical mass of around $1.4{M}_{\ensuremath{\bigodot}}$ is not massive enough to be described as an HNS.

Mixed phase transition from hypernuclear matter to deconfined quark matter fulfilling mass-radius constraints of neutron stars

A recent solution of the hyperon puzzle by a first order phase transition to color superconducting quark matter is revisited in order to replace the Maxwell construction by an interpolation method which describes a mixed phase. To do this, we apply for the first time the finite-range polynomial interpolation method for constructing a transition between hadronic and quark matter phases to the situation that is characterized in the literature as the reconfinement problem. For the description of the hadronic phase the lowest order constrained variational method is used while for the quark phase the nonlocal Nambu–Jona–Lasinio model with constant and with density-dependent parameters is employed. Applying the replacement interpolation method to both quark matter models results in a hybrid equation of state that allows a coexistence of nuclear matter, hypernuclear matter and quark matter in a mixed phase between the pure hadronic and quark phases which can also be realized in the structure of the corresponding hybrid star sequences. The predicted hybrid stars fulfill the constraints on the mass-radius relation for neutron stars obtained from recent observations.

Nonlocal Nambu\u2013Jona-Lasinio model and chiral chemical potential

We derive the critical temperature in a nonlocal Nambu–Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the gluon propagator in Yang–Mills theory and has the property to fit in excellent way the form factor arising from the instanton liquid picture for the vacuum of the theory. Nambu–Jona-Lasinio model is derived form quantum chromodynamics providing all the constants of the theory without any need for fits. We show that the critical temperature in this case always exists and increases as the square of the chiral chemical potential. The expression we obtain for the critical temperature depends on the mass gap that naturally arises from Yang–Mills theory at low-energy as also confirmed by lattice computations.

Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu–Jona-Lasinio model

We study the dynamics of inhomogeneous scalar and pseudoscalar chiral order parameters within the framework of the time-dependent Ginzburg-Landau equations. We utilize a nonlocal chiral quark model to obtain the phase diagram of the model as function of temperature and baryon chemical potential and study the formation of metastable spatial domains of matter where the order parameters acquire a spatial modulation in the course their dynamical evolution. We found that, before reaching the expected equilibrium homogeneous state, both scalar and pseudoscalar chiral condensates go through long-lived metastable inhomogeneous structures. For different initial configurations of the order parameters, the lifetimes of the inhomogeneous structures are compared to timescales in a relativistic heavy-ion collision.

Dynamics of inhomogeneous chiral condensates

We study the dynamics of the formation of inhomogeneous chirally broken phases in the final stages of a heavy-ion collision, with particular interest on the time scales involved in the formation process. The study is conducted within the framework of a Ginzburg-Landau time evolution, driven by a free energy functional motivated by the Nambu–Jona-Lasinio model. Expansion of the medium is modeled by one-dimensional Bjorken flow and its effect on the formation of inhomogeneous condensates is investigated. We also use a free energy functional from a nonlocal Nambu–Jona-Lasinio model which predicts metastable phases that lead to long-lived inhomogeneous condensates before reaching an equilibrium phase with homogeneous condensates.

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].

Strongly interacting matter under external magnetic fields within nonlocal NJL-type models

We study the behavior of strongly interacting matter under an external magnetic field in the context of nonlocal Nambu–Jona-Lasinio (NJL) -like models. We find that at zero temperature the condensates display the well-known Magnetic Catalysis effect, showing a good quantitative agreement with lattice QCD (LQCD) results. Moreover, when extended to finite temperature we find that (contrary to what happens in the local NJL model) the Inverse Magnetic Catalysis (IMC) effect is naturally incorporated. We also analyze the magnetic susceptibility of the QCD vacuum in the limit of small magnetic field, considering two different model parametrizations, and compare our numerical results to those obtained in other theoretical approaches and in LQCD calculations.

Critical temperature of chiral symmetry restoration for quark matter with a chiral chemical potential

In this article we study the restoration of chiral symmetry at a finite temperature for quark matter with a chiral chemical potential, , by means of a nonlocal Nambu–Jona–Lasinio model. This model allows the introduction of, in the simplest way possible, a Euclidean momentum, pE, dependent quark mass function which decays (neglecting logarithms) as for large pE, in agreement with the asymptotic behaviour expected in quantum chromodynamics in the presence of a nonperturbative quark condensate. We focus on the critical temperature for chiral symmetry restoration in the chiral limit, Tc, versus , as well as on the order of the phase transition. We find that Tc increases with , and that the transition remains of the second order for the whole range of considered.

