Proper heavy-quark potential from a spectral decomposition of the thermal Wilson loop

Abstract

We propose a non-perturbative and gauge invariant derivation of the static potential between a heavy-quark ($Q$) and an anti-quark ($\bar{Q}$) at finite temperature. This proper potential is defined through the spectral function (SPF) of the thermal Wilson loop and can be shown to satisfy the Schrödinger equation for the heavy $Q\bar{Q}$ pair in the thermal medium. In general, the proper potential has a real and an imaginary part,corresponding to the peak position and width of the SPF. The validity of using a Schrödinger equation for heavy $Q\bar{Q}$ can also be checked from the structure of the SPF. To test this idea, quenched QCD simulations on anisotropic lattices ($a_{\sigma }=4a_{\tau }=0.039\mathrm{fm}$, $N_{\sigma }^3\times N_{\tau }=20^2\times (96-32)$) are performed. The real part of the proper potential below the deconfinement temperature ($T=0.78T_c$) exhibits the well known Coulombic and confining behavior. At ($T=2.33T_c$) we find that it coincides with the Debye screened potential obtained from Polyakov-line correlations in the color-singlet channel under Coulomb gauge fixing. The physical meaning of the spectral structure of the thermal Wilson loop and the use of the maximum entropy method (MEM) to extract the real and imaginary part of the proper potential are also discussed.

7 pages, 8 figures, Talk given at the XXVII International Symposium on Lattice Field Theory (LATTICE 2009), July 25-31, 2009, Beijing, China

References in corpus (6)

• Real and imaginary-time $Q\bar{Q}$ correlators in a thermal medium
• Charmonium at high temperature in two-flavor QCD
• Nonperturbative determination of the QCD potential at O(1/m)
• QCD Thermodynamics from the Lattice
• Fixed Scale Approach to Equation of State in Lattice QCD
• Heavy Quark Interactions and Quarkonium Binding

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