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

Abstract: 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.