Hadronic transport coefficients from the linear σ model at finite temperature

Abstract

We investigate general frameworks for calculating transport coefficients for quasiparticle theories at finite temperature. Hadronic transport coefficients are then computed using the linear σ model (LSM). The bulk viscosity over entropy density (ζ /s) is evaluated in the relaxation time approximation (RTA) and the specific shear viscosity (η/s) and static electrical conductivity (σ el /T) are both obtained in the RTA and using a functional variational approach. Results are shown for different values of the scalar-isoscalar hadron vacuum mass with in-medium masses for the interacting fields. The advantages and limitations of the LSM for studies of strongly interacting matter out of equilibrium are discussed and results are compared with others in the literature.

Transport properties of the strongly-interacting Quark-Gluon plasma

“…At vanishing quark chemical potential µ q = 0 we compare our results to the predictions from the AdS/CFT (grey dotted line) [99,202], evaluations from the N f = 2 linear sigma model [199] (dashed-dotted purple line), the DQPM predictions [2] (green dash-dotted line)…”

“…( 158) for the evaluation of the relaxation time. We compare to the results from various models: URQMD [197] (solid green line with circles), PHSD [84] (solid blue line with triangles), SMASH [198] (solid grey line with squares), the N f = 2 linear sigma model [199] (dashed-dotted purple line), the N f = 3 NJL model [81] (dashed magenta line), DQPM [2] (dotted green line). The dashed gray line demonstrates the Kovtun-Son-Starinets bound [99] (η/s) KSS = 1/(4π).…”

“…[111] (blue stars). We compare to predictions from the various models: the kinetic partonic cascade model BAMPS [112] (the dark-green solid line with triangles), the non-conformal holographic EMD model [49] (dashed black line), the DQPM [2] (dotted green line), and below T c = 0.158 GeV we show evaluations from hadronic models: the HRG model within the Chapman-Enskog expansion of the BE [52, 104] (dashed cyan line), the N f = 2 linear sigma model [199] (dashed doted purple line), SMASH [105,114] (solid grey line with squares). The figure is taken from [5].…”

“…EMD model [49] (dashed black line), DQPM [2] (dotted green line), and below T c = 0.158 GeV we show evaluations from hadronic models: HRG model within the Chapman-Enskog expansion of the BE [52,104] (dashed cyan line), N f = 2 linear sigma model [199] (dashed doted purple line), and SMASH [105,114] (solid grey line with squares). The PNJL results for both methods of quark relaxation time predict a similar increase with temperature, which is again due to the increase of the quark densities with temperature.…”

“…4.21 Ratio of specific shear viscosity η/s to the scaled electric conductivity σ Q /T as a function of scaled temperature T /T c for µ q ≥ 0. For µ q = 0 we show the estimations from various models: the QP model [98] (dashed grey line), the DQPM [2] (dotted red line), the AdS/CFT [99,202] (dotted grey line), the N f = 2 linear sigma model [199] (dashed doted purple line). The figure is taken from [5] The scaled baryon diffusion coefficient, κ BB /T 2 (left), and the scaled electric diffusion coefficient, κ QQ /T 2 (right), for a partonic system with constant cross sections, σ tot = 10 mb at µ B = 0 as a function of T from different approaches.…”