Color screening potential at finite density in two-flavor lattice QCD with Wilson fermions

We investigate the chemical-potential (μ) dependence of static-quark free energies in both the real and imaginary μ regions, performing lattice QCD simulations at imaginary μ and extrapolating the results to the real-μ region with analytic continuation. Lattice QCD calculations are done on a 163×4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group-improved Iwasaki gauge action. Static-quark potentials are evaluated from the Polyakov-loop correlation functions in the deconfinement phase. To perform the analytic continuation, the potential calculated at imaginary μ=iμ_I is expanded into a Taylor expansion series of iμ_I/T up to fourth order and the pure imaginary variable iμ_I/T is replaced by the real one μ_R/T. At real μ, the fourth-order term sizably weakens the μ dependence of the potential. At long distance, all of the color-singlet and -nonsinglet potentials tend to twice the single-quark free energy, indicating that the interactions between static quarks are fully color screened for finite μ. For both real and imaginary μ, the color-singlet qq̄ and the color-antitriplet qq interactions are attractive, whereas the color-octet qq̄ and the color-sextet qq interactions are repulsive. The attractive interactions have a stronger μ/T dependence than the repulsive interactions. The color-Debye screening mass is extracted from the color-singlet potential at imaginary μ, and the mass is extrapolated to real μ by analytic continuation. The screening mass thus obtained has a stronger μ dependence than the prediction of hard-thermal-loop perturbation theory at both real and imaginary μ.