Search

Within the framework of the generalized linear sigma model with glueballs recently proposed, 1 , 2 we study the schematic spectroscopy of scalar and pseudoscalar mesons in the SU(3) flavor limit and explore their quark and glue contents. In this framework, for both scalars and pseudoscalars, the two octet physical states are admixtures of quark–antiquark and four-quark components, and the three singlet states contain quark–antiquark, four-quark and glue components. We identify the two scalar octets with a 0 (9 8 0) and a 0 (1 4 5 0) and the two pseudoscalar octets with π (1 3 7) and π (1 3 0 0). We show that, as expected, the light pseudoscalar octet is made dominantly of quark–antiquarks whereas the light scalar octet has a reversed substructure with a dominant four-quark component. The case of singlets is more complex due to surplus of states up to around 2 GeV. We consider all 35 permutations for identifying the three pseudoscalar singlets of our model with three of the seven experimental candidates. Our numerical simulation unambiguously identifies the lightest and the heaviest pseudoscalar singlets with η (5 4 7) and η (2 2 2 5) , respectively, and favors the identification of the middle singlet with either η (1 2 9 5) or η (1 4 0 5) (or, to a lesser extent, with η (1 4 7 5)) and thereby allows a probe of their substructures. We then estimate the quark and glue components and find that the three pseudoscalar singlets (from lightest to heaviest) are mainly of quark–antiquark, four-quark and glue substructure, while the corresponding three scalar singlets (from lightest to heaviest) are of four-quark, quark–antiquark and glue contents. The masses of pure pseudoscalar and scalar glueballs are estimated around 2.0 and 1.6 GeV, respectively. [ABSTRACT FROM AUTHOR]

The (Polyakov) Nambu–Jona‐Lasinio approach is an effective theory for low energies, which shares with Quantumchromodynamics the global symmetries. This approach is easy to handle and allows for analytical results for many of the observables that are of interest for the studies of ultrarelativistic heavy ion collisions but also for the merger and collisions of neutron stars. It allows in particular to study the density and temperature dependence of quark masses and of the masses of mesons and baryons as well as the chiral phase transition. In recent times, this transition came in the focus of interest because it is expected that the upcoming experiments at the Fair (Germany) and Nuclotron‐based Ion Collider fAcility (Russia) facilities will observe a Quark‐Gluon‐Plasma at finite baryon chemical potential. [ABSTRACT FROM AUTHOR]

We study inverse magnetic catalysis in the Nambu–Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis is still the dominant effect at low temperature, the meson dressed quark mass drops down with increasing magnetic field at high temperature due to the dimension reduction of the Goldstone mode in the Pauli–Villars regularization scheme.

The integral parameters of neutron stars are studied taking into account the hadron-quark phase transition, which leads to the formation of a core of quark matter in the central part of a star. The quark matter is described using the local Nambu-Jona-Lasinio (NJL) model. The thermodynamic characteristics of the hadron matter are calculated in the framework of an extended version of the relativistic mean field (RMF) model that includes the contribution of the scalar-isovector δ -meson effective field. A Maxwell construction is used to determine the parameters of the phase transition. It is shown that for the equation of state examined here, stable hybrid stars correspond to a narrow range of values for the central density ρc ∈ (1.71÷1.73]·1015 g/cm3. In our model hybrid stars lie on the same branch as neutron stars, so that a branch with a third family is not formed. The maximum mass of a stable hybrid star is found to be _ Mmax = 2.05M⨀. The configuration with the maximum mass has a quark core with mass Mcore ≈ 10-3 M⨀ and radius Rcore ≈ 0.6 km. [ABSTRACT FROM AUTHOR]

