Static quark anti-quark interactions in zero and finite temperature QCD. I. Heavy quark free energies, running coupling and quarkonium binding

TL;DR

This work analyzes heavy quark interactions in 2-flavor QCD by computing zero-temperature heavy quark potentials and finite-temperature quark–antiquark free energies across color channels. It introduces and leverages the qq running coupling $\alpha_{qq}(r,T)$, renormalizes free energies through a plateau $F_\infty(T)$, and extracts a non-perturbative Debye mass $m_D(T)$ to characterize color screening above $T_c$. By defining scales $r_{med}$ and $r_{max}$, the study distinguishes short-distance vacuum-like behavior from medium-modified interactions and connects these to quarkonium binding, suggesting $J/\psi$ may survive near $T_c$ while $\chi_c$ and $\psi'$ are suppressed. The results indicate strong non-perturbative effects near the transition with progressively perturbative-like behavior at higher temperatures, and they provide essential inputs for modeling quarkonium in the quark-gluon plasma. Overall, the paper advances a non-perturbative, lattice-based framework to relate heavy-quark observables to screening, string breaking, and renormalization phenomena in finite-temperature QCD with dynamical quarks.

Abstract

We analyze heavy quark free energies in 2-flavor QCD at finite temperature and the corresponding heavy quark potential at zero temperature. Static quark anti-quark sources in color singlet, octet and color averaged channels are used to probe thermal modifications of the medium. The temperature dependence of the running coupling, $α_{qq}(r,T)$, is analyzed at short and large distances and is compared to zero temperature as well as quenched calculations. In parts we also compare our results to recent findings in 3-flavor QCD. We find that the characteristic length scale below which the running coupling shows almost no temperature dependence is almost twice as large as the Debye screening radius. Our analysis supports recent findings which suggest that $χ_c$ and $ψ\prime$ are suppressed already at the (pseudo-) critical temperature and thus give a probe for quark gluon plasma production in heavy ion collision experiments, while $J/ψ$ may survive the transition and will dissolve at higher temperatures.

Figures (13)

• Figure 1: (a) The color singlet quark anti-quark free energies, $F_1(r,T)$, at several temperatures close to the phase transition as function of distance in physical units. Shown are results from lattice studies of $2$-flavor QCD. The solid line represents in each figure the $T=0$ heavy quark potential, $V(r)$. The dashed error band corresponds to the string breaking energy at zero temperature, $V(r_{\text{breaking}})\simeq1000-1200$ MeV, based on the estimate of the string breaking distance, $r_{\text{breaking}}\simeq1.2-1.4$ fm Pennanen:2000yk. (b) The color averaged free energy, $F_{\bar{q} q}(r,T)$, normalized such that $F_{av}(r,T)\equiv F_{\bar{q} q}(r,T)-T\ln9$Kaczmarek:2002mc approaches the heavy quark potential, $V(r)$ (line), at the smallest distance available on the lattice. The symbols are chosen as in (a).
• Figure 2: (a) The heavy quark potential at $T=0$ from Karsch:2000kv obtained from 2-flavor QCD lattice simulations with quark masses $ma=0.1$ for different values of the lattice coupling $\beta$. Fig. 2(b) shows an enlargement of the short distance distance regime. The data are matched to the bosonic string potential (dashed line) at large distances. Included is also the fit to the Cornell form (solid line) given in Eq. (\ref{['t=0ansatz']}). Note here that the heavy quark potential from quenched lattice QCD and the string model potential coincide already at $r\sqrt{\sigma}\;\hbox{$>$$\sim$}\;0.8$Necco:2001xgLuscher:2002qv ($r\;\hbox{$>$$\sim$}\;0.4$ fm).
• Figure 3: The short distance part of the running coupling $\alpha_{qq}(r)$ in 2-flavor QCD at zero temperature defined in Eq. (\ref{['alp_qq']}) as function of the distance $r$ (in physical units). The symbols for the different $\beta$-values are chosen as indicated in Fig. \ref{['peik']}(a). The lines are discussed in the text.
• Figure 4: Heavy quark free energies for $2$ flavors of dynamical quarks at a quark mass of $m/T=0.4$ calculated on $16^3\times 4$ lattices. Shown are the free energies in different color channels, the singlet ($F_1$), octet ($F_8$) and color averaged ($F_{\bar{q} q}$) free energies normalized here as discussed in Kaczmarek:2002mc to the zero temperature potential obtained in Sec. \ref{['sect0']} (solid line).
• Figure 5: The running coupling in the $qq$-scheme defined in Eq. (\ref{['alp_rT']}) calculated from derivatives of the color singlet free energies with respect to $r$ at several temperatures as function of distance below and above deconfinement. We also show the corresponding coupling at zero temperature (solid line) from Eq. (\ref{['t=0ansatz']}) and compare the results again to the results in pure gauge theory (thick solid and dashed lines) Necco:2001ghNecco:2001xg.