Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD

TL;DR

This study investigates the symmetry properties of spatial meson correlators in high-temperature lattice QCD across multiple flavors and temperatures, revealing hierarchical symmetry restoration and flavor-dependent emergence of approximate symmetries.

Contribution

It extends previous work by analyzing six-flavor meson correlators, demonstrating hierarchical symmetry restoration and flavor sector influences on symmetry emergence at high temperatures.

Findings

Hierarchical restoration of chiral symmetries from SU(2) to SU(4) with increasing temperature.

Temperature windows for approximate SU(2)_{CS} symmetry are dominated by heavy flavor sectors.

Correlators show flavor-dependent symmetry patterns at temperatures up to 1540 MeV.

Abstract

The spatial $z$-correlators of meson operators in $N_f=2+1+1$ lattice QCD with optimal domain-wall quarks at the physical point are studied for seven temperatures in the range of 190-1540 MeV. The meson operators include a complete set of Dirac bilinears (scalar, pseudoscalar, vector, axial vector, tensor vector, and axial-tensor vector), and each for six flavor combinations ($\bar u d$, $\bar u s$, $\bar s s$, $\bar u c$, $\bar s c$, and $\bar c c$). In Ref. \cite{Chiu:2023hnm}, we focused on the meson correlators of $u$ and $d$ quarks, and discussed their implications for the effective restoration of $SU(2)_L \times SU(2)_R$ and $U(1)_A$ chiral symmetries, as well as the emergence of approximate $SU(2)_{CS}$ chiral spin symmetry. In this work, we extend our study to meson correlators of six flavor contents, and first observe the hierarchical restoration of chiral symmetries in QCD, from $SU(2)_L \times SU(2)_R \times U(1)_A $ to $SU(3)_L \times SU(3)_R \times U(1)_A $, and to $SU(4)_L \times SU(4)_R \times U(1)_A $, as the temperature is increased from 190 MeV to 1540 MeV. Moreover, we compare the temperature windows for the emergence of the approximate $SU(2)_{CS}$ symmetry in light and heavy vector mesons, and find that the temperature windows are dominated by the $(\bar u c, \bar s c, \bar c c)$ sectors.