Nambu-Jona-Lasinio Research Articles

Anomalous enhancement of dilepton production as a precursor of color superconductivity

Abstract We compute the modification of the photon self-energy due to dynamical diquark fluctuations developed near the critical temperature of two-flavor superconductivity, which is one of the color superconducting phases, through the Aslamasov–Larkin, Maki–Thompson, and density of states terms, which are responsible for the paraconductivity in metals at vanishing energy and momentum. The analysis is performed through an investigation of the diquark fluctuations within the normal phase determined by the mean-field approximation in the massless two-flavor Nambu–Jona-Lasinio model. It is shown that the rate has a significant enhancement in low-invariant-mass regions over a rather wide range of temperatures in the normal phase. This enhancement is worth exploring in the relativistic heavy-ion collisions, which may thereby reveal the significance of the diquark fluctuations in dense quark matter.

The decays τ → a1πντ, τ → K1πντ and τ → K1Kντ in the extended U(3) ×U(3) chiral NJL model

The branching fractions of the decays [Formula: see text], [Formula: see text] and [Formula: see text] are calculated in the framework of the extended [Formula: see text] chiral Nambu–Jona-Lasinio model. There are no experimental data for these decays in the present time, thus the obtained results are considered as predictions. The comparison of these results to the theoretical results of other authors is carried out.

Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors and colors using the Nambu-Jona-Lasinio (NJL) model of quarks in the Schwinger-Dyson equation framework, dressed with a color-flavor dependence of effective coupling. For fixed and varying , we observe that the dynamical chiral symmetry is broken when exceeds its critical value . For a fixed and varying , we observe that the dynamical chiral symmetry is restored when reaches its critical value . Strong interplay is observed between and , i.e., larger values of tend to strengthen the dynamical generated quark mass and quark-antiquark condensate, while higher values of suppress both parameters. We further sketch the quantum chromodynamics (QCD) phase diagram at a finite temperature T and quark chemical potential μ for various and . At finite T and μ, we observe that the critical number of colors is enhanced, whereas the critical number of flavors is suppressed as T and μ increase. Consequently, the critical temperature , , and co-ordinates of the critical endpoint in the QCD phase diagram are enhanced as increases and suppressed when increases. Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.

Magnetized pole-mass of neutral ρ meson within full RPA evaluation

In this work we calculate the pole-mass of the ρ0 meson with different spin projections sz=0,±1 in the context of the magnetized two-flavor Nambu–Jona–Lasinio model. Making use of the mean field approximation to obtain the effective quark mass as a function of the magnetic field, we apply the random phase approximation (RPA) to the vector channel in order to calculate the polarization function for each spin component. We adopt the magnetic field independent regularization (MFIR) in our evaluations as a method of separating divergences and the Pauli-Villars regularization for the vacuum contributions. The ρ0 meson mass with spin projection sz=±1 is always catalyzed with the magnitude of the magnetic field, showing good agreement with Lattice QCD results. The mass projection sz=0 has a non-monotonic behavior, decreasing until the minimum at eB≲0.15 GeV2, which is in contrast with available LQCD data.

Exploring hybrid star EOS with constraints from tidal deformability of GW170817

With an interpolation method on the P-μ plane, a hybrid equation of state is explored. The quark phase is described by a self-consistent two-flavor Nambu–Jona-Lasinio model. It retains the contribution from the vector channel in the Fierz-transformed Lagrangian by introducing a weighting parameter α. We study the dependence of hybrid EOS and mass-radius relation on α. It is found that increasing α makes the hybrid EOS softer. We can get stellar mass larger than 2M⊙. Further, we calculate the tidal deformability Λ˜ for binary stars and compare it with some theoretical analysis results on GW170817.

Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization

Magnetic field dependent corrections for the coupling constant of the Nambu-Jona-Lasinio model are calculated by considering the one-loop background field method. These coupling constants turn out to break chiral and flavor symmetries and they lead to a slight improvement of the numerical values of the up and down quark condensates when compared to results from lattice QCD. The corresponding magnetic field dependencies of the neutral pion and kaon masses are also presented and compared with available lattice QCD calculations. The resulting magnetic field correction to the $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing angle is also estimated.

