Lattice QCD computation of the SU(3) string tension critical curve

Abstract

We investigate the critical curve of the string tension $\ensuremath{\sigma}(T)$ as a function of temperature in quenched gauge invariant SU(3) lattice gauge theory. We extract $\ensuremath{\sigma}(T)$ from the color averaged free energy of a static quark-antiquark pair. To compute the free energy, we utilize a pair of gauge invariant Polyakov loop and antiloop correlations and apply the multihit procedure to enhance the signal-to-noise ratio. We find that the string tension departs from the zero temperature ${\ensuremath{\sigma}}_{0}$ at $T\ensuremath{\simeq}0.5{T}_{c}$. We cover the relevant temperature range from $0.5{T}_{c}$ up to the confinement temperature ${T}_{c}$ using 54 different sets of pure gauge lattice configurations with four temporal extensions (4, 6, 8, 12), different $\ensuremath{\beta}$, and a spatial volume of ${48}^{3}$ in lattice units.