In pursuit of sketching the effective magnetized QCD phase diagram, we find conditions on the critical coupling for chiral symmetry breaking in the Nambu–Jona-Lasinio model in a nontrivial thermo-magnetic environment. Critical values for the plasma parameters, namely, temperature and magnetic field strength for this to happen are hence found in the mean field limit. The magnetized phase diagram is drawn from the criticality condition for different models of the effective coupling describing the inverse magnetic catalysis effect. [ABSTRACT FROM AUTHOR]

In this paper, we firstly combine the 2 + 1 flavors Nambu-Jona-Lasinio (NJL) model with propertime regularization (PTR) to study the equation of state (EOS) and fix the corresponding parameters in 2 + 1 flavors system. Based on this model, we calculate chiral susceptibility and quark number susceptibility and we find a crossover with chemical potential from 220 to 400 MeV. Then we consider the chemical equilibrium and electric charge neutrality conditions in electroweak reactions, which give some constrains of chemical potentials of different quark flavors. At last, we find that the 2 + 1 flavors system is more stable than 2 flavors system after a comparison and discussion of these two cases. [ABSTRACT FROM AUTHOR]

Spontaneous magnetization and magnetic susceptibility originated from the pseudovector-type four-point interaction between quarks are calculated in quark matter with zero temperature and finite quark chemical potential by using the two-flavor Nambu-Jona-Lasinio model. It is shown that both the chiral condensate and spin polarized condensate coexist in a narrow region of the quark chemical potential. And then, it is also shown that, in this narrow region, the spontaneous magnetization appears. Also, the magnetic susceptibility due to quarks with the positive energy is evaluated in the spin polarized phase. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a simple generalization of bosonic string theory in the framework of the theory of fractional variational problems. Specifically, we present a fractional extension of the Polyakov action, for which we compute the general form of the equations of motion and discuss the connection between the new fractional action and a generalization the Nambu-Goto action. Consequently, we analyze the symmetries of the modified Polyakov action and try to fix the gauge, following the classical procedures. Then we solve the equations of motion in a simplified setting. Finally, we present a Hamiltonian description of the classical fractional bosonic string and introduce the fractional light-cone gauge. It is important to remark that, throughout the whole paper, we thoroughly discuss how to recover the known results as an “integer” limit of the presented model. [ABSTRACT FROM AUTHOR]

In this short review we tried to give an outline of investigations of charged pion condensation (PC) in dense baryonic (quark) matter in the framework of effective Nambu−Jona-Lasinio (NJL)-type models. The possibility of charged PC phase in dense quark matter with isospin asymmetry is investigated. First, it is demonstrated that this phase can be realized in the framework of massless NJL model. However, the existence of this phase is enormously fragile to the values of current quark mass and we show that charged PC phase is forbidden in electrically neutral dense quark matter with β -equilibrium when current quark masses are close to their physical value of 5.5 MeV. Nevertheless, then it is shown that in real physical systems there could be conditions promoting the appearance of charged PC phenomenon in dense quark matter; specifically, it was shown that if one takes into consideration the fact that system can have finite size, then a dense charged PC phase can be realized there. It was also demonstrated that the possibility of inhomogeneous pion condensate might allow this phase to appear. In addition, more recently it was revealed that there is another interesting factor that can induce a charged PC phase in dense quark matter even without isospin imbalance. It is a chiral imbalance of the system (non-zero difference between densities of left- and right-handed quarks). These results can be interesting in heavy ion collision experiments, where it is expected to get high baryon densities. It is of interest also in the context of neutron stars, where quark matter might be realized in the core and very high baryon and isospin densities are attained.

We review various connections between condensed matter systems with the Nambu−Jona-Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu−Jona-Lasinio model and nonlinear sigma models enables us to investigate various properties underlying both theories. In this review, we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu−Jona-Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in nonlinear sigma models owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.

In this review, we present of an overview of several interesting properties of QCD at finite imaginary chemical potential and those applications to exploring the QCD phase diagram. The most important properties of QCD at a finite imaginary chemical potential are the Roberge–Weiss periodicity and the transition. We summarize how these properties play a crucial role in understanding QCD properties at finite temperature and density. This review covers several topics in the investigation of the QCD phase diagram based on the imaginary chemical potential.

We explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal bath. We find that the iterative procedure shows a different behavior depending on the regularization scheme used. It is stable and very accurate when a hard cut-off is employed. Nevertheless, for the Paul-Villars and proper time regularization schemes, there exists a value of the coupling constant (different in each case) from where the procedure becomes chaotic and does not converge any longer.

The phase transition from a neutron star to a quark star and its relation to gamma-ray bursts are investigated. A new model: the 2+1 flavor Nambu-Jona-Lasinio (NJL) model with the method of proper-time regularization (PTR) is utilized for the quark phase; while the Relativistic Mean Field (RMF) theory is used for the hadronic phase. The process of phase transition is studied by considering the chemical potential, paying special attention to the phase transition point and the emergence of strange quark matter. Characteristics of compact stars are illustrated, and the energy release during the phase transition is found to be ~1052 erg. [ABSTRACT FROM AUTHOR]

We present an effective field theory model for QCD at finite temperature with quarks. We discuss the mean field theory, the fixing of parameters, and a prediction for the curvature of the critical line. We proceed to write down a pionic theory of fluctuations around the mean field, and discuss how the parameters of this pionic effective theory descend from the model with quarks. [ABSTRACT FROM AUTHOR]

We evaluate nonperturbatively the quark quasidistribution amplitude and the valence quark quasidistribution function of the pion in the framework of chiral quark models, namely the Nambu–Jona-Lasinio model and the Spectral Quark Model. We arrive at simple analytic expressions, where the nonperturbative dependence on the longitudinal momentum of the pion can be explicitly assessed. The model results for the quark quasidistribution amplitude of the pion compare favorably to the data obtained from the Euclidean lattice simulations. The quark distribution amplitude, arising in the limit of infinite longitudinal momentum of the pion, agrees, after suitable QCD evolution, to the recent data extracted from Euclidean lattices, as well as to the old data from transverse lattice simulations. [ABSTRACT FROM AUTHOR]

In this paper, we explore the critical end point in the phase diagram of a thermomagnetic nonlocal Nambu-Jona-Lasinio model in the weak field limit. We work with the Gaussian regulator, and find that a crossover takes place at , . The crossover turns to a first-order phase transition as the chemical potential or the magnetic field increases. The critical end point of the phase diagram occurs at a higher temperature and lower chemical potential as the magnetic field increases. This result is in accordance to similar findings in other effective models. We also find that there is a critical magnetic field, for which a first-order phase transition takes place even at . [ABSTRACT FROM AUTHOR]

For the investigation of back-reactions of composite mesons in the NJL model, a variational path-integral treatment is formulated which yields an effective action A eff [ D σ , D π ; S ] , depending on the propagators D σ , D π of σ − and π −mesons and on the full quark propagator S . The stationarity conditions δ A eff / δ S = 0 , δ A eff / δ D σ = 0 , δ A eff / δ D π = 0 , then lead to coupled Schwinger–Dyson (SD) equations for the quark self-energy and the meson polarization functions. These results reproduce and extend results of the so-called “Φ−derivable” approach and provide a functional formulation for diagrammatic resummations of 1 / N c − corrections in the NJL model. Finally, we perform a low-momentum estimate of the quark and meson loop contributions to the polarization function of the pion and on this basis discuss the Goldstone theorem. [ABSTRACT FROM AUTHOR]

The processes in the threshold domain are considered in the framework of the extended Nambu-Jona-Lasinio model. The channels with the ground , and radially excited , intermediate meson states are taken into account. It is shown that in the process , the probability of the subprocesses with -mesons significantly exceeds the probability of the subprocesses with -mesons, whereas, in the process , - and -channels give approximately equal contributions. The mechanism of this effect is discussed. The radiative decay widths of , , and are calculated. [ABSTRACT FROM AUTHOR]

