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Register a new userSpin polarization and color superconductivity in the Nambu--Jona-Lasinio model at finite temperature
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We investigate the possible existence of spin polarization and color superconductivity in the Nambu--Jona-Lasinio model with a tensor-type interaction at finite density and temperature. The thermodynamic potential is calculated by the functional integral method. Numerical results indicate that at low temperature and quark chemical potential the chiral condensed phase exists, and at intermediate chemical potential the color superconducting phase appears. In addition, depending on the magnitude of the tensor coupling, at large chemical potential and low temperature, a color superconducting phase and a spin polarized phase may coexist while at intermediate temperatures only the spin polarized phase occurs.
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We derive the next-to-leading order correction to the Nambu-Jona-Lasinio model starting from quantum chromodynamics. So, we are able to fix the constants of the Nambu-Jona-Lasinio model from quantum chromodynamics and analyze the behavior of strong interactions at low energies. The technique is to expand in powers of currents the generating functional. We apply it to a simple Yukawa model with self-interaction showing how this has a Nambu-Jona-Lasinio model and its higher order corrections as a low-energy limit. The same is shown to happen for quantum chromodynamics in the chiral limit with two quarks. We prove that a consistent thermodynamic behaviour is obtained as expected for the given parameters.
The effects of meson fluctuations are studied in a nonlocal generalization of the Nambu-Jona-Lasinio model, by including terms of next-to-leading order (NLO) in 1/N_c. In the model with only scalar and pseudoscalar interactions NLO contributions to the quark condensate are found to be very small. This is a result of cancellation between virtual mesons and Fock terms, which occurs for the parameter sets of most interest. In the quark self-energy, similar cancellations arise in the tadpole diagrams, although not in other NLO pieces which contribute at the sim 25% level. The effects on pion properties are also found to be small. NLO contributions from real $pipi$ intermediate states increase the sigma meson mass by $sim 30%$. In an extended model with vector and axial interactions, there are indications that NLO effects could be larger.
Thermodynamic properties of strongly interacting matter are investigated using the Polyakov loop enhanced Nambu$-$Jona-Lasinio model along with some modifications to include the hadrons. Various observables are shown to have a close agreement with the numerical data of QCD on lattice. The advantage of the present scheme over a similar study using a switching function is that here no extra parameters are to be fitted. As a result the present scheme can be easily extended for finite chemical potentials.
We consider the three flavor Nambu-Jona-Lasinio model with the t Hooft interaction incorporating the U(1)_A anomaly. In order to set the coupling strength of the t Hooft term, we employ the topological susceptibility $chi$ instead of the eta meson mass. The value for $chi$ is taken from lattice simulations. We also calculate $chi$ at finite temperature within the model. Comparing it with the lattice data, we extract information about the behavior of the U(1)_A anomaly at finite temperature. We conclude that within the present framework, the effective restoration of the U(1)_A symmetry does not necessarily take place even at high temperature where the chiral symmetry is restored.
We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon number one soliton in a hot quark matter in the NJL model as well as in a hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in mean-field approximation, we find a chiral phase transition from Goldstone to Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence - at finite temperatures not close to the critical one they are less affected than in the cold matter. Whereas the quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, the nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first order phase transition. We solve the B=1 solitonic sector of the NJL model in the presence of an external hot quark and nucleon medium. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of a cold matter. At some critical temperature, which for the nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from the nucleon to the quark matter.
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