Search

In this paper, we study the 2-flavor equation of state of the quantum chromodynamics at zero temperature and finite chemical potentials with a modified Nambu–Jona–Lasinio model, where the beta equilibrium and electric charge neutrality conditions of the system (including u, d quarks, electrons and muons) are considered. The related chiral phase transition is also discussed in this paper. For comparison, we show the results with four different parameter sets, and find only quantitative differences. As chemical potential increases, the crossover instead of first-order chiral phase transition happens. Finally, we calculate the binding energy per baryon for different parameter sets, and find that the 2-flavor quark system with a smaller G 1 (or a larger m) possesses the lower binding energy per baryon, indicated to be more stable than the other case. [ABSTRACT FROM AUTHOR]

We present a detailed study concerning a new physics scenario involving four fermion operators of the Nambu-Jona-Lasinio type characterized by a strong-coupling ultraviolet fixed point where composite particles are formed as bound states of elementary fermions at the scale Λ = O TeV . After implementing the model in the Universal FeynRules Output format, we focus on the phenomenology of the scalar leptoquarks at the LHC and the High-Luminosity option. Leptoquark particles have undergone extensive scrutiny in the literature and experimental searches, primarily relying on pair production and, more recently, incorporating single, Drell-Yan t-channel, and lepton-induced processes. This study marks, for the first time, the examination of these production modes at varying jet multiplicities. Novel mechanisms emerge, enhancing the total production cross section. A global strategy is devised to capture all final state particles produced in association with leptoquarks or originating from their decay, which we termed "exclusive", in an analogy to the nomenclature used in nuclear reactions. The assessment of the significance in current and future LHC runs, focusing on the case of a leptoquark coupling to a muon–c quark pair, reveals greater sensitivity compared to ongoing searches. Given this heightened discovery potential, we advocate the incorporation of exclusive leptoquark searches in future investigations at the LHC. [ABSTRACT FROM AUTHOR]

Quark–Gluon plasma driven by the strong force is subject to the conservativeness of the baryon number, net electric charge, strangeness, etc. However, the fluctuations around their mean values at specific temperatures and chemical potentials can provide viable signals for the production of Quark–Gluon plasma. These fluctuations can be captured theoretically as moments of different orders in the expansion of pressure or the thermodynamic potential of the system under concern. Here, we look for possible explanations in the methodologies used for capturing them by using the framework of the Polyakov–Nambu–Jona-Lasinio (PNJL) model under the 2 + 1 flavor consideration with mean-field approximation. The various quantities thus explored can act to signify meaningfully near the phase transitions. Justifications are also made for some of the quantities capable of serving necessarily under experimental scenarios. Additionally, variations in certain quantities are also made for the different collision energies explored in the high-energy experiments. Rectification of the quantitative accuracy, especially in the low-temperature hadronic sector, is of prime concern, and it is also addressed. It was found that most of the observables stay in close proximity with the existing lattice QCD results at the continuum limit, with some artifacts still remaining, especially in the strange sector, which needs further attention. [ABSTRACT FROM AUTHOR]

We derive a Nambu–Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories, providing a set of Dyson–Schwinger equations in differential form. In the local case, we obtain closed-form solutions in the simplest case of the scalar field and extend it to the Yang–Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang–Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson–Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive a gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g., for quantum chromodynamics at lower energies.

Matter prevailing during the early stages of the Universe or under extreme conditions in high-energy heavy-ion experiments supposedly possesses a rich phase structure. During the evolution of such a system, the complicated pictures of transitions among various phases are studied as part of hydrodynamics. This system, on most occasions, is considered to be non-viscous. However, various theoretical studies reveal the importance of incorporating viscous effects into the analysis. Here, the paper discusses the behavioral patterns of transport coefficients with varying temperatures and chemical potentials to obtain a qualitative, if not quantitative, picture of the same. Discussions are also shared regarding their impacts on such an exotic system for different energies, as explored in the experimental domain. This theoretical analysis, made using the structure of the Polyakov–Nambu–Jona-Lasinio (PNJL) model with a 2+1-flavor quark–antiquark system reveals important aspects of the inclusion of viscous effects in the hydrodynamic studies of QGP. [ABSTRACT FROM AUTHOR]

