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

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.

Comments: 46 pages, 19 figures. arXiv admin note: text overlap with arXiv:2302.06073