Nambu-Jona-Lasinio Research Articles

Pion superfluid phase transition under an external magnetic field including the inverse magnetic catalysis effect

Pion superfluid phase transition under external magnetic field including the inverse magnetic catalysis (IMC) effect is investigated by the Pauli-Villars regularized NJL model. Based on the Goldstone's theorem, we apply the massless Goldstone boson ($\pi^+$ meson) to determine the onset of pion superfluid phase. The inverse magnetic catalysis effect is introduced by the magnetic field dependent coupling $G(eB)$, which is a decreasing function of magnetic field. At fixed temperature and baryon chemical potential, the critical isospin chemical potential for pion superfluid phase transition including IMC effect increases as the magnetic field grows, which is similar as the case without IMC effect. This demonstrates that magnetic field disfavors the pion superfluid phase when considering or ignoring IMC effect. The critical isospin chemical potential at fixed magnetic field, temperature and baryon chemical potential is shifted to higher value by the IMC effect. Since it is more difficult to form pion superfluid with weaker coupling.

Fate of the first-order chiral phase transition in QCD: Implications for dark QCD studied via a Nambu–Jona-Lasinio model

The first-order nature of the chiral phase transition in QCD-like theories can play crucial roles to address a dark side of the Universe, where the created out-of equilibrium is essential to serve as cosmological and astrophysical probes such as gravitational wave productions, which have extensively been explored. This interdisciplinary physics is built based on a widely-accepted conjecture that the thermal chiral phase transition in QCD-like theories with massless (light) three flavors is of first order. We find that such a first order feature may not hold, when ordinary or dark quarks are externally coupled to a weak enough background field of photon or dark photon (which we collectively call a ``magnetic" field). We assume that a weak ``magnetic" background field could be originated from some ``magnetogenesis" in the early Universe. We work on a Nambu-Jona-Lasinio model which can describe the chiral phase transition in a wide class of QCD-like theories. We show that in the case with massless (light) three flavors, the first-order feature goes away when $2 f_\pi^2 \lesssim eB ( \ll (4 \pi f_\pi)^2)$, where $eB$ is the ``magnetic" field strength and $f_\pi$ the pion decay constant at the vacuum. This disappearance is the generic consequence of the presence of the ``magnetically" induced scale anomaly and the ``magnetic" catalysis for the chiral symmetry breaking, and would impact or constrain modeling dark QCD coupled to an external ``magnetic" field.

Phenomenological study of the anisotropic quark matter in the two-flavor Nambu–Jona–Lasinio model

Phenomenological study of the anisotropic quark matter in the two-flavor Nambu–Jona–Lasinio model

Chiral vortical catalysis

Gluon interaction introduces remarkable corrections to the magnetic polarization effects on the chiral fermions, which is known as the inverse magnetic catalysis. It is a natural speculation that the vorticity, which has many similar properties as magnetic field, would bring non-negligible contribution to the chiral rotational suppression. Using an intuitive semi-classical background field method we studied the rotation dependence of the effective strong interaction coupling constant. Contrary to the magnetic field case the rotation increases the effective coupling which would slow down the condensate melting with temperature. This could be named as the chiral vortical catalysis or inverse rotation suppression. Imposing such dependence on the 4-fermion coupling in the NJL model, we numerically checked this analysis qualitatively. The pseudo critical temperature is shown to rise with the rotation and approach saturation eventually which may be induced by the model cutoff.

Properties of strange quark matter under strong rotation

We investigate the rotating quark matter in the three-flavor Nambu--Jona-Lasinio (NJL) model. The chiral condensation, spin polarization, and number susceptibility of the light and strange quarks are carefully studied at finite temperatures without or with finite chemical potential in this model. We find that the rotation suppresses the chiral condensation and enhances the first-order quark spin polarization, however for the second-order quark spin polarization and quark number susceptibility the effect is complicated and interesting. When extending to the situation with finite chemical potential, we find the angular velocity also plays a crucial role, at small angular velocity the chemical potential enhances the susceptibility, however in the middle region of angular velocity the effect of the chemical potential is suppressed by the angular velocity and susceptibility can be changed considerably, it can be observed that at very low temperature in the presence of quark chemical potential the quark number susceptibility has two maxima with increasing angular velocity. Furthermore, it is found that at sufficiently large angular velocity the contributions played by the light quark and the strange quark to these phenomena are almost equal. We also discuss the chiral phase transition of rotating quark matter in the three-flavor NJL model. We expect these studies to be used to understand the chiral symmetry breaking and restoration as well as probe the QCD phase transition.