We derive a Nambu–Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories, providing a set of Dyson–Schwinger equations in differential form. In the local case, we obtain closed-form solutions in the simplest case of the scalar field and extend it to the Yang–Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang–Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson–Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive a gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g., for quantum chromodynamics at lower energies. [ABSTRACT FROM AUTHOR]

A modified Nambu–Jona-Lasinio Model with lattice structure is very instructive. It shows several similar problems and their solutions as the Lattice QCD. We study the limits of the large box size, small cell size and realistic pion mass. In particular, we study the relation of the discrete (bound state) solutions to the physical scattering states, for example the pion–pion scattering. [ABSTRACT FROM AUTHOR]

Large uncertainties in the determinations of the equation of state of dense stellar matter allow for the intriguing possibility that the bulk quark matter in beta equilibrium might be the true ground state of the matter at zero pressure. Also, quarks will form Cooper pairs very readily since the dominant interaction between quarks is attractive in some channels. As a result, quark matter will generically exhibit color superconductivity, with the favored pairing pattern at intermediately high densities being two-flavor pairing. In the light of several possible candidates for such self-bound quark stars, including the very low-mass central compact object in supernova remnant HESS J1731-347 reported recently, we carry out a one-field theoretic model, the Nambu–Jona–Lasinio model, to investigate the stability of the beta-stable two-flavor color superconducting (2SC) phase of quark matter, but find no physically allowed parameter space for the existence of 2SC quark stars. [ABSTRACT FROM AUTHOR]

We study the convergence of the Ginzburg–Landau (GL) expansion in the context of the Bardeen–Cooper–Schrieffer (BCS) theory for superconductivity and the Nambu–Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature T and chemical potential μ. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap Δ and dynamical quark mass M are given by Δconv = π T and |$M_{\rm conv} = \sqrt{\mu ^2 + (\pi T)^2}$|⁠ , respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition. [ABSTRACT FROM AUTHOR]

The violation of the U (1) axial symmetry in QCD is stricter than the chiral S U (2) breaking simply because of the presence of the quantum axial anomaly. If the QCD gauge coupling is sent to zero (the asymptotic free limit, where the U (1) axial anomaly does not exist), the strength of the U (1) axial breaking coincides with that of the chiral S U (2) breaking, which we, in short, call an axial–chiral coincidence. This coincidence is trivial since QCD then becomes a non-interacting theory. Actually, there exists another limit in the QCD parameter space, where an axial–chiral coincidence occurs even with nonzero QCD gauge coupling, which can be dubbed a nontrivial coincidence: it is the case with the massive light quarks (m l ≠ 0) and the massless strange quark ( m s = 0 ) due to the flavor-singlet nature of the topological susceptibility. This coincidence is robust and tied to the anomalous chiral Ward–Takahashi identity, which is operative even at hot QCD. This implies that the chiral S U (2) symmetry is restored simultaneously with the U (1) axial symmetry at high temperatures. This simultaneous restoration is independent of m l (≠ 0) and, hence, is irrespective of the order of the chiral phase transition. In this paper, we discuss how the real-life QCD can be evolved from the nontrivial chiral–axial coincidence limit by working on a Nambu–Jona–Lasinio model with the U (1) axial anomaly contribution properly incorporated. It is shown that, at high temperatures, the large differences between the restorations of the chiral S U (2) symmetry and the U (1) axial symmetry for two light quarks and a sufficiently large current mass for the strange quark are induced by a significant interference of the topological susceptibility. Thus, the deviation from the nontrivial coincidence, which is monitored by the strange quark mass controlling the topological susceptibility, provides a new way of understanding the chiral S U (2) and U (1) axial breaking in QCD. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

