Heavy quark potential at finite imaginary chemical potential

TL;DR

This study explores how the static-quark free energies and screening masses depend on chemical potential, using lattice QCD simulations with analytic continuation from imaginary to real chemical potential, revealing stronger $$ dependence than perturbative predictions.

Contribution

The paper introduces a method to analyze the $$ dependence of static-quark potentials at finite imaginary chemical potential and extrapolates results to real $$ using Taylor expansion and analytic continuation.

Findings

4th-order term significantly affects $$ dependence at real $$

Screening mass shows stronger $$ dependence than perturbative theory

Potential and screening mass are successfully extrapolated from imaginary to real $$

Abstract

We investigate chemical-potential ($\mu$) dependence of the static-quark free energies in both the real and imaginary $\mu$ regions, using the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potentials are evaluated from Polyakov-loop correlators in the deconfinement phase and the imaginary $\mu=i\mu_{\rm I}$ region and extrapolated to the real $\mu$ region with analytic continuation. 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. Also, 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 $\mu$.