Shear viscosity of quark matter at finite temperature in magnetic fields

TL;DR

This study investigates how shear viscosity in quark matter varies with temperature and magnetic fields using a modified instanton model, revealing temperature-dependent behaviors and negligible magnetic effects in the chiral-restored phase.

Contribution

It introduces a temperature-modified instanton model combined with the Schwinger method to analyze shear viscosity under strong magnetic fields in quark matter.

Findings

Shear viscosity increases with temperature beyond T_0=170 MeV with TDP parameters.

Shear viscosity decreases beyond T_0 with temperature-independent parameters.

Magnetic field effects on shear viscosity are negligible in the chiral-restored phase.

Abstract

We have applied the Green-Kubo formula to investigate the shear viscosity in the SU(2) light-flavor quark matter at finite temperature under the external strong magnetic field e|B| ~ m^2_pi. For this purpose, we employ the temperature-modified instanton model and the Schwinger method to induce the magnetic field. The quark spectral function with the finite width motivated by the instanton model is adopted to compute the shear viscosity. We find that shear viscosity increases as temperature increases even beyond the transition temperature T_0=170 MeV if temperature-dependent (TDP) model parameters is used. On the other hand, with temperature-independent ones the shear viscosity starts to drop when temperature goes beyond T_0. Although the magnetic field reduces the shear viscosity in terms of the magnetic catalysis, its effects are almost negligible in the chiral-restored phase even for very strong magnetic field, e|B| ~ 10^20 gauss. We also compute the ratio of the shear viscosity and entropy density eta/s. Our numerical results are well compatible with other theoretical results for a wide temperature regions. We obtain the parameterization of the temperature-dependent ratio from our numerical result as eta/s=0.27-0.87/t+1.19/t^2-0.28/t^3 with t = T/T_0 for T=(100 ~ 350) MeV and e|B|=0.