A new sort of chiral transformations for spin-1 states is obtained as a result of a linearized diagonalization of π a 1 mixing in the effective meson Lagrangian. Using this symmetry argument, we argue that there is no physical distinction between such theory and the theory in which a covariant nonlinear diagonalization is used instead. As an illuminating example, the Nambu–Jona-Lasinio type model with the broken S U ( 2 ) × S U ( 2 ) chiral symmetry in the one-quark-loop approximation is considered. [ABSTRACT FROM AUTHOR]

In this paper, the coupling strength G of the Nambu-Jona-Lasinio (NJL) model is modified by incorporating quark's feedback into the gluon propagator. The modified two-flavor NJL model with the quark-dependent coupling strength is explored. The quark condensate in this framework has a conspicuous agreement with the lattice quantum chromodynamics (QCD) results at finite temperature. Then, it is compared with the original NJL model in both zero (chiral limit) and nonzero current quark mass. The QCD phase diagram and susceptibilities are investigated in the temperature-chemical potential plane. Therefore, the pseudo-critical temperature and the critical end point (CEP) are worked out and compared with original NJL model or lattice QCD results. In addition, the pion mass and decay constant are studied at finite temperature. [ABSTRACT FROM AUTHOR]

To investigate the finite-volume effects on the chiral symmetry restoration and the deconfinement transition for a quantum chromodynamics (QCD) system with (two quark flavors), we apply the Polyakov-loop extended Nambu-Jona-Lasinio model by introducing a chiral chemical potential artificially. The final numerical results indicate that the introduced chiral chemical potential does not change the critical exponents, but shifts the location of critical end point (CEP) significantly; the ratios for the chiral chemical potentials and temperatures at CEP, and , are significantly affected by the system size . The behavior is that increases slowly with when is 'large' and decreases first and then increases with when is 'small.' It is also found that for a fixed , there is a , where the critical end point vanishes and the whole phase diagram becomes a crossover when . Therefore, we suggest that for the heavy-ion collision experiments, which is to study the possible location of CEP, the finite-volume behavior should be taken into account. [ABSTRACT FROM AUTHOR]

The phenomenon of inverse magnetic catalysis of chiral symmetry in QCD predicted by lattice simulations can be reproduced within the Nambu-Jona-Lasinio model if the coupling G of the model decreases with the strength B of the magnetic field and temperature T. The thermo-magnetic dependence of G( B, T) is obtained by fitting recent lattice QCD predictions for the chiral transition order parameter. Different thermodynamic quantities of magnetized quark matter evaluated with G( B, T) are compared with the ones obtained at constant coupling, G. The model with G( B, T) predicts a more dramatic chiral transition as the field intensity increases. In addition, the pressure and magnetization always increase with B for a given temperature. Being parametrized by four magnetic-field-dependent coefficients and having a rather simple exponential thermal dependence our accurate ansatz for the coupling constant can be easily implemented to improve typical model applications to magnetized quark matter. [ABSTRACT FROM AUTHOR]

The π 0 neutral meson pole mass is calculated in a strongly magnetized medium using the SU(2) Nambu–Jona–Lasinio model within the random phase approximation (RPA) at zero temperature and zero baryonic density. We employ a magnetic field dependent coupling, G ( e B ) , fitted to reproduce lattice QCD results for the quark condensates. Divergent quantities are handled with a magnetic field independent regularization scheme in order to avoid unphysical oscillations. A comparison between the running and the fixed couplings reveals that the former produces results much closer to the predictions from recent lattice calculations. In particular, we find that the π 0 meson mass systematically decreases when the magnetic field increases while the scalar mass remains almost constant. We also investigate how the magnetic background influences other mesonic properties such as f π 0 and g π 0 q q . [ABSTRACT FROM AUTHOR]

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. . At this level there is no splitting of the critical temperatures for chiral and deconfinement phase transitions. [ABSTRACT FROM AUTHOR]

