The effect of charm quark on the QCD chiral phase diagram

Abstract

We study the influence of charm quark dynamics on the chiral phase structure of Quantum Chromodynamics (QCD) using the recently developed miniDSE scheme of the Dyson-Schwinger equations. By calculating the quark propagator in $2+1$ and $2+1+1$ flavor QCD, we quantify the impact of including the charm quark as a dynamical degree of freedom on the QCD phase diagram. Our results show that the charm quark induces a moderate but noticeable shift to lower chemical potential in the location of the critical endpoint (CEP) by approximately 2-3%. The result in this work indicates that the heavy-flavor dynamics can subtly influence the QCD phase structure and should be taken into account in particular for searching the CEP of QCD.

Figures (4)

• Figure 1: Feynman diagrams of the difference DSE \ref{['eq:diffDSEforGluonProp']}. The black-solid lines with gray-hatched blobs represent the charm quark propagators, and the spiraling lines with gray- or white-hatched blobs denote the gluon propagator in $2+1$ or $2+1+1$ flavors.
• Figure 2: Dimensionless gluon self-energies $\Pi_2(k)$ evaluated from the DSE \ref{['eq:charmQuarkLoop']} (blue-solid line) and the dim. reg. \ref{['eq:AnalyticalCharmLoop']} (Orange-solid line) at the vacuum.
• Figure 3: Top panel: the dressing function $Z_A(k)$ of the gluon propagator in the $2+1$ flavor case (black-solid line), and in the $2+1+1$ flavor case with charm loop evaluated from DSE (red-solid line). Bottom panel: the mass function $M_l(p)$ of the light quark flavors in the $2+1$ flavor case (blue-solid line), and in the $2+1+1$ flavor case with charm loop from DSE (orange-dashed line). These results are obtained by solving the coupled DSEa in the vacuum.
• Figure 4: QCD chiral phase diagram obtained within the current framework (solid lines) with benchmark results of the critical end point (colored marks). The benchmark results come from the Ref. Lu:2023mkn with the miniDSE scheme (yellow triangle), the fRG method Fu:2019hdw, the fRG-DSE scheme with STI construction Gao:2020qsj (green triangle) and with the self-consistent setup Gao:2020fbl (orange triangle), and from the DSE method Gunkel:2021oya. The solid lines correspond to the cases of the $2+1$ flavor (blue line) and the $2+1+1$ flavor with the DSE charm loop \ref{['eq:charmQuarkLoop']} (red line).