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Register a new userEstimating transport coefficients in hot and dense quark matter
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We compute the transport coefficients, namely, the coefficients of shear and bulk viscosity as well as thermal conductivity for hot and dense quark matter. The calculations are performed within the Nambu- Jona Lasinio (NJL) model. The estimation of the transport coefficients is made using a quasiparticle approach of solving the Boltzmann kinetic equation within the relaxation time approximation. The transition rates are calculated in a manifestly covariant manner to estimate the thermal-averaged cross sections for quark-quark and quark-antiquark scattering. The calculations are performed for finite chemical potential also. Within the parameters of the model, the ratio of shear viscosity to entropy density has a minimum at the Mott transition temperature. At vanishing chemical potential, the ratio of bulk viscosity to entropy density, on the other hand, decreases with temperature with a sharp decrease near the critical temperature, and vanishes beyond it. At finite chemical potential, however, it increases slowly with temperature beyond the Mott temperature. The coefficient of thermal conductivity also shows a minimum at the critical temperature.
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A thermal gradient and/or a chemical potential gradient in a conducting medium can lead to an electric field, an effect known as thermoelectric effect or Seebeck effect. In the context of heavy-ion collisions, we estimate the thermoelectric transport coefficients for quark matter within the ambit of the Nambu-Jona Lasinio (NJL) model. We estimate the thermal conductivity, electrical conductivity, and the Seebeck coefficient of hot and dense quark matter. These coefficients are calculated using the relativistic Boltzmann transport equation within relaxation time approximation. The relaxation times for the quarks are estimated from the quark-quark and quark-antiquark scattering through in-medium meson exchange within the NJL model.
We describe the Mott dissociation of pions and kaons within a Beth-Uhlenbeck approach based on the PNJL model, which allows for a unified description of bound, resonant and scattering states. Within this model we evaluate the temperature and chemical potential dependent modification of the phase shifts both in the pseudoscalar and scalar isovector meson channels for $N_f=2+1$ quark flavors. We show that the character change of the pseudoscalar bound states to resonances in the continuum at the Mott transition temperature is signaled by a jump of the phase shift at the threshold from $pi$ to zero, in accordance with the Levinson theorem. In particular, we demonstrate the importance of accounting for the scattering continuum states, which ensures that the total phase shift in each of the meson channels vanishes at high energies, thus eliminating mesonic correlations from the thermodynamics at high temperatures. In this way, we prove that the present approach provides a unified description of the transition from a meson gas to a quark-gluon plasma. We discuss the occurrence of an anomalous mode for mesons composed of quarks with unequal masses which is particularly pronounced for $K^+$ and $kappa^+$ states at finite densities a a possible mechanism to explain the horn effect for the $K^+/pi^+$ ratio in heavy-ion collisions.
We investigate chiral symmetry breaking and strong CP violation effects in the phase diagram of strongly interacting matter. We demonstrate the effect of strong CP violating terms on the phase structure at finite temperature and densities in a 3-flavor Nambu-Jona-Lasinio (NJL) model including the Kobayashi-Maskawa-tHooft (KMT) determinant term. This is investigated using an explicit structure for the ground state in terms of quark-antiquark condensates for both in the scalar and the pseudoscalar channels. CP restoring transition with temperature at zero baryon density is found to be a second order transition at $theta = pi$ while the same at finite chemical potential and small temperature turns out to be a first order transition. Within the model, the tri-critical point turns out to be $(T_c,mu_c)simeq(273,94)$ MeV at $theta = pi$ for such a transition.
We present calculations for the shear viscosity of the hot and dense quark-gluon plasma (QGP) using the partonic scattering cross sections as a function of temperature $T$ and baryon chemical potential $mu_B$ from the dynamical quasiparticle model (DQPM) that is matched to reproduce the equation of state of the partonic system above the deconfinement temperature $T_c$ from lattice QCD. To this aim we calculate the collisional widths for the partonic degrees of freedom at finite $T$ and $mu_B$ in the time-like sector and conclude that the quasiparticle limit holds sufficiently well. Furthermore, the ratio of shear viscosity $eta$ over entropy density $s$, i.e. $eta/s$, is evaluated using these collisional widths and are compared to lQCD calculations for $mu_B$ = 0 as well. We find that the ratio $eta/s$ is in agreement with the results of calculations within the original DQPM on the basis of the Kubo formalism. Furthermore, there is only a very modest change of $eta/s$ with the baryon chemical $mu_B$ as a function of the scaled temperature $T/T_c(mu_B)$.
An important first step in the program of hadronization of chiral quark models is the bosonization in meson and diquark channels. This procedure is presented at finite temperatures and chemical potentials for the SU(2) flavor case of the NJL model with special emphasis on the mixing between scalar meson and scalar diquark modes which occurs in the 2SC color superconducting phase. The thermodynamic potential is obtained in the gaussian approximation for the meson and diquark fields and it is given the Beth-Uhlenbeck form. This allows a detailed discussion of bound state dissociation in hot, dense matter (Mott effect) in terms of the in-medium scattering phase shift of two-particle correlations. It is shown for the case without meson-diquark mixing that the phase shift can be separated into a continuum and a resonance part. In the latter, the Mott transition manifests itself by a change of the phase shift at threshold by pi in accordance with Levinsons theorem, when a bound state transforms to a resonance in the scattering continuum. The consequences for the contribution of pionic correlations to the pressure are discussed by evaluating the Beth-Uhlenbeck equation of state in different approximations. A similar discussion is performed for the scalar diquark channel in the normal phase. Further developments and applications of the developed approach are outlined.
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