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Thermal static Potential at Finite Density in (2+1)-flavor QCD

Jishnu Goswami, Dibyendu Bala, Olaf Kaczmarek

Abstract

We study the thermal static potential for (2+1)-flavor QCD at nonzero density through a Taylor expansion around vanishing chemical potentials. From Taylor expanded Wilson line correlators, we extract the $\hatμ^2$ coefficient of the real and imaginary part of the potential in light and strange flavor channels and in the baryon number and electric charge channels. We observe an enhancement of in-medium screening at intermediate and large separations. The effect is visible in both the real and imaginary parts to the extracted $\hatμ^2$ contribution of the static potentials and provides a first step toward constraining in-medium heavy-quark interactions relevant for the Beam Energy Scan program at RHIC and future FAIR experiments.

Thermal static Potential at Finite Density in (2+1)-flavor QCD

Abstract

We study the thermal static potential for (2+1)-flavor QCD at nonzero density through a Taylor expansion around vanishing chemical potentials. From Taylor expanded Wilson line correlators, we extract the coefficient of the real and imaginary part of the potential in light and strange flavor channels and in the baryon number and electric charge channels. We observe an enhancement of in-medium screening at intermediate and large separations. The effect is visible in both the real and imaginary parts to the extracted contribution of the static potentials and provides a first step toward constraining in-medium heavy-quark interactions relevant for the Beam Energy Scan program at RHIC and future FAIR experiments.

Paper Structure

This paper contains 7 sections, 11 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Lattice action, simulation details, and Wilson-line correlators at nonzero chemical potentials
  3. Wilson-line correlator at nonzero chemical potentials
  4. Potential fitting ansatz and $\hat{\mu}^2$ parameterization
  5. Flow based subtraction of zero density part of static potential $V_0$
  6. Results
  7. Summary and outlook

Figures (5)

  • Figure 1: Second order Taylor expansion coefficient $Y^u_2$ (left) and $Y^s_2$ (right) of the Wilson line correlator, shown as a function of Euclidean time separation $\tau$ at fixed spatial separation $r=1~\rm{fm}$ and temperature $T = 151.92~\rm{MeV}$ for two flow times,$\tau_f/a^2=0.2$ and $0.4$.
  • Figure 2: Second-order Taylor-expansion coefficients of the thermal static potential in the flavor basis. Shown are $(V_2^{u})_{\mathrm{Re}}$, $(V_2^{u})_{\mathrm{Im}}$, $(V_2^{s})_{\mathrm{Re}}$, and $(V_2^{s})_{\mathrm{Im}}$ as functions of the separation $r$ at $T=151.92~\mathrm{MeV}$ for $\tau_f/a^2=0.2$ and $0.4$.
  • Figure 3: Second-order Taylor-expansion coefficients of the thermal static potential in the conserved-charge basis. Shown are $(V_2^{B})_{\mathrm{Re}}$, $(V_2^{B})_{\mathrm{Im}}$, $(V_2^{Q})_{\mathrm{Re}}$, and $(V_2^{Q})_{\mathrm{Im}}$ as functions of the separation $r$ at $T=151.92~\mathrm{MeV}$ for $\tau_f/a^2=0.2$ and $0.4$.
  • Figure 4: Static thermal potential at vanishing chemical potential for two flow times, $\tau_f/a^2=0.2$, $0.4$, at $T=151.92$ MeV. Left: bare potential $V_0(r)$. Right: renormalized potential $V_0^{\rm ren}(r)=V_0(r)-\delta V_0(\tau_f/a^2)$ as a function of separation $r$.
  • Figure 5: Real part of the renormalized static potential in the light quark channel as a function of $\hat{\mu}_u$ for selected separations at temperature $T=151.92~\rm{MeV}$ and flow time $\tau_f/a^2=0.4$. For each separations we compare the leading order(LO) and (LO + NLO) calculations.