We examine the behavior of highly magnetized two‐light‐flavor quark matter within the context of a nonlocal NJL‐type model. This analysis assumes the chiral limit mc=0$$ \left({m}_c=0\right) $$ and incorporates the interaction between fermions and the Polyakov loop. Our calculations utilize a covariant Gaussian form factor. We present phase diagrams on the T−μ$$ T-\mu $$ plane, illustrating different magnetic field strengths. Additionally, we examine the critical endpoint's placement and the de Haas‐Van Alphen transitions within the chiral restored phase, observing their temperature‐dependent characteristics. [ABSTRACT FROM AUTHOR]

The Nambu–Jona‐Lasinio model is known for its simplicity and capacity to reproduce some of the basic characteristics of the quantum chromodynamics phase diagram. However, since it is a nonrenormalizable model, there are regularization issues that should be treated conveniently. This is the case when considering the quark anomalous magnetic moment (AMM) when external constant magnetic fields are present. Regularization procedures based on entangled functions between the magnetic field and the cutoff of the model can predict first‐order phase transitions for chiral symmetry restoration at finite values of magnetic fields and inverse magnetic catalysis. The strengths of magnetic fields explored in NJL model and lattice QCD do not show first‐order phase transition. In the present work, we show that some of the previous results are regularization‐dependent effects and how to handle the divergences using the vacuum magnetic regularization scheme. [ABSTRACT FROM AUTHOR]

We investigate the surface and curvature tensions of three‐flavor cold quark matter in a state of electric charge neutrality and chemical equilibrium under weak interactions, employing the Nambu–Jona–Lasinio model with the inclusion of vector interactions. To account for finite‐size effects we adopt the multiple‐reflection expansion framework and present our results for various input parameters. Our results indicate that both surface and curvature tensions increase with heightened vector interactions and density. Furthermore, we note that the restoration of chiral symmetry in the strange quark sector leads to a modest reduction in curvature tension and a substantial increase in surface tension. [ABSTRACT FROM AUTHOR]

We have investigated the structural properties of strange quark stars (SQSs) in a modified theory of gravity known as massive gravity. In order to obtain the equation of state (EOS) of strange quark matter, we have employed a modified version of the Nambu–Jona-Lasinio model (MNJL) which includes a combination of NJL Lagrangian and its Fierz transformation by using weighting factors (1 - α) and α. Additionally, we have also calculated dimensionless tidal deformability (Λ) in massive gravity. To constrain the allowed values of the parameters appearing in massive gravity, we have imposed the condition Λ 1.4 M ⊙ ≲ 580. Notably, in the MNJL model, the value of α varies between zero and one. As α increases, the EOS becomes stiffer, and the value of Λ increases accordingly. We have demonstrated that by softening the EOS with increasing the bag constant, one can obtain objects in massive gravity that not only satisfy the constraint Λ 1.4 M ⊙ ≲ 580 , but they also fall within the unknown mass gap region (2.5 M ⊙ - 5 M ⊙). To establish that the obtained objects in this region are not black holes, we have calculated Schwarzschild radius, compactness, and Λ M TOV in massive gravity. [ABSTRACT FROM AUTHOR]

We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology and geometry. We use the discrete topological Dirac operator to define an action for a massless self-interacting topological Dirac field inspired by the Nambu–Jona-Lasinio model. The mass of the network is strictly speaking the mass of this topological Dirac field defined on the network; it results from the chiral symmetry breaking of the model and satisfies a self-consistent gap equation. Interestingly, it is shown that the mass of a network depends on its spectral properties, topology, and geometry. Due to the breaking of the matter–antimatter symmetry observed for the harmonic modes of the discrete topological Dirac operator, two possible definitions of the network mass can be given. For both possible definitions, the mass of the network comes from a gap equation with the difference among the two definitions encoded in the value of the bare mass. Indeed, the bare mass can be determined either by the Betti number β 0 or by the Betti number β 1 of the network. We provide numerical results on the mass of different networks, including random graphs, scale-free, and real weighted collaboration networks. We also discuss the generalization of these results to higher-order networks, defining the mass of simplicial complexes. The observed dependence of the mass of the considered topological Dirac field with the topology and geometry of the network could lead to interesting physics in the scenario in which the considered Dirac field is coupled with a dynamical evolution of the underlying network structure. [ABSTRACT FROM AUTHOR]

