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

Abstract

We investigate the chemical-potential ($\ensuremath{\mu}$) dependence of static-quark free energies in both the real and imaginary $\ensuremath{\mu}$ regions, performing lattice QCD simulations at imaginary $\ensuremath{\mu}$ and extrapolating the results to the real-$\ensuremath{\mu}$ region with analytic continuation. Lattice QCD calculations are done on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ 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 $\ensuremath{\mu}=i{\ensuremath{\mu}}_{\mathrm{I}}$ is expanded into a Taylor expansion series of $i{\ensuremath{\mu}}_{\mathrm{I}}/T$ up to fourth order and the pure imaginary variable $i{\ensuremath{\mu}}_{\mathrm{I}}/T$ is replaced by the real one ${\ensuremath{\mu}}_{\mathrm{R}}/T$. At real $\ensuremath{\mu}$, the fourth-order term sizably weakens the $\ensuremath{\mu}$ 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 $\ensuremath{\mu}$. For both real and imaginary $\ensuremath{\mu}$, the color-singlet $q\overline{q}$ and the color-antitriplet $qq$ interactions are attractive, whereas the color-octet $q\overline{q}$ and the color-sextet $qq$ interactions are repulsive. The attractive interactions have a stronger $\ensuremath{\mu}/T$ dependence than the repulsive interactions. The color-Debye screening mass is extracted from the color-singlet potential at imaginary $\ensuremath{\mu}$, and the mass is extrapolated to real $\ensuremath{\mu}$ by analytic continuation. The screening mass thus obtained has a stronger $\ensuremath{\mu}$ dependence than the prediction of hard-thermal-loop perturbation theory at both real and imaginary $\ensuremath{\mu}$.