Shear viscosity due to Landau damping from the quark-pion interaction

Abstract

We have calculated the shear viscosity coefficient η of the strongly interacting matter in the relaxation time approximation, where a quasiparticle description of quarks with their dynamical masses is considered from the Nambu-Jona-Lasinio model. Due to the thermodynamic scattering of quarks with pseudoscalar-type condensate (i.e., pion), a nonzero Landau damping will be acquired by the propagating quarks. This Landau damping may be obtained from the Landau cut contribution of the in-medium self-energy of a quark-pion loop, which is evaluated in the framework of real-time thermal field theory. From the basic idea of the QCD asymptotic freedom at high temperatures and densities, a weakly interacting quark gluon plasma (QGP) is naturally expected to be produced in heavy ion collision (HIC) experiments. However, the experimental data from the BNL Relativistic Heavy Ion Collider (RHIC), especially the measured elliptic flow, indicate that nuclear matter is a strongly interacting liquid instead of a weakly interacting gas. The recent hydrodynamical calculations [1,2] as well as some calculations of kinetic transport theory [3,4] conclude that the matter produced in a HIC must have very small shear viscosity. The shear viscosity of the fluid is generally quantified by the the coefficient η and it physically interprets the ability to transfer momentum over a distance of the mean free path. Hence the lower values of η means the constituents of the matter interact strongly to transfer the momentum easily. Whereas a weakly interacting system must have large η because in this case the momentum transfer between the constituents becomes strenuous.Several theoretical attempts have been taken to calculate the η of the strongly interacting matter at very high [5], intermediate [6,7], and low [8][9][10][11][12][13][14][15][16] temperatures, where some special attention was drawn to the smallness of its original value with respect to its lower bound (η =s 4π, where s is the entropy density), commonly known as the KSS bound [26]. A most interesting fact, which has been added with the recent theoretical understanding of η for strongly interacting matter, is that the η/s may reach a minimum in the vicinity of a phase transition [19][20][21][22][23] (see also [27]) like the liquid-gas phase transition of certain materials, e.g., nitrogen, helium, or water. These investigations demand a better understanding to zoom in on the temperature T dependence of η of the strongly interacting matter near the phase transition. Inspired by this motivation, in this Brief Report we have addressed the η(T ) due to forward and backward scattering of the quark-pion interaction.In the relaxation time approximation, the η of the quark [23] and pion [15,16] medium (for μ = 0) can be expressed aswhereand n π = 1 e βωπ −1 are, respectively, the Fermi-Dirac distribution of the quark and the Bose-Einstein distribution of the pion withπ . The Q and π are Landau damping of the quark and pion, respectively. Following the quasiparticle description of the Nambu-J...

Transport coefficients of two-flavor quark matter from the Kubo formalism

“…The understanding of the elliptic flow observed at heavy-ion collider experiments in terms of dissipative hydrodynamics, in particular the description of the elliptic flow by a low shear viscosity-to-entropy density ratio of the deconfined quark phase stimulated extensive studies of the shear viscosity of strongly interacting matter. Transport coefficients of QCD matter have been investigated using various methods including perturbative QCD [23][24][25][26][27][28][29][30], equilibrium correlation functions within the Kubo formalism [31][32][33][34][35][36][37][38], transport simulations of the Boltzmann equation [39][40][41][42], relaxation-time approxima-arXiv:1702.04291v3 [nucl-th] 11 Jun 2017 tion to the Boltzmann equation [43][44][45][46], lattice methods [47][48][49][50][51][52] and holographic methods [53][54][55][56][57][58] with the main emphasis on the low values of the shear viscosityto-entropy density ratio indicated by the hydrodynamical modeling of heavy-ion collision experiments [1][2][3][4][5]…”

Shear viscosity from Kubo formalism: NJL model study

“…Therefore the one-loop results are restricted to T 210 MeV. We compare our results to those from a kinetic approach using the two-favor NJL model [14] (open circles) and [51] (open triangles). Our values based on the Kubo formalism are larger but feature the same order of magnitude and the same qualitative behavior.…”

“…8. The term involving the Bose distribution describes Landau damping, a process also known from high-T QCD calculations [50], and recently applied to the calculation of the shear viscosity from kinetic theory [51]. In the NJL model Landau damping arises from the scattering of quarks on the mesonic collective modes in the thermal medium.…”

Quark number susceptibility: Revisited with fluctuation-dissipation theorem in mean field theories

“…Interestingly the NJL model has also been studied within the Monte Carlo framework [101,102]. Studies of various transport coefficients in the NJL model framework have also been reported recently [103,104].…”