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

We have studied the transport coefficients as a tool to probe the collision integral appearing in the Boltzmann transport equation. For this purpose, we have estimated the transport coefficients (momentum: η,ζ, heat: κ, and charge: σₑₗ) in the kinetic theory approach with the collision integrals in Bhatnagar-Gross-Krook (BGK) and relaxation-time (RT) approximations and ask whether we can distinguish between the two collision integrals. For example, η gets enhanced while ζ gets reduced with respect to RT. As a corollary, we then investigate the interplay among the aforesaid transport coefficients, viz. fluidity and transition point of QCD medium by evaluating the ratios, η/s and ζ/s, respectively, nature of flow (Reynolds number, RI), sound attenuation (Prandtl number, Pr), and competition between the momentum and charge diffusion (γ), etc. as further plausible tools to decipher the same. With BGK collision integral, the ratios η/s (increase) and ζ/s (decrease) show opposite behavior, whereas Pr, RI, γ, and the ratio ζ/η get reduced with respect to RT. We then examine how a strong magnetic field modulates the impact of the collision integral, which, in a way, explores the dimensionality dependence of the transport phenomena, especially momentum transport because the quark dynamics is effectively restricted to 1D only and only the lowest Landau levels are populated. As a result, η (ζ) gets reduced (amplified), which will have ramifications on the ratios, viz. η/s (ζ/s) becomes smaller (larger), enhancement of Pr, γ, and ζ/η, etc. In this study, the thermomagnetic medium effects have been incorporated by adopting a thermodynamically consistent quasiparticle 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.