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

TL;DR

This study uses lattice QCD simulations with Wilson fermions to analyze how the static-quark free energies and screening masses depend on chemical potential, employing analytic continuation from imaginary to real or the first time.

Contribution

It introduces a method to evaluate  dependence in lattice QCD using analytic continuation from imaginary or two-flavor Wilson fermions, providing new insights into color screening at finite density.

Findings

Color screening mass increases with or both real and imaginary .

At long distances, potentials tend to twice the single-quark free energy.

Attractive interactions are more sensitive to  than repulsive ones.

Abstract

We investigate 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}\times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potential is evaluated from the Polyakov-loop correlation functions in the deconfinement phase. As the analytic continuation, the potential calculated at imaginary \mu=i\mu_{\rm I} is expanded into a Taylor-expansion series of i\mu_{\rm I}/T up to 4th order and the pure imaginary variable i\mu_{\rm I}/T is replaced by the real one \mu_{\rm R}/T. At real \mu, the 4th-order term weakens \mu dependence of the potential sizably. At long distance, all of the color singlet and non-singlet potentials tend to twice the single-quark free energy, indicating that the interactions between heavy quarks are fully color-screened for finite \mu. For both real and imaginary \mu, the color-singlet q{\bar q} and the color-antitriplet qq interaction are attractive, whereas the color-octet q{\bar q} and the color-sextet qq interaction are repulsive. The attractive interactions have 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 stronger \mu dependence than the prediction of the leading-order thermal perturbation theory at both real and imaginary \mu.