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

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.