Neutral pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model: Mixing effects

Mixing effects on the mass spectrum of light neutral pseudoscalar and vector mesons in the presence of an external uniform magnetic field $\vec B$ are studied in the framework of a two-flavor NJL-like model. The model includes isoscalar and isovector couplings both in the scalar-pseudoscalar and vector sectors, and also incorporates flavor mixing through a 't Hooft-like term. Numerical results for the $B$ dependence of meson masses are compared with present lattice QCD results. In particular, it is shown that the mixing between pseudoscalar and vector meson states leads to a significant reduction of the mass of the lightest state. The role of chiral symmetry and the effect of the alignment of quark magnetic moments in the presence of the magnetic field are discussed.

Notes on further refining de Sitter swampland conjecture with inflationary models

In this paper, we challenge some inflationary models with the recent new conjecture of the swampland program, namely, further refining the de Sitter swampland conjecture. So far, different inflation models have been studied with refined dS swampland conjecture in various conditions. Some of these models were in line with this conjecture, and some were in direct tension with it. Therefore, a modified model that combines the first and second conditions of refined dS conjecture was proposed. It has a limitation on its constant parameters such as a , b = 1 − a and q . We challenge several inflation models with the new conjecture, which contradicts the refined dS conjecture. We discuss the constraints and adjustments of each of a , b = 1 − a , and q and the compatibility or incompatibility of the inflation models with further refining the de Sitter swampland conjecture. We will compare the results with the models studied by refined dS conjecture. We conclude that many inflation models are fully compatible with the mentioned conjecture. If the new conjecture is accurate, these inflationary models live in the landscape instead of the swampland. • Further refining de sitter swampland conjecture. • Minimal gauge inflation model. • Minimal plateau inflationary model. • Gauged Nambu–Jona–Lasinio inflation. • limitations applied to its free constant parameters.

The role of Debye mass in the chiral crossover in a strong magnetic field

In this paper, the Debye mass of quarks is investigated in the Nambu–Jona-Lasinio model at zero and nonzero chemical potentials. In a uniform plasma, the Debye mass usually behaves as a monotonous increasing function of the temperature, the chemical potential and the magnetic field. At the fixed coupling interaction G, we find that the magnetic catalysis (MC) on the occurrence of the chiral restoration could be revealed by the susceptibility of the Debye mass dm D /dT at low chemical potential and by the quantity Tdm D /dT in the region of moderate densities. However, the inverse MC is realized under a thermomagnetic coupling constant G(B, T) by the behavior of the Debye mass at both zero and nonzero chemical potentials.

The decays η′→ πρ and ρ → πη in the chiral NJL model

The branching fractions of the decays [Formula: see text] and [Formula: see text] are calculated in the chiral quark NJL model. The decays exist due to the mass difference between [Formula: see text]- and [Formula: see text]-quarks leading to [Formula: see text] and [Formula: see text] mixing. Two different approaches are applied: the approximate calculation of this process, taking into account the transitions [Formula: see text] and [Formula: see text] explicitly without diagonalization and a more precise approach consisting in the diagonalization of the singlet and octet states leading to the physical fields [Formula: see text], [Formula: see text] and [Formula: see text]. The obtained results are in satisfactory agreement with current experimental data.

Repulsive character induced by optimized perturbation techniques on the Polyakov-loop-extended Nambu—Jona-Lasinio model.

The determination of the critical point on the QCD phase diagram depends experimentally on thermodynamic quantities related to the cumulants of the pressure. These quantities appear as coefficients in the Taylor expansion of the pressure and, specifically for the second order cumulant c 2, QCD results on the lattice (LQCD) show that it raises with the temperature towards the Stefan-Boltzmann limit. On the other hand, when one evaluates c 2 within quark effective models considering a repulsion on the vector channel parametrized by GV , this observable reaches a maximum just after Tc , deviating itself from LQCD predictions. Here we apply the Optimized Perturbation Theory (OPT) method to the two flavor Polyakov–Nambu–Jona-Lasinio model (at GV = 0) to confront our results with those furnished by LQCD simulations. We show that c 2 behaves satisfactorily at low-T and close to Tc , but, with GV ≠ 0, it develops a maximum at high-T. Our conclusions indicate that it would be possible that the correct high temperature behavior of c 2 beyond LN limit could be properly achieved by effective quark models if they also mimic the so-called asymptotic freedom phenomenon.

Regularization issues for a cold and dense quark matter with a chiral imbalance

In this work we investigate the effects of the chiral chemical potential, μ 5, in the two flavor cold and dense quark matter with two different regularization procedures within the Nambu–Jona-Lasinio (NJL SU(2)) model: the Traditional Regularization Scheme (TRS) and the Medium Separation Scheme (MSS). We study the effects of different choices for the parametrization of the model for both regularization schemes. More specifically we were interested in the behavior of the effective quark masses as a function of chiral and quark chemical potentials.