We study the possibly-existing molecular pentaquark states with open charm and bottom flavors, i.e., the states with the quark contents c b ¯ q q q and b c ¯ q q q ( q = u , d , s ). We investigate the meson-baryon interactions through the coupled-channel unitary approach within the local hidden-gauge formalism, and extract the poles by solving the Bethe-Salpeter equation in coupled channels. These poles qualify as molecular pentaquark states, which are dynamically generated from the meson-baryon interactions through the exchange of vector mesons. Our results suggest the existence of the Σ c (∗) B (∗) and Σ b (∗) D ¯ (∗) molecular states with isospin I = 1 / 2 , the Ξ c (′ , ∗) B (∗) and Ξ b (′ , ∗) D ¯ (∗) molecular states with isospin I = 0 and I = 1 , as well as the Ω c (∗) B (∗) and Ω b (∗) D ¯ (∗) molecular states with isospin I = 1 / 2 . [ABSTRACT FROM AUTHOR]

In this paper, we employ gauge/gravity duality to investigate the string breaking and melting of doubly-heavy tetraquark that includes two heavy quarks and two light antiquarks in a holographic model at finite temperature. Firstly, four different configurations of QQ q ¯ q ¯ are studied at different separation distances of the heavy quarks at finite temperatures. At high temperature, QQ q ¯ q ¯ will melt at certain distances and the screening distance has been given for different temperatures. As the temperature continues to increase, some configurations of doubly-heavy tetraquark can not exist. Furthermore, we investigate three decay modes of QQ q ¯ q ¯ and compare the potential energy of QQ q ¯ q ¯ with that of QQq at finite temperature. [ABSTRACT FROM AUTHOR]

We have studied the strong decay properties of the recently observed T c s ¯ 0 a (2900) + + / 0 by considering it as a c u d ¯ s ¯ / c d u ¯ s ¯ fully open-flavor tetraquark state with I (J P) = 1 (0 +) . In the framework of QCD sum rules, we have calculated the three-point correlation functions of the two-body strong decay processes T c s ¯ 0 a (2900) + + → D s + π + , D + K + , D s ∗ + ρ + and D s 1 + π + . The full width of T c s ¯ 0 a (2900) + + / 0 is obtained as 161.7 ± 94.8 MeV, which is consistent with the experimental observation. We predict the relative branching ratios as Γ (T → D s π) : Γ (T → D K) : Γ (T → D s ∗ ρ) : Γ (T → D s 1 π) ≈ 1.00 : 1.10 : 0.04 : 0.43 , implying that the main decay modes of T c s ¯ 0 a (2900) + + / 0 state are D s π and DK channels in our calculations. However, the P-wave decay mode D s 1 π is also comparable and important by including the uncertainties. To further identify the nature of T c s ¯ 0 a (2900) + + / 0 , we suggest confirming them in the DK and D s π final states, and measuring the above ratios in future experiments. [ABSTRACT FROM AUTHOR]

We study a lattice Nambu–Jona-Lasinio model with interacting staggered fermions in the Kogut–Susskind Hamiltonian formalism. The model has a discrete chiral symmetry but not the usual continuous chiral symmetry. In a strong coupling regime for the four-fermion interaction, we prove that the mass of the fermions is spontaneously generated at sufficiently low non-zero temperatures in the dimensions ν ≥ 3 of the model and zero temperature in ν ≥ 2 . Due to the phase transition, the discrete chiral symmetry of the model is broken. Our analysis is based on the reflection positivity for fermions and the method of the infrared bound. [ABSTRACT FROM AUTHOR]

A modified Nambu–Jona-Lasinio Model with lattice structure is very instructive. It shows several similar problems and their solutions as the Lattice QCD. We study the limits of the large box size, small cell size and realistic pion mass. In particular, we study the relation of the discrete (bound state) solutions to the physical scattering states, for example the pion–pion scattering.