Interacting ud and uds quark matter at finite densities and quark stars

The stability and equation of state of quark matter are studied within both two-flavor and ($2+1$)-flavor Nambu-Jona-Lasinio (NJL) models including the vector interactions. With a free parameter $\ensuremath{\alpha}$, the Lagrangian is constructed by two parts, the original NJL Lagrangian and the Fierz transformation of it, as $\mathcal{L}=(1\ensuremath{-}\ensuremath{\alpha}){\mathcal{L}}_{\mathrm{NJL}}+\ensuremath{\alpha}{\mathcal{L}}_{\text{Fierz}}$. We find that there is a possibility for both $ud$ nonstrange and $uds$ strange matter being absolute stable, depending on the interplay of the confinement with quark vector interaction and the exchange interaction channels. The calculated quark star properties can reconcile with the recently measured masses and radii of PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$, as well as the tidal deformability of GW170817. Furthermore, the more strongly interacting quark matter in the nonstrange stars allows a stiffer equation of state and consequently a higher maximum mass ($\ensuremath{\sim}2.7\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$) than the strange ones ($\ensuremath{\sim}2.1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$). The sound velocities in strange and nonstrange quark star matter are briefly discussed compared to those of neutron star matter.

Quark Matter in the NJL Model with a Vector Interaction and the Structure of Hybrid Stars

Quark Matter in the NJL Model with a Vector Interaction and the Structure of Hybrid Stars

QCD chiral condensate and pseudoscalar-meson properties in the nuclear medium at finite temperature

The pion and kaon properties in a nuclear medium at nonvanishing temperature as well as the quantum chromodynamics (QCD) chiral condensate in the presence of a magnetic field for various baryon densities are studied in the Nambu–Jona–Lasinio (NJL) model with the help of the proper-time regularization (PTR) scheme, simulating a QCD confinement. The density dependence of the quark mass in symmetric nuclear matter is obtained from the quark-meson coupling (QMC) model, which shares the same covariant feature with the NJL model, at quark level. We then analyze the QCD chiral condensates and dynamical masses for various baryon densities at finite temperature and magnetic field as well as the pion and kaon masses, pion and kaon weak-decay constants, pion- and kaon-quark coupling constants, and wave function renormalization factors for various baryon densities at finite temperature. We find that the QCD chiral condensates suppress with increasing temperature and baryon density and enhance under the presence of a magnetic field, which are consistent with other model predictions. Interestingly, the wave function renormalization factors for the pion and kaon increase with respect to temperature and reduce as the baryon density increases are found.

Effects of a Finite Volume in the Phase Structure of QCD

Working in the SU(2) flavor version of the NJL model, we study the effect of taking a finite system volume on a strongly interacting system of quarks, and, in particular, the location of the chiral phase transition and the CEP. We consider two shapes for the volume, spherical and cubic regions with different sizes and different boundary conditions. To analyze the QCD phase diagram, we use a novel criterion to study the crossover zone. A comparison between the results obtained from the two different shapes and several boundary conditions is carried out. We use the method of Multiple Reflection Expansion to determine the density of states and three kinds of boundary conditions over the cubic shape. These boundary conditions are: periodic, anti-periodic and stationary boundary conditions on the quark fields.

Hybrid stars and the QCD phase transition with an NJL-type model

In this paper, we introduce a self-consistent mean field approximation to study the QCD phase transition and the structure of hybrid stars within the framework of NJL model. In our practice, a phenomenological parameter $\alpha$ is introduced, which reflects the weights of "direct" channel and "exchange" channel under a finite chemical potential. The mass-radius relation is obtained by solving the Tolman-Oppenheimer-Volkoff equation using a crossover equation of state (EOS). We calculate the density distribution in a two solar-mass hybrid star to show the effects of different parameters. We also calculate the tidal Love number $k_2$ and the deformability $(\Lambda)$. It is found that the stiffness of the EOS increases with $\alpha $, which allows us to obtain a hybrid star with a maximum mass of 2.40 solar-mass through our model. The observation of over 2.06 solar-mass neutron stars may indicates that the chiral transition may be a crossover on the whole $T-\mu$ plane.

