Aspects of the chiral crossover transition in (2+1)-flavor QCD with M\"{o}bius domain-wall fermions

The non-singlet part of the chiral symmetry in QCD with two light flavors is known to be restored through a crossover transition at a pseudo-critical temperature. However, the temperature dependence of the singlet part of the chiral symmetry and whether it is effectively restored at the same temperature is not well understood. Using (2+1)-flavor QCD configurations generated using the M\"{o}bius domain-wall discretization on an $N_\tau=8$ lattice, we construct suitable observables where the singlet and non-singlet chiral symmetries are disentangled in order to study their temperature dependence across the crossover transition. From the peak of the disconnected part of the chiral susceptibility, we obtain a pseudo-critical temperature $T_{pc}=158.7{}_{{}-2.3}^{{}+2.6}$ MeV where the non-singlet part of the chiral symmetry is effectively restored. From a calculation of the topological susceptibility and its temperature dependence we find that the singlet $U_A(1)$ part of the chiral symmetry is not effectively restored at $T<186$ MeV.