We study the cosmological implications of the Nambu-Jona-Lasinio (NJL) model when the coupling constant is field dependent. The NJL model has a four-fermion interaction describing two different phases due to quantum interaction effects and determined by the strength of the coupling constant . It describes massless fermions for weak coupling and a massive fermions and strong coupling, where a fermion condensate is formed. In the original NJL model, the coupling constant is indeed constant, and in this work we consider a modified version of the NJL model by introducing a dynamical field dependent coupling motivated by string theory. The effective potential as a function of the varying coupling (aimed to implement a natural phase transition) is seen to develop a negative divergence, i.e. becomes a 'bottomless well' in certain limit region. Although we explain how an lower unbounded potential is not necessarily unacceptable in a cosmological context, the divergence can be removed if we consider a mass term for the coupling like field. We found that for a proper set of parameters, the total potential obtained has two minima, one located at the origin (the trivial solution, in which the fluid associated with the fields behave like matter); and the other related to the nontrivial solution. This last solution has three possibilities: (1) if the minimum is positive , the system behaves as a cosmological constant, thus leading eventually to an accelerated universe; (2) if the minimized potential vanishes , then we have matter with no acceleration; (3) finally a negative minimum leads an eventually collapsing universe with a flat geometry. Therefore, a possible interpretation as dark matter (DM) or dark energy (DE) is allowed among the behaviors implicated in the model. [ABSTRACT FROM AUTHOR]

Using a three- and four-dimensional Pauli-Villars regularization scheme, we investigate quark-antiquark and diquark condensation in the framework of the Nambu-Jona-Lasinio model. Using the particle Fermi momentum as a cutoff parameter, we study the energy gap width and coherence length for the meson condensate 〈 $$q\bar q$$ 〉. We also study the energy gap width and critical coherence length ( the distance over which there would be no diquark condensation) for the diquark 〈 qq〉 and the dependence on the Fermi momentum. We obtain an estimate of the Fermi momentum value for meson and diquark condensates with an energy gap width of the order of 100 MeV. [ABSTRACT FROM AUTHOR]

The well-known [ρ(770), ω(782)] → γ[π, η] electromagnetic decays have been considered within the Nambu-Jona-Lasinio model taking into account contributions from intermediate transitions between axial-vector and pseudoscalar vertices using the [f1(1285), a1(1260)] → γ[ρ(770), ω(782)] vertices recently obtained within this model. The results are in satisfactory agreement with experimental data. [ABSTRACT FROM AUTHOR]

The NJL model for the octet baryons, using proper time regularisation to simulate some of the features of confinement, is solved self-consistently in nuclear matter. This provides an alternative framework to the MIT bag model which has been used in the quark–meson coupling model. After fitting the parameters of the model to the saturation properties of symmetric nuclear matter the model is used to explore the equation of state of pure neutron matter as well as nuclear matter at densities relevant to heavy ion collisions. With a view to future studies of high mass neutron stars, the binding of hyperons is also explored. [ABSTRACT FROM AUTHOR]

The processes and are calculated in the framework of the extended Nambu-Jona-Lasinio model. The intermediate vector mesons , , and their first radially excited states are taken into account. The obtained results are in satisfactory agreement with the experimental data. The predictions for the cross-sections of the reactions , and were made. [ABSTRACT FROM AUTHOR]

The full and differential widths of the decay are calculated in the framework of the extended Nambu-Jona-Lasinio model.The contributions of the subprocesses with the intermediate vector mesons (770) and (1450) are taken into account. The obtained results are in satisfactory agreement with the experimental data. [ABSTRACT FROM AUTHOR]

We study inverse magnetic catalysis in the Nambu–Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis is still the dominant effect at low temperature, the meson dressed quark mass drops down with increasing magnetic field at high temperature due to the dimension reduction of the Goldstone mode in the Pauli–Villars regularization scheme. [ABSTRACT FROM AUTHOR]

