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 O(alpha_s^2) in continuum, and analyze the result at various distance scales. At short distances (r << 1/pi T) the behaviour matches that of the gauge-independent zero-temperature potential; on the other hand at large distances (r >> 1/pi T) 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 O(alpha_s^2), finding for pure SU(Nc) 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.

38 pages. v2: reference added, published version. v3: erratum added for sec.5, main results unchanged

References in corpus (16)

• Static quark-antiquark pairs at finite temperature
• Real and imaginary-time $Q\bar{Q}$ correlators in a thermal medium
• Renormalized Polyakov loops in many representations
• Heavy quarkonium in any channel in resummed hot QCD
• Non-relativistic bound states at finite temperature (I): the hydrogen atom
• The Polyakov Loop and its Relation to Static Quark Potentials and Free Energies
• Polyakov loop and correlator of Polyakov loops at next-to-next-to-leading order
• Heavy Quark Potential at Finite Temperature Using the Holographic Correspondence
• Renormalized Polyakov Loop in the Deconfined Phase of SU(N) Gauge Theory and Gauge/String Duality
• The Spatial String Tension and Dimensional Reduction in QCD
• On the smallest screening masses in hot QCD
• Heavy quark medium polarization at next-to-leading order
• Spatial string tension of finite temperature QCD matter in gauge/gravity duality
• Spatial correlators in strongly coupled plasmas
• Static quark anti-quark pair in SU(2) gauge theory
• Free energies of heavy quarks in full-QCD lattice simulations with Wilson-type quark action

Cited by in corpus (53)

• Heavy quarkonium: progress, puzzles, and opportunities
• SU(N) gauge theories at large N
• A novel Bayesian approach to spectral function reconstruction
• Heavy Quarkonium in Extreme Conditions
• Static quark-antiquark potential in the quark-gluon plasma from lattice QCD
• Perturbative Thermal QCD: Formalism and Applications
• Polyakov loop in 2+1 flavor QCD from low to high temperatures
• Production and Elliptic Flow of Dileptons and Photons in the semi-Quark Gluon Plasma
• Quarkonium at finite temperature: Towards realistic phenomenology from first principles
• How Wide is the Transition to Deconfinement?
• Color screening in (2+1)-flavor QCD
• Polyakov loop and correlator of Polyakov loops at next-to-next-to-leading order
• Improved Gauss law model and in-medium heavy quarkonium at finite density and velocity
• Heavy quark potential in quark-gluon Plasma: Deep neural network meets lattice quantum chromodynamics
• Casimir scaling and renormalization of Polyakov loops in large-N gauge theories
• Introductory lectures to large-N QCD phenomenology and lattice results
• Quarkonium in Hot Medium
• Heavy Ion Collisions with Transverse Dynamics from Evolving AdS Geometries
• Time-dependent heavy-quark potential at finite temperature from gauge-gravity duality
• Colour-electric spectral function at next-to-leading order
• Ultraviolet asymptotics of scalar and pseudoscalar correlators in hot Yang-Mills theory
• A first look at Bottomonium melting via a stochastic potential
• Dilepton and photon production in the presence of a nontrivial Polyakov loop
• A hard thermal loop benchmark for the extraction of the nonperturbative $Q\bar{Q}$ potential
• Collisional energy loss above the critical temperature in QCD
• QCD-Thermodynamics using 5-dim Gravity
• Massive vector current correlator in thermal QCD
• Dynamical Locking of the Chiral and the Deconfinement Phase Transition in QCD
• Correlations between perturbation theory and power corrections in QCD at zero and finite temperature
• The Polyakov loop at next-to-next-to leading order
• In-medium P-wave quarkonium from the complex lattice QCD potential
• Renormalization of the cyclic Wilson loop
• Polyakov loop correlator in perturbation theory
• The Heavy Quark Free Energy in QCD and in Gauge Theories with Gravity Duals
• Intermediate distance correlators in hot Yang-Mills theory
• The Polyakov loop in various representations in the confined phase of QCD
• Using Wilson flow to study the SU(3) deconfinement transition
• From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma
• Gravity Dual Corrections to the Heavy Quark Potential at Finite-Temperature
• The force-force-correlator in hot QCD perturbatively and from the lattice
• Static quark correlators and quarkonium properties at non-zero temperature
• Chiral symmetry breaking and confinement effects on dilepton and photon production around $T_c$
• Static meson correlators in 2+1 flavor QCD at non-zero temperature
• Dependence of the static quark free energy on ${\mu }_B$ and the crossover temperature of $N_f=2+1$ QCD
• Renormalization of Loop Functions in QCD
• Effective Field Theories of QCD for Heavy Quarkonia at Finite Temperature
• The in-medium heavy quark potential from quenched and dynamical lattice QCD
• Heavy quark-antiquark free energy and thermodynamics of string-hadron avoided crossings
• Single quark entropy and the Polyakov loop
• Renormalization of Polyakov loops in different representations and the large-N limit
• $q\bar{q}$ Potential at Finite T and Weak Coupling in $\mathcal{N}=4$
• Ultraviolet divergences in the cyclic Wilson loop and their renormalization
• Loop functions in thermal QCD