Regularization dependence of pion generalized parton distributions * *Supported by the National Natural Science Foundation of China (11775118)

Pion generalized parton distributions are calculated within the framework of the Nambu–Jona-Lasinio model using different regularization schemes, including the proper time regularization scheme, the three-dimensional (3D) momentum cutoff scheme, the four-dimensional momentum cutoff scheme, and the Pauli-Villars regularization scheme. Furthermore, we check the theoretical constraints of pion generalized parton distributions required by the symmetries of quantum chromodynamics in different regularization schemes. The diagrams of pion parton distribution functions are plotted, in addition, we evaluate the Mellin moments of generalized parton distributions, which are related to the electromagnetic and gravitational form factors of pion. Pion generalized parton distributions are continuous but not differential at , when considering the effect of the contact contribution term, generalized parton distributions become not continuous at in all the four regularization schemes. Generalized parton distributions in impact parameter space are considered, the width distribution of u quark in the pion and the mean-squared are calculated. The light-front transverse-spin distributions are studied when quark polarized in the light-front-transverse direction, the transverse-spin density is no longer symmetric around , the peaks shift to , we compare the average transverse shift and in different regularization schemes. The light-cone energy radius and the light-cone charge radius are also evaluated, we found that in the proper time regularization scheme the values of these quantities were the largest, in the 3D momentum cutoff scheme they were the smallest.

π0–η–η' Mixing in the Theory with Four-Quark Interactions

Mass formulas, mixing angles, and decay constants of the pseudoscalar π0, η, and η' mesons have been obtained in the theory with four-quark interactions with an accuracy to mathcal{O}(1{text{/}}N_{{text{c}}}^{2}) terms inclusively. Unlike the standard Nambu–Jona-Lasinio model, the meson Lagrangian has been obtained using the Volterra series, which allows a more detailed description of effects caused by the inequality of quark masses. The results have been compared to similar calculations in the 1/Nc chiral perturbation theory. The first corrections to the interaction violating the Zweig formulas have been calculated, and it has been shown that they are important for the description of the mass spectrum of the η–η' mesons.

Strangeness content of the pion in the U(3) Nambu–Jona–Lasinio model

Abstract The Nambu–Jona–Lasinio model is considered with flavor-dependent coupling constants G i j ( ψ ¯ λ i ψ ) ( ψ ¯ λ j ψ ) + ( ψ ¯ i γ 5 λ i ψ ) ( ψ ¯ i γ 5 λ j ψ ) for i , j = 0 , 1 … N f 2 − 1 , and N f = 3. A self-consistent calculation of quark effective masses and coupling constants is performed, making the strange quark effective mass vary considerably. Quantum mechanical mixings between up, down and strange constituent quarks yield a strangeness content (s-content) of the light u and d quark constituent and of the pion. Different types of estimates for the strangeness contribution for the pion mass are provided. Mixing-type interactions, G i≠j , induce light meson mixings, and estimates for the π 0 − η and η − η′ mixings are provided. The η − π 0 mixing is argued to be an indication of the s-content of the pion.

Bayesian analysis of the properties of hybrid stars with the Nambu–Jona-Lasinio model

We implement a Bayesian analysis of the properties of non-rotating hybrid stars at equilibrium with quark matter cores, as described by the SU(3) Nambu--Jona-Lasinio (NJL) model. The hadronic phase is described by a unified metamodeling approach, with a prior parameter space covering the present uncertainties on nuclear matter properties with nucleonic degrees of freedom. The parameter space of the NJL model includes vector-isoscalar and vector-isovector couplings and, additionally, an effective bag constant for the quark pressure is introduced as a free parameter. The phase transition is assumed to be first order with charge neutral phases, following the Maxwell construction. Our Bayesian framework includes filters on the experimental and theoretical low-density nuclear physics knowledge (atomic masses, ab initio calculations of the EoS) and high density constraints from astrophysical observations (maximum mass of J0348+0432, binary tidal deformability of the GW170817 event). We find that microscopic vector interactions play an important role in quark matter in order to stiffen the equation of state sufficiently to reach high star masses, in agreement with previous studies. Even within a very large prior for both the hadronic phase and the quark phase and the important freedom brought by the effective bag constant, our posterior quark cores tend to be relatively small and only appear in very heavy stars ($M\gtrsim 2 M_\odot$). Coincidentally, the inclusion of the nucleon-quark transition (deconfinement transition) only weakly affects the radii of compact stars, foreshadowing a very low observability of a possible phase transition using x-ray radii measurements.

Properties of Hot Quark Matter with Neutrino Confinement in the NJL Model

The thermodynamic characteristics of hot $\beta$-equilibrium three-flavor quark matter with neutrino confinement are studied in terms of the local SU(3) Nambu-Jona-Lasinio (NJL) model, which also accounts for the 't Hooft interaction which leads to mixing of quark flavors. For different temperatures $T \in [20 \div 100]$ MeV and baryon number densities $n_B \in [0 \div 1.8]$ fm$^{-3}$ the constituent quark masses, quark condensates, and relative contributions of individual types of particles to the pressure and chemical potentials of the constituent particles are determined. In order to determine the role of neutrinos in the hot quark matter, the pressures and energies in states with and without neutrinos are compared. Keywords: hot quark matter: neutrino confinement: NJL model: equation of state.

