Transport Coefficients from pQCD to the Hadron Resonance Gas at finite BSQ densities

TL;DR

We address the QCD shear viscosity across the phase diagram at finite BSQ densities by bridging high-temperature pQCD and a low-temperature excluded-volume HRG via an interpolation of the kinematic ratio $(\eta T)/w$, with $w=\varepsilon+p$. The method combines LO and almost-NLO pQCD results with an EV-HRG description and a normalization scheme to ensure consistency at $\mu=0$, producing continuous curves $(\eta T)/w(T,\mu_B,\mu_S,\mu_Q)$. The work demonstrates that NLO corrections are sizeable but converge better at large $\mu/T$, while perturbation theory remains challenging at realistic densities. The resulting $(\eta T)/w$ maps provide inputs for viscous hydrodynamic simulations of heavy-ion collisions over a broad BSQ range, including RHIC Beam Energy Scan and LHC BSQ-fluctuation studies.

Abstract

We calculate the shear viscosity, $η$, in two limits: perturbative QCD and an excluded-volume hadron resonance gas (HRG), at finite BSQ densities. Using an interpolation framework, we connect these regimes. In addition, we present results for (almost) next-to-leading order weak-coupling shear viscosity for QCD at finite $μ_B$, and discuss the convergence of the perturbative series.

Figures (2)

• Figure 1: (a):$\eta T/w$ with $r=0.25$ fm for isentropes; colors indicate isentropes defined by $s/\rho_B$.(b):$\eta T/w$ vs. $T$ for $r=0.25$ fm; three chemical-potential scenarios, dots show interpolation region. Plots taken from Danhoni:2024ewq
• Figure 2: (a): Kinematic shear viscosity vs. $T$ for $\mu=0,3,6$. Dashed: NLO, solid: LO.(b): Ratio $\eta_{\mathrm{NLO}}/\eta_{\mathrm{LO}}$ for three $\mu$ across $T$. $\mu_{\mathrm{EQCD}}=2.7T$. Plots taken from Danhoni:2024ewq.