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the u and d quark-mass differences on gluon and sea quark distribution functions of the pion and kaon in the framework of the Nambu–Jona-Lasino (NJL) model, which is a quark-level chiral effective theory of QCD, with the help of the proper-time regularization scheme to simulate color confinement of QCD. From the analysis, one finds that the charge symmetry (CS) gluon distribution for the pion has a good agreement with the prediction results obtained from the recent lattice QCD simulation and JAM global fit QCD analysis at a higher scale of Q 2 = 5 GeV2. The size of the CSB effects on gluon and sea quark distributions for the pion with the realistic ratios of m u / m d = 0. 5 at Q 2 = 5 GeV2 are, respectively, estimated by 1.3% and 2.0% at x ≃ 1 in comparison with those for m u / m d = 1. 0 , while those for the kaon are approximately about 0.3% and 0.5% at x ≃ 1 , respectively. A remarkable result is found that the CSB effects on gluon distribution for the kaon are smaller than that for the pion, which has a similar prediction result as that for the CS case. [ABSTRACT FROM AUTHOR]

In 1995, Glendenning, Kettner and Weber postulated the existence of a new class of compact stars resembling white dwarfs but containing a small strange quark-matter core surrounded by hadronic layers attaining much higher densities than those found in white dwarfs. In our previous study, we have shown that it could be possible to unmask these so-called strange dwarfs through gravitational-wave observations with future space-based detectors such as the Laser Interferometer Space Antenna. We calculated more realistic equations of state for the hadronic envelope, but the quark core was treated using the simplest MIT bag model. In this paper, we investigate more closely the role of the possibly solid core in the structure and the tidal deformability of strange dwarfs in the full general relativistic framework by considering different models of strange quark matter in the crystalline color -superconducting phase. We find that the effect of the extreme rigidity of the elastic core on the tidal deformability is almost completely canceled by the surrounding hadronic layers. However, in all cases, the tidal deformability of strange dwarfs remains sufficiently lower than that of white dwarfs, to be potentially observable with gravitational waves despite the uncertainties in the strange quark-matter equation of state. [ABSTRACT FROM AUTHOR]

The quark-antiquark components of the U(3) lightest scalar meson nonet are investigated by considering the Nambu-Jona-Lasinio model with flavor-dependent coupling constants that were derived by considering (non-perturbative) gluon exchange. The strange quark effective mass ( M s * ) is varied such that the strangeness content of these scalar mesons can be analyzed further. The neutral states S 0, S 8, and S 3 are adopted as the most relevant quark-antiquark components, respectively, of the σ (500), f 0(980) and A 0 0 (980) mesons. As a result, the mass hierarchy between states S 0 and S 8, and K 0 * (700) − A 0 (980) mesons, can be, respectively, inverted and corrected for quite low values of the strange quark constituent mass. In addition, for some particular values of M s * , the masses of σ (500) and f 0(980) can also be obtained by considering the mixing coupling constant G 08. However, the masses of all the nine mesons are not described simultaneously in a self-consistent procedure and this goes along with the need of non-quark-antiquark states to completely describe their masses. A neutral-meson mixing matrix is defined and the leading mixing angle is found by fitting a correct value of the σ (500) − f 0(980) mass difference. Two different estimates for the strengths of the mixings A 0 0 → f 0 and f 0 → A 0 0 are proposed, leading to somewhat different behaviors. First by assuming leading transitions to intermediary flavor eigenstates and second by considering a dynamical evolution. The results may be in good agreement with experimental values from BESS-III depending on the value of the strange quark effective mass. [ABSTRACT FROM AUTHOR]

