Dimensionally regularized Polyakov loop correlators in hot QCD

Abstract

A popular observable in finite-temperature lattice QCD is the so-called singlet quark-antiquark free energy, conventionally defined in Coulomb gauge. In an effort to interpret the existing numerical data on this observable, we compute it at order \( \mathcal{O}\left( {\alpha_s^2} \right) \) in continuum, and analyze the result at various distance scales. At short distances (r ≪ 1/πT) the behaviour matches that of the gauge-independent zero-temperature potential; on the other hand at large distances (r ≫ 1/πT) the singlet free energy appears to have a gauge-fixing related power-law tail. At infinite distance the result again becomes physical in the sense that it goes over to a gauge-independent disconnected contribution, the square of the expectation value of the trace of the Polyakov loop; we recompute this quantity at \( \mathcal{O}\left( {\alpha_s^2} \right) \), finding for pure SU(N c ) a different non-logarithmic term than in previous literature, and adding for full QCD the quark contribution. We also discuss the value of the singlet free energy in a general covariant gauge, as well as the behaviour of the cyclic Wilson loop that is obtained if the singlet free energy is made gauge-independent by inserting straight spacelike Wilson lines into the observable. Comparisons with lattice data are carried out where possible.