By extending the $$\Phi $$ -derivable approach in the Nambu-Jona-Lasinio model to a finite magnetic field we calculate the properties of pion, $$\sigma $$ , and $$\rho $$ mesons in a magnetic field at finite temperature not only in the quark-antiquark bound state scheme but also in the pion-pion scattering resonant state scenario. Our calculation as a result makes manifest that the masses of $$\pi ^{0}$$ and $$\sigma $$ meson can be nearly degenerate at the pseudo-critical temperature which increases with increasing magnetic field strength, and the $$\pi ^{\pm }$$ mass ascends suddenly at almost the same critical temperature. Meanwhile the $$\rho $$ mesons' masses decrease with the temperature but increase with the magnetic field strength. We also check the Gell-Mann-Oakes-Renner relation and find that the relation can be violated clearly with increasing temperature, and the effect of the magnetic field becomes pronounced around the critical temperature. With different criteria, we analyze the effect of the magnetic field on the chiral phase transition and find that the pseudo-critical temperature of the chiral phase cross, $$T_\mathrm{c}^{\chi }$$ , is always enhanced by the magnetic field. Moreover, our calculations indicate that the $$\rho $$ mesons will get melted as the chiral symmetry has not yet been restored, but the $$\sigma $$ meson does not disassociate even at very high temperature. Particularly, it is the first to show that there does not exist a vector meson condensate in the QCD vacuum in the pion-pion scattering scheme. [ABSTRACT FROM AUTHOR]

The decays τ → (η, η') K-ν are described in the framework of the extended Nambu-Jona-Lasinio model. Both full and differential widths of these decays are calculated. The vector and scalar channels are considered. In the vector channel, the subprocesses with the intermediate K*(892) and K*(1410) mesons play the main role. In the scalar channel, the subprocesses with the intermediate and K(800) and K(1430) mesons are taken into account. The scalar channel gives an insignificant contribution to the full width of the decay τ → η K-ν. The obtained results are in satisfactory agreement with the experimental data. The prediction for the width of the process τ → η′ K-ν is made. [ABSTRACT FROM AUTHOR]

In this paper, we use the two-flavor Nambu-Jona-Lasinio (NJL) model to study the quantum chromodynamics (QCD) chiral phase transition. To deal with the ultraviolet (UV) issue, we adopt the popular proper time regularization (PTR), which is commonly used not only for hadron physics but also for the studies with magnetic fields. This regularization scheme can introduce the infrared (IR) cutoff to include quark confinement. We generalize the PTR to zero temperature and finite chemical potential case use a completely new method, and then study the chiral susceptibility, both in the chiral limit case and with finite current quark mass. The chiral phase transition is second-order in and and crossover at and . Three sets of parameters are used to make sure that the results do not depend on the parameter choice. [ABSTRACT FROM AUTHOR]

We introduce the notion of a universal odd generalized Poisson superalgebra associated with an associative algebra A, by generalizing a construction made in the work of De Sole and Kac [Jpn. J. Math. 8, 1-145 (2013)]. By making use of this notion we give a complete classification of simple linearly compact (generalized) n-Nambu- Poisson algebras over an algebraically closed field of characteristic zero. [ABSTRACT FROM AUTHOR]

We study the three-flavor Nambu–Jona-Lasinio model with various regularization procedures. We perform parameter fitting in each regularization and apply the obtained parameter sets to evaluate various physical quantities, several light meson masses, decay constant and the topological susceptibility. The model parameters are adopted even at very high cutoff scale compare to the hadronic scale to study the asymptotic behavior of the model. It is found that all the regularization methods except for the dimensional one actually lead reliable physical predictions for the kaon decay constant, sigma meson mass and topological susceptibility without restricting the ultra-violet cutoff below the hadronic scale. [ABSTRACT FROM AUTHOR]