Effects of the quark anomalous magnetic moment in the thermodynamical properties of the magnetized two flavor Nambu–Jona-Lasinio model

The influence of the anomalous magnetic moment (AMM) of quarks in the chiral phase transition is studied in the context of the hot and magnetized two flavor Nambu–Jona-Lasinio model. Making use of the mean field approximation (MFA) and the vacuum magnetic regularization (VMR) scheme, we obtain the effective quark masses as a function of the magnetic field for the two usual different sets of AMM. Basic thermodynamical properties are explored and compared with the zero AMM-case, as the pressure, entropy, energy density, interaction measure and the specific heat. The main differences are present in the thermodynamical quantities when one consider a sizable value of AMM, in which an underestimation over the transition region is observed.

Thermodynamical properties of hot and magnetized quark matter within the SU(2) Polyakov-Nambu-Jona-Lasinio model: vacuum magnetic regularization scheme

In this work we implement the recent proposed vacuum magnetic regularization (VMR) scheme to the two flavor Polyakov–Nambu–Jona-Lasinio model in order to describe some basic thermodynamic properties such as the pressure, entropy and energy density. We show that this procedure allows the evaluation of the renormalized magnetization, which agrees with LQCD data. Potential physical differences are also explored when other three possible regularization schemes are adopted to describe the chiral condensate.

Quantum simulation of chiral phase transitions

The Nambu–Jona-Lasinio (NJL) model has been widely studied for investigating the chiral phase structure of strongly interacting matter. The study of the thermodynamics of field theories within the framework of Lattice Field Theory is limited by the sign problem, which prevents Monte Carlo evaluation of the functional integral at a finite chemical potential. Using the quantum imaginary time evolution (QITE) algorithm, we construct a quantum simulation for the (1 + 1) dimensional NJL model at finite temperature and finite chemical potential. We observe consistency among digital quantum simulation, exact diagonalization and analytical solution, indicating further applications of quantum computing in simulating QCD thermodynamics.

Relativistic mean field model parametrizations in the light of GW170817, GW190814, and PSR J0740+6620

Three parametrizations DOPS1, DOPS2, and DOPS3 (named after the Department of Physics Shimla) of the relativistic mean field model have been proposed with the inclusion of all possible self and mixed interactions between the scalar-isoscalar ($\ensuremath{\sigma}$), vector-isoscalar ($\ensuremath{\omega}$), and vector-isovector ($\ensuremath{\rho}$) mesons up to quartic order. The generated parameter sets are in harmony with the finite and bulk nuclear matter properties. A set of equations of state (EOSs) composed of pure hadronic (nucleonic) matter and nucleonic with quark matter (hybrid EOSs) for superdense hadron-quark matter in $\ensuremath{\beta}$ equilibrium is obtained. The quark matter phase is calculated by using the three-flavor Nambu-Jona-Lasinio (NJL) model. The maximum mass of a nonrotating neutron star with DOPS1 parametrization is found to be around $2.6M\ensuremath{\bigodot}$ for the pure nucleonic matter, which satisfies the recent gravitational wave analysis of GW190814 [Abbott et al., Astrophys. J. Lett. 896, L44 (2020)] with possible maximum mass constraint indicating that the secondary component of GW190814 could be a nonrotating heaviest neutron star composed of pure nucleonic matter. EOSs computed with the DOPS2 and DOPS3 parametrizations satisfy the x-ray observational data [Steiner et al., Astrophys. J. 722, 33 (2010)] and the recent observations of GW170817 maximum mass constraint of a stable nonrotating neutron star in the range $2.01\ifmmode\pm\else\textpm\fi{}0.04--2.16\ifmmode\pm\else\textpm\fi{}0.03M\ensuremath{\bigodot}$ [Rezzolla et al., Astrophys. J. Lett. 852, L25 (2018)] and also in good agreement with constraints on mass and radius measurement for PSR $\mathrm{J}0740+6620$ (NICER) [Riley et al., Astrophys. J. Lett. 918, L27 (2021); Miller et al., Astrophys. J. Lett. 918, L28 (2021)]. The hybrid EOSs obtained with the NJL model also satisfy astrophysical constraints on the maximum mass of a neutron star from PSR J1614-2230 [Demorest et al., Nature (London) 467, 1081 (2010)]. We also present the results for dimensionless tidal deformability, $\mathrm{\ensuremath{\Lambda}}$ which are consistent with the waveform models analysis of GW170817.

