Transport coefficients in thermal QCD: A probe to the collision integral

Abstract

We have studied the transport coefficients as a tool to probe the collision integral appeared in the Boltzmann equation. For this purpose, we have estimated the transport coefficients (momentum: \{$\eta$,$\zeta$\}, heat: \{$\kappa$\}, and charge: \{$\sigma_{\rm el}$\}) in the kinetic theory with Bhatnagar-Gross-Krook (BGK) and the collision integral in RTA and ask whether we can distinguish between the two collision integrals. For example, $\eta$ gets enhanced while $\zeta$ gets reduced w.r.t. to RTA. As a corollary, we then investigate the interplay among the aforesaid transport coefficients, {\em viz.} fluidity and transition point of QCD medium by evaluating the ratios, $\eta/s$ and $\zeta/s$, respectively, nature of flow (Reynolds number, RI), sound attenuation (Prandtl number, Pr), and competition between the momentum and charge diffusion ($\gamma$) etc. as further plausible tools to decipher the same. With BGK collision integral, the ratios, $\eta/s$ (increase) and $\zeta/s$ (decrease) shows opposite behavior whereas Pr, RI, $\gamma$ and the ratio $\zeta/\eta$ get reduced w.r.t RTA. We then examine how a strong $B$ modulate the impact of collision integral, which, in a way, explore the dimensionality dependence of the momentum transport because the quark dynamics gets restricted to 1-D only and only the lowest Landau levels are populated. As a result, $\eta$ ($\zeta$) gets reduced (amplified), which will have ramifications on the ratios, {\em viz.} $\eta/s$ ($\zeta/s$) becomes smaller (larger), enhancement of Pr, $\gamma$ and $\zeta/\eta$ etc. In this study, the thermo-magnetic medium effects have been incorporated by adopting a quasi-particle model, where the medium generated masses of the partons have been obtained from the pole of their resummed propagators calculated using perturbative thermal QCD in strong $B$.