Proper heavy-quark potential from a spectral decomposition of the thermal Wilson loop (熱場の量子論とその応用)

概要

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We propose a non-perturbative and gauge invariant derivation of the static potential between a heavy-quark (Q) and an anti-quark Q^^- at finite temperature. (For a perturbative study see e.g.) This proper potential is defined through the spectral function (SPF) of the thermal Wilson loop and can be shown to satisfy the Schrodinger equation for the heavy QQ^^- 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 Schrodinger equation for heavy QQ^^- can also be checked from the structure of the SPF. To test this idea, quenched QCD simulations on anisotropic lattices (a_σ=4a_τ=0.039fm, N^3_σ×N_τ=20^2×(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. Future directions including the reconstruction of the full spectral structure using the maximum entropy method (MEM) are pointed out and the possibility to non-perturbatively determine real and imaginary part of the proper potential is emphasized.
2010-05-20