Light mesons and phase structures in μ B -T-eB and μ I -T-eB spaces * *Supported by the National Natural Science Foundation of China (11775165)

Light mesons are investigated in and spaces using a two-flavor NJL model and used to determine chiral symmetry restoration and the pion superfluid phase transition. In space, during the chiral symmetry restoration process, the mass of the pseudo-Goldstone mode increases, with sudden jumps. At the critical end point, the meson exhibits a sharp but continuous mass increase, with a sudden mass jump at the Mott transition. In the nearby first order chiral phase transition region, we observe two mass jumps, one induced by the Mott transition and the other by the quark mass jump. The mass of the Higgs mode σ first decreases and then increases with chiral symmetry restoration, only showing a jump at the first order chiral phase transition. We plot a chiral phase diagram in terms of the change in quark mass, the Mott transition of the pseudo-Goldstone mode , and the minimum mass of the Higgs mode σ. Owing to explicit breaking of chiral symmetry in the physical case, the chiral restoration phase boundaries on the plane from the order parameter side and meson side are different. The and σ mass jumps will be helpful to the experimental search for the chiral phase diagram and critical end point. On the plane, the competition between the pion superfluid phase transition and chiral symmetry restoration under magnetic fields is studied in terms of the Goldstone mode and pseudo-Goldstone mode . In contrast to the two mass jumps of in the first order chiral phase transition region, the meson displays several mass jumps in the chiral crossover region. At the critical end point, also has sharp but continuous mass change, with a mass jump at the Mott transition. The isospin symmetry is strict, and the pion superfluid phase transition is uniquely determined by the massless Goldstone mode . The separation of chiral restoration and the pion superfluid phase boundaries is enhanced by the external magnetic field.

Pion damping width and pion spectral function in hot pion gas

The temperature behavior of the pion width in the hadronic phase is investigated in the framework of the Nambu–Jona–Lasinio (NJL) model. The contribution to the width from the pion–pion collision is considered with a scalar sigma-meson as an intermediate state. It is shown that the pion width significantly broadens at [Formula: see text][Formula: see text]GeV. Using the two-step iteration method, suggested by Kadanoff and Baym, the pion spectral function in a hot pion gas is calculated at different temperatures.

Effects of the quark anomalous magnetic moment in the chiral symmetry restoration: magnetic catalysis and inverse magnetic catalysis

In this work, we consider the effect of a constant anomalous magnetic moment (AMM) of quarks in the SU(2) Nambu–Jona-Lasinio model in the mean field approximation. To this end, we use the Schwinger ansatz, which represents a linear magnetic field term in the Lagrangian. A regularization method inspired in the vacuum magnetic regularization (VMR) is adopted to avoid ultraviolet divergences. Our results indicate a smooth decrease of the pseudocritical temperature and quark condensates for magnetic fields B le 0.1 GeV^2 when a sizable AMM is considered. We found only a small window for Inverse Magnetic Catalysis (IMC), in contradiction with NJL predictions made in the literature. For a low value of AMM, we observe for all ranges of magnetic fields considered that the pseudocritical temperature increases with the magnetic field, indicating only Magnetic Catalysis (MC). In our approach, for nonvanishing quark AMM, the chiral symmetry restoration happens always as a smooth crossover and never turns into a first order phase transition.

The Hadron-quark Crossover in Neutron Star within Gaussian Process Regression Method

The equations of state of the neutron star at the hadron-quark crossover region are interpolated with the Gaussian process regression (GPR) method, which can reduce the randomness of present interpolation schemes. The relativistic mean-field (RMF) model and Nambu–Jona-Lasinio (NJL) model are employed to describe the hadronic phase and quark phase, respectively. In the RMF model, the coupling term between ω and ρ mesons is considered to control the density-dependent behaviors of symmetry energy, i.e., the slope of symmetry energy L. Furthermore, the vector interaction between quarks is included in the NJL model to obtain the additional repulsive contributions. Their coupling strengths and the crossover windows are discussed in the present framework under the constraints on the neutron star from gravitational-wave detections, massive neutron star measurements, mass–radius simultaneous observation of the NICER Collaboration, and the neutron skin thickness of 208Pb from PREX-II. It is found that the slope of symmetry energy, L, should be around 50−90 MeV and the crossover window is (0.3, 0.6) fm−3 with these observables. Furthermore, the uncertainties of neutron star masses and radii in the hadron-quark crossover regions are also predicted by the GPR method.

E+e– → a1π, e+e– → K1(1270)K, and e+e– → K1(1400)K Processes within the Chiral Quark Nambu–Jona-Lasinio Model

e+e– → a1π, e+e– → K1(1270)K, and e+e– → K1(1400)K Processes within the Chiral Quark Nambu–Jona-Lasinio Model