Medium effects on the thermal conductivity of a hot pion gas

Abstract

We investigate the effect of the medium on the thermal conductivity of a pion gas out of chemical equilibrium by solving the relativistic transport equation in the Chapman-Enskog and relaxation time approximations. Using an effective model for the ππ cross-section involving ρ and σ meson exchange, medium effects are incorporated through thermal one-loop self-energies. The temperature dependence of the thermal conductivity is observed to be significantly affected.The observation of large elliptic flow of hadrons in heavy ion collisions at RHIC has led to the description of quark-gluon plasma as a nearly perfect fluid [1]. This interpretation is based on the small but finite value of the shear viscosity to entropy density ratio required in a relativistic hydrodynamic description of the collision. The effects of dissipation on the dynamical evolution of matter produced in relativistic heavy ion collisions have thus been a major topic of discussion in recent times [2]. At the microscopic level dissipative phenomena are studied by considering small departures from equilibrium. In kinetic theory the transport of momenta and heat as a result of collisions is quantitatively expressed in terms of coefficients of viscosity and thermal conductivity [3,4]. A large number of studies on the viscous coefficients have been performed in the transport approach. The shear viscosity η has been most commonly discussed followed by the bulk viscosity ζ, both for partonic as well as hadronic systems . The interesting issue concerning the behaviour of the viscosities in the vicinity of the transition from partonic to hadronic matter have also been discussed [1,12,14,15,[18][19][20]. While the value of η/s is expected to go through a minimum near the critical temperature [1, 18], ζ/s is believed to be large or diverging [12,15,19] at or near the transition.The effects of heat flow in heavy ion collisions has received much less attention. This is presumably on account of the fact that the net baryon number in the central rapidity region at the RHIC and LHC is very small. However, at FAIR energies or in the low energy runs at RHIC the baryon chemical potential is expected to be significant and heat conduction by baryons may play a more important role. On the other hand, a thermal system consisting of pions can sustain heat conduction despite the fact that the pions themselves do not carry baryon number [5]. This is due to the fact that the total number of pions in heavy ion collisions is essentially conserved. Pion number changing reactions are not sustained towards the late stages where collisions are mostly elastic and the system undergoes chemical freezeout. As the system expands and cools a pion chemical potential develops in order to keep the pion number fixed. Based on such a scenario a few studies of heat conduction by pions have been carried out. Using the experimental ππ cross-section the thermal conductivity of a pion gas was estimated in [5][6][7] whereas in [22] a unitarized scattering amplitude was employed. The heat conductiv...

Estimating transport coefficients in hot and dense quark matter

“…This is due to the fact that it is possible to have pion scattering in a medium where to number of pions are conserved. This has been the basis of estimating thermal conductivity at zero baryon density [44,49,50] using chiral perturbation theory. We may note here that, since pions are not the elementary degree of freedom in the NJL model, there is no elementary pion-pion interaction within the model.…”

“…[49]. Thermal conductivity has also been calculated for vanishing baryon density but with a conserved pion number in a pionic medium which can be relevant for heavy-ion collision system between kinetic and chemical freeze-out [49,50].…”

Thermal conductivity of hot pionic medium due to pion self-energy for πσ and πρ loops

“…This is because the thermal conduction does not take place very well in the system, where net baryon density is approximately zero. [3][4][5] Most of the hydrodynamical simulations are focused on describing the baryon-free matter, which is expected to be created in the central rapidity region at the RHIC and LHC. However, thermal conductivity definitely demands its attention to describe the expanding fire ball at forward rapidities or at smaller collision energies, such as those at FAIR and in the low-energy runs at RHIC.…”

Medium effects on the relaxation of dissipative flows in a hot pion gas

“…The bulk viscosity ζ is generally much smaller than η as seen in e.g. [14,15]. Consequently, bulk viscosity and thermal conductivity are usually ignored in the set of hydrodynamic equations.…”

“…[13]). Recently, the effect of the medium on the viscosities [14] and thermal conductivity [15] was studied using the Chapman-Enskog approach and significant modification in the temperature dependence of the coefficients was observed.…”