Thermal evolution of hybrid stars within the framework of a nonlocal Nambu–Jona-Lasinio model

We study the thermal evolution of neutron stars containing deconfined quark matter in their core. Such objects are generally referred to as quark-hybrid stars. The confined hadronic matter in their core is described in the framework of non-linear relativistic nuclear field theory. For the quark phase we use a non-local extension of the SU(3) Nambu Jona-Lasinio model with vector interactions. The Gibbs condition is used to model phase equilibrium between confined hadronic matter and deconfined quark matter. Our study indicates that high-mass neutron stars may contain between 35 and 40 % deconfined quark-hybrid matter in their cores. Neutron stars with canonical masses of around $1.4\, M_\odot$ would not contain deconfined quark matter. The central proton fractions of the stars are found to be high, enabling them to cool rapidly. Very good agreement with the temperature evolution established for the neutron star in Cassiopeia A (Cas A) is obtained for one of our models (based on the popular NL3 nuclear parametrization), if the protons in the core of our stellar models are strongly paired, the repulsion among the quarks is mildly repulsive, and the mass of Cas A has a canonical value of $1.4\, M_\odot$.

Weak magnetic field effects on chiral critical temperature in a nonlocal Nambu–Jona-Lasinio model

In this paper we study the nonlocal Nambu–Jona-Lasinio model with a Gaussian regulator in the chiral limit. Finite temperature effects and the presence of a homogeneous magnetic field are considered. The magnetic evolution of the critical temperature for chiral symmetry restoration is then obtained. Here, we restrict ourselves to the case of low magnetic field values, being this a complementary discussion to the existing analysis in nonlocal models in the strong magnetic field regime.

Unstable quasiparticles as a source of thermodynamic instabilities in the thermal nonlocal Nambu—Jona-Lasinio model

It has already been shown that in thermal nonlocal Nambu---Jona-Lasinio models some unphysical behavior, such as a negative pressure, may arise. In this paper, it is shown how this behavior can be related to the presence of highly unstable poles of the propagator of the model, for both the Gaussian and Lorentzian regulator cases. Computations are carried out within the real time formalism, which allows us to isolate the contributions from different poles and identify the source of these instabilities. It has also been shown in recent papers how these instabilities are softened by the inclusion of the Polyakov loop when a Gaussian regulator is considered. This paper shows how the softening of instabilities can be understood by studying the effect of the Polyakov loop on the poles of the propagator for the Gaussian regulator.

Chiral symmetry breaking from two-loop effective potential of the holographic non-local NJL model

We calculate the two-loop effective potential of the non-local Nambu–Jona–Lasinio (NJL) model derived from the Sakai–Sugimoto model in string theory. In contrast to the conventional NJL with 4-fermion contact interaction, the chiral symmetry was previously found to be dynamically broken for an arbitrary weak coupling at the one-loop level. As a confirmation, the approximate numerical solutions to the gap equation at the one-loop level are explicitly demonstrated for weak couplings. We then calculate the one- and two-loop contributions to the effective potential of the non-local NJL model and found that the two-loop contribution is negative. The two-loop potential for the chiral-symmetric vacuum is also negative but larger than the combined effective potential of the chiral broken vacuum at the two-loop level. The chiral symmetry breaking thus persists for the arbitrary weak coupling at the two-loop level.

