Static Quark-Antiquark Potential in the Quark-Gluon Plasma from Lattice QCD

We present a state-of-the-art determination of the complex valued static quark-antiquark potential at phenomenologically relevant temperatures around the deconfinement phase transition. Its values are obtained from nonperturbative lattice QCD simulations using spectral functions extracted via a novel Bayesian inference prescription. We find that the real part, both in a gluonic medium, as well as in realistic QCD with light $u$, $d$, and $s$ quarks, lies close to the color singlet free energies in Coulomb gauge and shows Debye screening above the (pseudo)critical temperature $T_c$. The imaginary part is estimated in the gluonic medium, where we find that it is of the same order of magnitude as in hard-thermal loop resummed perturbation theory in the deconfined phase.

Figure 1

Spectral reconstruction: on-axis Wilson line correlator data (top) at $N_{\tau }=24$ and (bottom) the spectral functions obtained by the new Bayesian reconstruction method.

Figure 2

Gluonic medium. Top: the shifted real part of the static interquark potential (open symbols) compared to the color singlet free energies (gray circles). Error bars represent statistical uncertainty; error bands include also systematics (see main text). Bottom: $\mathrm{Im}[V]$ (symbols) shifted and compared to the HTL predictions (solid lines).

Figure 3

Quark-gluon plasma: the real part of the static interquark potential (open symbols) compared to the color singlet free energies in Coulomb gauge (gray circles).