Symmetries in high-temperature lattice QCD with (u, d, s, c, b) optimal domain-wall quarks

We investigate the spatial $z$-correlators of meson operators in $N_f=2+1+1+1$ lattice QCD with optimal domain-wall quarks across eight temperatures ranging from 325 to 3250 MeV. The meson operators include a complete set of Dirac bilinears for ten flavor combinations. Our findings reveal a hierarchical restoration of chiral symmetry in QCD with $(u,d,s,c,b)$ quarks, progressing sequentially from $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_A$ to $SU(3{)}_L\times SU(3{)}_R\times U(1{)}_A$, then to $SU(4{)}_L\times SU(4{)}_R\times U(1{)}_A$, and finally to $SU(5{)}_L\times SU(5{)}_R\times U(1{)}_A$ as the temperature increases. Additionally, we explore the emergence of the $SU(2{)}_{CS}$ chiral-spin symmetry and compare the temperature windows for all flavor combinations. Our results indicate that the temperature windows for the emergent $SU(2{)}_{CS}$ symmetry are primarily dominated by the $\bar{u}b$ and $\bar{s}b$ sectors.