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

We investigate the chemical-potential (mu) dependence of static-quark free energies in both the real and imaginary mu regions, performing lattice QCD simulations at imaginary mu and extrapolating the results to the real-mu region with analytic continuation. Lattice QCD calculations are done on a 16(3) x 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 mu = i mu(I) is expanded into a Taylor expansion series of i mu(I)/T up to fourth order and the pure imaginary variable i mu(I)/T is replaced by the real one mu(R)/T. At real mu, the fourth-order term sizably weakens the mu 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 mu. For both real and imaginary mu, the color-singlet q (q) over bar and the color-antitriplet qq interactions are attractive, whereas the color-octet q (q) over bar and the color-sextet qq interactions are repulsive. The attractive interactions have a stronger mu/T dependence than the repulsive interactions. The color-Debye screening mass is extracted from the color-singlet potential at imaginary mu, and the mass is extrapolated to real mu by analytic continuation. The screening mass thus obtained has a stronger mu dependence than the prediction of hard-thermal-loop perturbation theory at both real and imaginary mu.