Application of Fixed Scale Approach to Static Quark Free Energies in Quenched and 2+1 Flavor Lattice QCD with Improved Wilson Quark Action

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The free energies of static quarks and the Debye screening masses in the quark gluon plasma are studied using Polyakov-line correlation functions in lattice QCD adopting the fixed-scale approach in which temperature is varied without changing the spatial volume and the renormalization factors. We calculate static-quark free energies in various color channels in the high temperature phase up to about 3.5 times the (pseudo-)critical temperature, performing lattice simulations both in quenched and 2+1 flavor QCD. For the quenched simulations, we adopt the plaquette gauge action on anisotropic 20^3×N_t lattices with N_t = 8-26 at the renormalized anisotropy a_s/a_t 〜__- 4. For 2+1 flavor QCD, we adopt the renormalization-group improved Iwasaki gluon action and the non-perturbatively O(a)-improved Wilson quark action on isotropic 32^3×N_t lattices with N_t = 4-12 at m_<PS>/m_V = 0.63 (0.74) for the light (strange) flavors. We find that the color-singlet free energies at high temperatures converge to the zero-temperature static-quark potential evaluated from the Wilson-loop at short distances. This is in accordance with the theoretical expectation that the short distance physics is insensitive to the temperature. At long distances, the free energies approach twice the single-quark free energies, implying that the interaction between static quarks is fully screened. We find that the static-quark free energies for various color channels turn out to be well described by the screened Coulomb form, and the color-channel dependence of the inter-quark interaction can be described by the kinetic Casimir factor inspired from the lowest order perturbation theory. We also discuss comparison with a prediction of the thermal perturbation theory and flavor dependence of the screening masses.

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