Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD

Abstract

We investigate the temperature dependence of the shear viscosity ($\eta$) and bulk viscosity ($\zeta$) of the gluon plasma using lattice QCD over the range 0.76--2.25$\,T_c$, extending from below the transition temperature $T_c$ across the transition region and into the deconfined phase. At each temperature, we employ three large, fine lattices, which enables controlled continuum extrapolations of the energy-momentum tensor correlators. Using gradient flow together with a recently developed blocking technique, we achieve percent-level precision for these correlators, providing strong constraints for a model-based spectral analysis. Since the inversion to real-time information is intrinsically ill posed, we extract viscosities by fitting spectral functions whose ultraviolet behavior is matched to the best available perturbative result, while the infrared region is described by a Lorentzian transport peak. The dominant modeling uncertainty associated with the transport peak width is bracketed by varying it over a physically motivated range set by thermal scales. We find that the shear-viscosity-to-entropy-density ratio, $\eta/s$, exhibits a minimum near the transition temperature $T_c$ and increases for $T>T_c$, whereas the bulk-viscosity-to-entropy-density ratio, $\zeta/s$, decreases monotonically over the entire temperature range studied.