Quark Density in Lattice QC$_2$D at Imaginary and Real Chemical Potential

Abstract

We study lattice two-color QCD (QC$_2$D) with two flavors of staggered fermions at imaginary and real quark chemical potential $\mu_q$ and $T>T_c$. We employ various methods of extrapolation of the quark number density from imaginary to real quark chemical potentials $\mu_q$, including series expansions as well as analytic continuation based on phenomenological models, and study their accuracy by comparing the results to the lattice data. Below the Roberge-Weiss temperature, $T<T_{RW}$, we find that the cluster expansion model provides an accurate analytic continuation of the baryon number density in the studied range of chemical potentials. On the other hand, the behavior of the reconstructed canonical partition functions indicates that the available models may require corrections at high quark densities. At $T>T_{RW}$ we show that the analytic continuation to the real values of $\mu_q$ based on trigonometric functions works equally well with the conventional method based on the Taylor expansion in powers of $\mu_q$.