Estimating transport coefficients in hot and dense quark matter

Abstract

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.

Bulk viscosity for pion and nucleon thermal fluctuation in the hadron resonance gas model

“…[34] decreases up to T ∼ 0.150 GeV after which a mild increment is observed. Most of the earlier works [20,21,25,27,28,32,[34][35][36][37] based on effective QCD model calculations [20,21,25,27,28] as well as effective hadronic model calculations [32,[34][35][36][37] predicted a decreasing function of ζ/s(T ) in the hadronic temperature domain, which is qualitatively similar with our results (dashed lines). These are not supporting the fact that ζ/s diverges or becomes large near the transition temperature as indicated by Refs.…”

“…Some of them [2,4,5] indicated divergence tendency of ζ/s near transition temperature, some of effective QCD model cal-culations [22][23][24]27] revealed peak structure near transition temperature, whereas most of the effective QCD model calculations [20,21,25,27,28] as well as effective hadronic model calculations [32,[34][35][36][37], including our present work, predict a decreasing function of ζ/s(T ) in the hadronic temperature domain, with few exceptional HRG calculations [33,36]. Our decreasing ζ/s(T, µ B = 0) is representing a strongly coupled picture in the hadronic temperature domain, whose smooth extrapolation to high temperature domain agrees with a weakly coupled picture [19].…”

“…A list of references are [2,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37], where Ref. [19] addressed high temperature perturbative QCD calculations of ζ, Refs.…”

“…[26][27][28] provided the discussions on Linear Sigma Model (LSM) estimation of ζ. These effective QCD model calculations [20][21][22][23][24][25][26][27][28] cover both QGP and hadronic phases while hadronic-model calculations of Refs. [32][33][34][35][36][37] are restricted within hadronic phase only.…”

“…[19] addressed high temperature perturbative QCD calculations of ζ, Refs. [20][21][22][23][24][25] have gone through Nambu-Jona-Lasinio (NJL) model calculations of ζ and Refs. [26][27][28] provided the discussions on Linear Sigma Model (LSM) estimation of ζ.…”