Shear Viscosity and Electrical Conductivity of Rotating Nuclear Medium in Hadron Resonance Gas and Nambu-Jona Lasinio Models

Abstract

Motivated by recent observations of spin polarization and alignment in heavy-ion collisions, we study the impact of rotation on the transport properties of strongly interacting matter within kinetic theory in the relaxation time approximation. Our analysis focuses on the anisotropic shear viscosity--parallel ($η_{\parallel}$), perpendicular ($η_{\perp}$), and Hall ($η_{\times}$)--and electrical conductivity--$σ_{\parallel}$, $σ_{\perp}$, and $σ_{\times}$--induced by the Coriolis force in a rotating medium. We employ two approaches: a combined quark-gluon plasma--hadron resonance gas (QGP--HRG) framework and a two-flavor Nambu--Jona-Lasinio (NJL) model. In the QGP--HRG description, noninteracting HRG (massless partonic) degrees of freedom are used below (above) the transition temperature. In the NJL model, rotation enters through spinorial connections in the Lagrangian, and the constituent quark masses are obtained over the full temperature range. Rotation suppresses the chiral condensate and slightly enhances the transport coefficients for phenomenologically relevant angular velocities. Assuming a temperature-dependent angular velocity consistent with standard cooling, we find that $η_{||,\perp,\times}/s$ and $σ_{\perp,\times}/T$ exhibit a valley-like temperature dependence, with reduced magnitudes compared to the isotropic $η/s$ and $σ/T$ obtained without rotation. At zero net baryon density, rotation generates a sizable nondissipative Hall-like conductivity, unlike the case with magnetic fields where baryon and antibaryon contributions cancel.

Figures (12)

• Figure 1: Schematic representation of an off-central HIC with OAM along the z-axis.
• Figure 2: Illustration of rotational patterns of partons in the reaction plane during off-central HIC.
• Figure 3: (Color online) The variation of angular velocity with temperature.
• Figure 4: Ratio of anisotropic shear viscosity components to entropy density as a function of temperature for a constant angular velocity $\Omega = 0.0064$ GeV (blue dash-dot curves) and a temperature-dependent angular velocity $\Omega = \Omega(T)$ (red solid curve), compared with the isotropic shear viscosity in the absence of rotation (green dotted curves). The critical temperature is taken to be 0.17 GeV.
• Figure 5: Constituent quark mass ($M$) as a function of angular velocity ($\Omega$) and temperature ($T$).