Quark deconfinement in high-mass neutron stars

In this paper, we explore whether or not quark deconfinement may occur in high-mass neutron stars such as J1614 \ensuremath{-} 2230 ($1.97\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.16em}{0ex}}{M}_{\ensuremath{\bigodot}}$) and J0348 + 0432 ($2.01\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.16em}{0ex}}{M}_{\ensuremath{\bigodot}}$). Our study is based on a nonlocal extension of the SU(3) Nambu--Jona-Lasinio (n3NJL) model with repulsive vector interactions among the quarks. This model goes beyond the frequently used local version of the Nambu--Jona-Lasinio (NJL) model by accounting for several key features of QCD which are not part of the local model. Confined hadronic matter is treated in the framework of nonlinear relativistic mean field theory. We find that both the local as well as the nonlocal NJL model predict the existence of extended regions of mixed quark-hadron (quark-hybrid) matter in high-mass neutron stars with masses of 2.1 to $2.4\phantom{\rule{0.16em}{0ex}}{M}_{\ensuremath{\bigodot}}$. Pure quark matter in the cores of neutron stars is obtained for certain parametrizations of the hadronic lagrangian and choices of the vector repulsion among quarks. The radii of high-mass neutron stars with quark-hybrid matter and/or pure quark matter cores in their centers are found to lie in the canonical range of 12 to 13 km.

Nonlocal Nambu–Jona-Lasinio model with a fractional Lorentzian regulator in the real time formalism

In this article we study the finite temperature and chemical potential effects in a nonlocal Nambu-Jona-Lasinio (nNJL) model in the real time formalism. We make the usual Wick rotation to get from imaginary to real time formalism. In doing so, we need to define our regulator in the complex plane q^2. This deffinition will be crucial in our later analysis. We study the poles in the propagator of this model and conclude that only some of them are of interst to us. Once we have a well defined model in real time formalism, we look at the chiral condensate to find the temperature at which chiral symmetry restoration will occur. We find a second order phase transition that turns to a first order one for high enough values of the chemical potential.

Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

The real-time formalism at finite temperature and chemical potential for the nonlocal Nambu--Jona-Lasinio model is developed in the presence of a Gaussian covariant regulator. We construct the most general thermal propagator, by means of the spectral function. As a result, the model involves the propagation of massive quasiparticles. The appearance of complex poles is interpreted as a confinement signal, and in this case we have unstable quasiparticles with a finite decay width. An expression for the propagator along the critical line, where complex poles start to appear, is also obtained. A generalization to other covariant regulators is proposed.

The nuclear matter stability in a non-local chiral quark model

We study the stability of the nuclear matter in a non-local Nambu–Jona-Lasinio model. We work out the equation of state in a relativistic Faddeev approach where we take into account the internal structure of nucleon. We show that the binding energy saturates when the nucleon as a composite particle made of quarks is incorporated. After truncation of the two-body channels to the scalar and axial-vector diquarks, a relativistic Faddeev equation for nucleon bound states in medium is solved in the covariant diquark–quark picture. We investigate the nucleon properties in the nuclear medium such as the role of diquarks within the nucleon and the in-medium modification of the nucleon mass and size.

Baryon structure in a quark-confining nonlocal Nambu–Jona–Lasinio model

We study the nucleon and diquarks in a nonlocal Nambu--Jona--Lasinio model. For certain parameters the model exhibits quark confinement, in the form of a propagator without real poles. After truncation of the two-body channels to the scalar and axial-vector diquarks, a relativistic Faddeev equation for nucleon bound states is solved in the covariant diquark--quark picture. The dependence of the nucleon mass on diquark masses is studied in detail. We find parameters that lead to a simultaneous reasonable description of pions and nucleons. Both the diquarks contribute attractively to the nucleon mass. Axial-vector diquark correlations are seen to be important, especially in the confining phase of the model. We study the possible implications of quark confinement for the description of the diquarks and the nucleon. In particular, we find that it leads to a more compact nucleon.

Mesonic fluctuations in a nonlocal Nambu–Jona-Lasinio model

The effects of meson fluctuations are studied in a nonlocal generalization of the Nambu–Jona-Lasinio model, by including terms of next-to-leading order (NLO) in 1/ N c . In the model with only scalar and pseudoscalar interactions NLO contributions to the quark condensate are found to be very small. This is a result of cancellation between virtual mesons and Fock terms, which occurs for the parameter sets of most interest. In the quark self-energy, similar cancellations arise in the tadpole diagrams, although not in other NLO pieces which contribute at the ∼25% level. The effects on pion properties are also found to be small. NLO contributions from real ππ intermediate states increase the sigma-meson mass by ∼30%. In an extended model with vector and axial interactions, there are indications that NLO effects could be larger.