This review covers several recent developments in the physics of dense QCD with an emphasis on the impact of multiple phase transitions on astrophysical manifestations of compact stars. To motivate the multi-phase modeling of dense QCD and delineate the perspectives, we start with a discussion of the structure of its phase diagram and the arrangement of possible color-superconducting and other phases. It is conjectured that pair-correlated quark matter in β -equilibrium is within the same universality class as spin-imbalanced cold atoms and the isospin asymmetrical nucleonic matter. This then implies the emergence of phases with broken space symmetries and tri-critical (Lifshitz) points. The beyond-mean-field structure of the quark propagator and its non-trivial implications are discussed in the cases of two- and three-flavor quark matter within the Eliashberg theory, which takes into account the frequency dependence (retardation) of the gap function. We then construct an equation of state (EoS) that extends the two-phase EoS of dense quark matter within the constant speed of sound parameterization by adding a conformal fluid with a speed of sound c conf. = 1 / 3 at densities ≥ 10 n sat , where n sat is the saturation density. With this input, we construct static, spherically symmetrical compact hybrid stars in the mass–radius diagram, recover such features as the twins and triplets, and show that the transition to conformal fluid leads to the spiraling-in of the tracks in this diagram. Stars on the spirals are classically unstable with respect to the radial oscillations but can be stabilized if the conversion timescale between quark and nucleonic phases at their interface is larger than the oscillation period. Finally, we review the impact of a transition from high-temperature gapped to low-temperature gapless two-flavor phase on the thermal evolution of hybrid stars. [ABSTRACT FROM AUTHOR]

Corrections to the Wess–Zumino–Witten anomaly caused by the explicit breaking of the chiral symmetry are studied using the effective meson Lagrangian based on the Nambu–Jona-Lasinio model with the simultaneous expansion in derivatives, current quark masses, and 1/Nc powers. The leading contribution and the first correction for the amplitudes of the π0, η, η' → γγ decays and the contact term in the amplitudes have been calculated. The results are compared with similar 1/Nc chiral perturbation calculations and existing experimental data. [ABSTRACT FROM AUTHOR]

We investigate the combined finite-size and thermo-magnetic effects on the properties of the quark matter, in the context of the two-flavored Nambu–Jona-Lasinio model. In particular, by using the mean-field approximation and the Schwinger proper time method in a toroidal topology with periodic or antiperiodic conditions, we evaluate the chiral phase transition, the constituent quark mass and the thermal and spatial susceptibilities under the change of the size, temperature and strength of external magnetic field. To take into account the inverse magnetic catalysis phenomenon, we make use of a recently proposed magnetized coupling constant. The findings suggest that the observables are strongly affected by the variation of the variables and also by the periodicity of the boundary conditions, with the final outcomes depending on the balance of these competing phenomena. [ABSTRACT FROM AUTHOR]

It is well known that the gluon anomaly is responsible for the mass of the U(1) Goldstone boson. It is also manifested in the properties of pseudo-Goldstone states: the gluon anomaly in the next order of the 1/Nc expansion induces interactions violating the Zweig rule. A necessary condition for this is the explicit breaking of the chiral symmetry by the masses of light quarks. One of the physical consequences is that the η–η' mixing does not affect the amplitude. Another consequence is the suppression of the first 1/Nc correction to the η–η' mixing angle. The mechanism of such suppression is discussed in detail. The conclusions are based on the 1/Nc expansion and the effective meson Lagrangian of the Nambu–Jona-Lasinio model and are compared with the results of the 1/Nc chiral perturbation theory. [ABSTRACT FROM AUTHOR]

In this paper, we study the influence of different regularization schemes on the critical endpoint (CEP) of chiral phase transition within a cubic box with volume V ∼ L 3 . A two-flavor Nambu–Jona-Lasinio model at finite temperature T and chemical potential μ is adopted as the effective model of the strong interacting matter. Due to the finite volume of the box, the momentum integral in gap equation is replaced by discrete summation, and an anti-periodic boundary condition for quark field is applied. We employ the Schwinger's proper time and the Pauli–Villars regularization (PVR) schemes, respectively. It is found that the first-order phase transition line displays an intriguing "staircase" behavior, and eventually disappears as T increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit V → ∞. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively. [ABSTRACT FROM AUTHOR]

A possibility of a pseudovector-type quark–antiquark condensed phase, which leads to a quark spin polarized phase, in the quark matter is investigated taking account of the vacuum effects leading to the chiral symmetry breaking by using the Nambu–Jona–Lasinio model. Also, possible Nambu–Goldstone modes on the pseudovector-type quark–antiquark condensate and the tensor-type quark–antiquark condensate, which also leads to the quark spin polarized phase, are investigated. [ABSTRACT FROM AUTHOR]

