Topological susceptibility in finite temperature QCD with physical $(u/d,s,c)$ domain-wall quarks

Abstract

We perform hybrid Monte-Carlo (HMC) simulation of lattice QCD with $N_f=2+1+1$ domain-wall quarks at the physical point, on the $64^3\times (64,20,16,12,10,8,6)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1$ domain-wall quarks at the physical point. In this paper, we determine the topological susceptibility of the QCD vacuum for $T>T_c\sim 150$ MeV. The topological charge of each gauge configuration is measured by the clover charge in the Wilson flow at the same flow time in physical units, and the topological susceptibility ${\chi }_t(a,T)$ is determined for each ensemble with lattice spacing $a$ and temperature $T$. Using the topological susceptibility ${\chi }_t(a,T)$ of 15 gauge ensembles with three lattice spacings and different temperatures in the range $T\sim 155-516$ MeV, we extract the topological susceptibility ${\chi }_t(T)$ in the continuum limit. To compare our results with others, we survey the continuum extrapolated ${\chi }_t(T)$ in lattice QCD with $N_f=2+1(+1)$ dynamical quarks at/near the physical point, and discuss their discrepancies. Moreover, a detailed discussion on the reweighting method for domain-wall fermion is presented.

Comments: 47 pages, 7 figures, v2: add a section on comparison with other lattice results and an appendix on renormalized chiral condensate, accepted for publication in PRD