Mass spectra and decay of mesons under strong external magnetic field * *Supported by the National Natural Science Foundation of China (11735007, 11890711, 11890710)

We study the mass spectra and decay process of σ and mesons under a strong external magnetic field. To achieve this goal, we deduce the thermodynamic potential in a two-flavor, hot and magnetized Nambu–Jona-Lasinio model. We calculate the energy gap equation through the random phase approximation (RPA). Then we use the Ritus method to calculate the decay triangle diagram and self-energy in the presence of a constant magnetic field B. Our results indicate that the magnetic field has little influence on the mass of at low temperatures. However, for quarks and σ mesons, their mass clearly changes, which reflects the influence of magnetic catalysis (MC). The presence of a magnetic field accelerates the decay of the meson while the presence of a chemical potential will decrease the decay process.

Nuclear Potentials Relevant to the Symmetry Energy in Chiral Models

We employ the extended Nambu-Jona-Lasinio (NJL), linear-σ models, and the density-dependent model with chiral limits to work out the mean fields and relevant properties of nuclear matter. To have the constraint from the data, we re-examine the Dirac optical potentials and symmetry potential based on the relativistic impulse approximation (RIA). Unlike the extended NJL and the density-dependent models with the chiral limit in terms of the vanishing scalar density, the extended linear-σ model with a sluggish changing scalar field loses the chiral limit at the high-density end. The various scalar fields can characterize the different Schrödinger-equivalent potentials and kinetic symmetry energy in the whole density region and the symmetry potential in the intermediate density region. The drop in the scalar field due to the chiral restoration results in a clear rise of the kinetic symmetry energy. The chiral limit in the models gives rise to the softening of the symmetry potential and thereof the symmetry energy at high densities.

Symmetry energy effects on the properties of hybrid stars

Symmetry energy is an important part of the equation of state of isospin asymmetry matter. However, the huge uncertainties of symmetry energy remain at suprasaturation densities, where the phase transitions of strongly interacting matter and the quark matter symmetry energy are likely to be taken into account. In this work, we investigate the properties of symmetry energy by using a hybrid star with the hadron-quark phase transition. The interaction among strange quark matter (SQM) in hybrid stars is based on a 3-flavor NJL model with different vector and isovector channels, while the equation of state (EOS) of the nuclear matter is obtained by considering the ImMDI-ST interaction by varying the parameters x, y, and z. Our results indicate that the various parameters and coupling constants of the interactions from the ImMDI-ST and NJL model can lead to widely different trends for the symmetry energy in the hadron-quark mixed phase and the different onsets of the hadron-quark phase transition. In addition, it has been found that the radii and tidal deformabilities of hybrid stars constrain mostly the density dependence of symmetry energy while the observed maximum masses of hybrid stars constrain mostly the EOS of symmetric nuclear and quark matter.

Gluon and valence quark distributions for the pion and kaon in nuclear matter

In this paper we study the gluon and valence quark distributions in the pion and kaon in nuclear medium for various nuclear densities as well as in vacuum within the Nambu--Jona-Lasinio (NJL) model with the help of the proper-time regularization scheme which simulates a confinement of QCD. The nuclear medium effect is also determined in the same model for the symmetric nuclear matter. We then analyze the gluon and valence quark distributions for the bound pion and kaon in symmetric nuclear matter as well as those in vacuum. We find that the valence quark and gluon distributions in vacuum have relatively good agreements with the experimental data, the lattice QCD simulations, and the JAM Monte-Carlo (MC) global fit QCD analysis. Evolving to the higher factorization scale $Q=4\text{ }\text{ }\mathrm{GeV}$, the in-medium gluon and valence-quark distributions of the pion for various nuclear densities are turned out to be almost unchanged in comparison to the vacuum cases. On the contrary, for the kaon, they increase significantly with respect to the densities. Finally, we find that the vacuum gluon distribution for the kaon is smaller than that for the pion, which is consistent with other theoretical predictions. This feature holds for the in-medium gluon distribution in the nuclear density up to the saturation density.