We have estimated parallel and perpendicular components of electrical conductivity and shear viscosity of quark matter at finite magnetic field and temperature by using their one-loop Kubo expressions in the framework of Nambu–Jona-Lasinio (NJL) model. At finite magnetic field, a non-trivial medium dependence of those quantities can be found. Previously these NJL-profiles have been addressed in relaxation time approximation, where cyclotron motion of quarks with medium dependent mass plays the key role. With respect to the earlier estimations, the present work provides further enriched profiles via Kubo framework, where field theoretical descriptions of quark transport with medium dependent mass and (Landau) quantized energy have been identified as the key ingredients. Hence the present study can be considered as the complete quantum field theoretical description of the transport coefficients in the framework of NJL model at finite temperature and magnetic field. [ABSTRACT FROM AUTHOR]

We investigate whether the soft mode that becomes massless at the QCD critical point (CP) causes an enhancement of the dilepton production rate (DPR) and electric conductivity around the CP through modification of the photon self-energy using the two-flavor Nambu–Jona-Lasinio model. The modification is described by the so-called Aslamazov–Larkin, Maki–Thompson, and density of states terms, which have been taken into account in our previous study on the DPR near the color-superconducting phase transition, with a replacement of the diquark modes with the soft mode of the QCD CP. We show that the coupling of photons with the soft modes brings about an enhancement of the DPR in the low-invariant-mass region and the conductivity near the CP, which would be observable in relativistic heavy-ion collisions. [ABSTRACT FROM AUTHOR]

The branching fractions of τ lepton decays with the production of strange scalar mesons both in the ground and first radially excited states and are calculated in the extended chiral quark Nambu–Jona-Lasinio model. All mesons are considered as systems. The obtained results should be considered as predictions for future experiments. [ABSTRACT FROM AUTHOR]

In this study, we calculate the pressure of the interacting pion gas using the Beth–Uhlenbeck approach to the relativistic virial expansion with Breit–Wigner phase shifts for the σ - and ϱ -meson resonances. The repulsive phase shift δ 0 2 is taken from the quark interchange model of Barnes and Swanson, which is in very good agreement with the experimental data. In this work we show that the cancellation of the attractive (I = 0) and repulsive (I = 2) isospin channel contributions to the scalar π π interaction in the low-energy region that is known for the vacuum phase shifts also takes place at a finite temperature. This happens despite the strong medium dependence of these phase shifts that enters our model by the temperature dependence of the σ -meson and constituent quark masses, because for these masses the relation M σ (T) ≈ 2 m q (T) holds and the scattering length approximation is valid as long as the strong decay channel σ → π π is open. Exploiting the Nambu–Jona-Lasinio model for describing the dynamical breaking of chiral symmetry in the vacuum and its restoration at a finite temperature, we justify with our approach that the σ -meson should be absent from the hadron resonance gas description at low temperatures because the above cancellation holds. However, since this cancellation breaks down in the vicinity of the hadronization transition, where due to chiral symmetry restoration the decay channel σ → π π closes and the σ -meson becomes a good resonance, the latter should be included into the statistical model description of chemical freeze-out in heavy-ion collisions. [ABSTRACT FROM AUTHOR]

The effect of neutrino oscillations on the thermodynamic characteristics of three-flavor hot quark matter in β-equilibrium that is opaque for neutrinos is examined in terms of the local SU(3) Nambu-Jona-Lasinio (NJL) model which also accounts for the 't Hooft interaction that leads to quark flavor mixing. The thermodynamic characteristics of quark matter are determined for two temperatures, T = 60 and 100 MeV, with neutrino oscillations taken into account. These results are compared with those obtained without taking neutrino oscillations into account. The calculations show that during cooling of quark matter that is opaque to neutrinos, the energy released per unit of baryon charge is 150 ÷ 350 MeV. [ABSTRACT FROM AUTHOR]

