Nonlocal Nambu Jona-Lasinio Research Articles

Yukawa theory in non-perturbative regimes: towards confinement, exact β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-function and conformal phase

We study possible hints towards confinement in a Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Z}_2$$\\end{document}-invariant Yukawa system with massless fermions and a real scalar field in the strongly-coupled regime. Using the tools developed for studying non-perturbative physics via Jacobi elliptical functions, for a given but not unique choice of the vacuum state, we find the exact Green’s function for the scalar sector so that, after integrating out the scalar degrees of freedom, we are able to recover the low-energy limit of the theory that is a fully non-local Nambu–Jona–Lasinio (NJL) model. We provide an analytical result for the renormalization group (RG) running of the self-interaction coupling in the scalar sector in the strongly-coupled regime. In the fermion sector, we provide some clues towards confinement, after deriving the gap equation with the non-local NJL model, a property which is well-known to not emerge in the local limit of this model. We conclude that, for the scalar-Yukawa theory in the non-perturbative domain with our choice of the vacuum state, the fundamental fermions of the theory form bound states and cannot be observed as asymptotic states.

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.

Confinement in QCD and generic Yang-Mills theories with matter representations

We derive the low-energy limit of quantum chromodynamics (QCD) and provide evidence that in the 't Hooft limit, i.e. for a very large number of colors and increasing 't Hooft coupling, quark confinement is recovered. The low energy limit of the theory turns out to be a non-local Nambu–Jona-Lasinio (NJL) model. The effect of non-locality, arising from a gluon propagator that fits quite well to the profile of an instanton liquid, is to produce a phase transition from a chiral condensate to an instanton liquid, as the coupling increases with lower momentum. This phase transition suffices to move the poles of the quark propagator to the complex plane. As a consequence, free quarks are no longer physical states in the spectrum of the theory.

Special point "trains" in the M-R diagram of hybrid stars

We present a systematic investigation of the possible locations for the special point (SP), a unique feature of hybrid neutron stars in the massradius diagram. The study is performed within the two-phase approach where the high-density (quark matter) phase is described by the covariant nonlocal Nambu–Jona-Lasinio (nlNJL) model equation of state (EOS) which is shown to be equivalent to a constant-sound-speed (CSS) EOS. For the nuclear matter phase around saturation density different relativistic density functional EOSs are used: DD2p00, its excluded-volume modification DD2p40 and the hypernuclear EOS DD2Y-T. In the present contribution we apply the Maxwell construction scheme for the deconfinement transition and demonstrate that a simultaneous variation of the vector and diquark coupling constants results in the occurrence of SP "trains" which are invariant against changing the nuclear matter EOS. We propose that the SP train corresponding to a variation of the diquark coupling at constant vector coupling is special since it serves as a lower bound for the line of maximum masses and accessible radii of massive hybrid stars.

Novel evaluation of the hadronic contribution to the muon’s g−2 from QCD

We evaluate the hadronic contribution to the $g-2$ of the muon by deriving the low-energy limit of quantum chromodynamics (QCD) and computing in this way the hadronic vacuum polarization. The low-energy limit is a non-local Nambu--Jona-Lasinio (NJL) model that has all the parameters fixed from QCD, and the only experimental input used is the confinement scale that is known from measurements of hadronic physics. Our estimations provide a novel analytical alternative to the current lattice computations and we find that our result is close to the similar computation performed from experimental data. We also comment on how this analytical approach technique, in general, may provide prospective estimates for hadronic computations from dark sectors and its implication in BSM model-building in future.

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.

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 Deconfinement in Rotating Neutron Stars

In this paper, we use a three flavor non-local Nambu–Jona-Lasinio (NJL) model, an improved effective model of Quantum Chromodynamics (QCD) at low energies, to investigate the existence of deconfined quarks in the cores of neutron stars. Particular emphasis is put on the possible existence of quark matter in the cores of rotating neutron stars (pulsars). In contrast to non-rotating neutron stars, whose particle compositions do not change with time (are frozen in), the type and structure of the matter in the cores of rotating neutron stars depends on the spin frequencies of these stars, which opens up a possible new window on the nature of matter deep in the cores of neutron stars. Our study shows that, depending on mass and rotational frequency, up to around 8% of the mass of a massive neutron star may be in the mixed quark-hadron phase, if the phase transition is treated as a Gibbs transition. We also find that the gravitational mass at which quark deconfinement occurs in rotating neutron stars varies quadratically with spin frequency, which can be fitted by a simple formula.

Hybrid Stars in the Framework of NJL Models

We compute models for the equation of state (EoS) of the matter in the cores of hybrid stars. Hadronic matter is treated in the non-linear relativistic mean-field approximation, and quark matter is modeled by three-flavor local and non-local Nambu−Jona-Lasinio (NJL) models with repulsive vector interactions. The transition from hadronic to quark matter is constructed by considering either a soft phase transition (Gibbs construction) or a sharp phase transition (Maxwell construction). We find that high-mass neutron stars with masses up to [Formula: see text] may contain a mixed phase with hadrons and quarks in their cores, if global charge conservation is imposed via the Gibbs conditions. However, if the Maxwell conditions is considered, the appearance of a pure quark matter core either destabilizes the star immediately (commonly for non-local NJL models) or leads to a very short hybrid star branch in the mass-radius relation (generally for local NJL models).

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.

Constant-sound-speed parametrization for Nambu–Jona-Lasinio models of quark matter in hybrid stars

The discovery of pulsars as heavy as 2 solar masses has led astrophysicists to rethink the core compositions of neutron stars, ruling out many models for the nuclear equations of state (EoS). We explore the hybrid stars that occur when hadronic matter is treated in a relativistic mean-field approximation and quark matter is modeled by three-flavor local and non-local Nambu Jona-Lasinio (NJL) models with repulsive vector interactions. The NJL models typically yield equations of state that feature a first order transition to quark matter. Assuming that the quark-hadron surface tension is high enough to disfavour mixed phases, and restricting to EoSes that allow stars to reach 2 solar masses, we find that the appearance of the quark matter core either destabilizes the star immediately (this is typical for non-local NJL models) or leads to a very short hybrid star branch in the mass-radius relation (this is typical for local NJL models). Using the Constant-Sound-Speed parametrization we can see that the reason for the near-absence of hybrid stars is that the transition pressure is fairly high and the transition is strongly first order.

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.

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.