Polyakov loop correlator in perturbation theory

Abstract

We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series reexponentiates into singlet and adjoint contributions. We calculate the order g 7 correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the reexponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first order in the quark-antiquark distance.

Determination of the QCD coupling from the static energy and the free energy

“…II. We use different strategies to handle the residual discretization artifacts, 4 We use perturbative running and decoupling to convert each grid value of αs(M Z , N f = 5) to the corresponding Λ N f =3 MS value, which we use in the analytical expressions of the force, Eqs. (2) and (3).…”

“…At distances much smaller than the inverse temperature rT 1, we can write using pNRQCD [4] F S (r, T ) = V s (r, µ us ) + δF S (r, T, µ us ),…”

“…We use finite temperature lattices with unprecedentedly fine lattice spacing a = 0.00848 fm [3]. The singlet static free energy is again a function of the static quark-antiquark distance and has been calculated on the lattice [3] and perturbatively [4]. The comparison be- tween the two offers a novel and independent method to extract a precise determination of α s .…”

Loop functions at finite temperature from perturbation theory to lattice QCD

“…The condition 1/r πT restricts the validity of the results to short distances. Under these conditions the Polyakov loop correlator, once divided by the Polyakov loop average squared, reads up to order g 6 [26] exp…”

Color screening in 2+1 flavor QCD and at weak coupling

“…Moreover, as discretization errors for r/a 3 due to the breaking of rotational symmetry in V S and F S are similar, ∆ V F S benefits from a strong compensation of errors. ∆ V F S has been calculated in pNRQCD up to O(α 3 s ) [8]. The result reads…”