The masses of the low-lying scalar mesons are investigated in the three-flavor Nambu–Jona-Lasinio (NJL) model by treating the scalar mesons as composite objects of a quark and an antiquark. It is known that a simple |$\bar{q}q$| picture fails to reproduce the so-called inverse mass ordering for the scalar mesons. Recently a new mechanism to reproduce the observed mass spectrum of the scalar mesons was proposed in a linear sigma model by introducing flavor symmetry breaking induced by the U(1) axial anomaly. Motivated by this proposal, we examine whether this new mechanism also works in the NJL model. By calculating the scalar meson masses, we find that the NJL model reproduces the observed mass ordering with sufficient strength of the new term. With this mechanism, it turns out that the constituent strange quark mass becomes degenerate to that of the up and down quarks if the inverse mass ordering is reproduced. We also discuss the scalar diquark masses to check the consistency of the degeneracy of the constituent quark masses with the light baryon masses. [ABSTRACT FROM AUTHOR]

We study the phase diagram in the T − μ plane for quark matter under the influence of a strong uniform magnetic field B→, in the framework of a non‐local extension of the two‐flavor Polyakov–Nambu–Jona‐Lasinio model. We analyze the deconfinement and chiral symmetry restoration transitions in the mean field approximation. For the considered parameterization, it is found that there is always a critical end point (CEP) in the T − μ plane that separates a first‐order transition line from a smooth crossover. The location of the CEP is studied as a function of the magnetic field. [ABSTRACT FROM AUTHOR]

Properties of strange quark matter (SQM) have been studied as diquark matter with diquark correlation. The dense SQM is under strong magnetic field due to electroweak interaction of quarks. Here it is suggested that u, d, s quarks get correlated to form diquark matter of different flavors. The diquarks are suggested to behave like quasiparticles under the influence of strong magnetic field inside the dense quark matter. In the current work diquarks are described as the composite fermions which behave like quasiparticle under the strong magneticfield in an analogy with the electrons behaving in strong magnetic field. The thermodynamic potential for SQM has been estimated and behavior is studied with respect to chemical potential. The equation of state and the velocity of sound through SQM are also studied. Some interesting observations are made. It is suggested that the composite fermion picture of diquark correlation lowers the binding energy of the system making the SQM a more stable state. [ABSTRACT FROM AUTHOR]

The branching fractions of the decays η ′ → π ρ and ρ → π η are calculated in the chiral quark NJL model. The decays exist due to the mass difference between u - and d -quarks leading to π 0 − η ′ and π 0 − η mixing. Two different approaches are applied: the approximate calculation of this process, taking into account the transitions π 0 − η ′ and π 0 − η explicitly without diagonalization and a more precise approach consisting in the diagonalization of the singlet and octet states leading to the physical fields π 0 , η and η ′ . The obtained results are in satisfactory agreement with current experimental data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The total cross sections for the e+e– → a1π, e+e– → K1(1270)K, and e+e– → K1(1400)K processes have been calculated within the U(3) × U(3) chiral Nambu–Jona-Lasinio model. Since experimental data on these processes are absent, the reported theoretical results can be treated as predictions. [ABSTRACT FROM AUTHOR]

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 ≤ 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. [ABSTRACT FROM AUTHOR]

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The branching fractions of the decays τ → a 1 π ν τ , τ → K 1 π ν τ and τ → K 1 K ν τ are calculated in the framework of the extended U (3) × U (3) 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. [ABSTRACT FROM AUTHOR]

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 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, we study the two-flavor Nambu and Jona-Lasinio (NJL) phase diagrams on the T–μ plane through three regularization methods. In one of these, we introduce an infrared three-momentum cutoff in addition to the usual ultraviolet regularization to the quark loop integrals and compare the obtained phase diagrams with those obtained from the NJL model with proper time regularization and Pauli–Villars regularization. We have found that the crossover appears as a band with a well-defined width in the T–μ plane. To determine the extension of the crossover zone, we propose a novel criterion, comparing it to another criterion that is commonly reported in the literature; we then obtain the phase diagrams for each criterion. We study the behavior of the phase diagrams under all these schemes, focusing on the influence of the regularization procedure on the crossover zone and the presence or absence of critical end points.