Abstract
We compute the topological susceptibility $\chi_t$ of lattice QCD with $2+1$ dynamical quark flavors described by the M\"obius domain wall fermion. Violation of chiral symmetry as measured by the residual mass is kept at $\sim$1 MeV or smaller. We measure the fluctuation of the topological charge density in a `slab' sub-volume of the simulated lattice using the method proposed by Bietenholz {\it et al.} The quark mass dependence of $\chi_t$ is consistent with the prediction of chiral perturbation theory, from which the chiral condensate is extracted as $\Sigma^{\overline{\rm MS}} (\mbox{2GeV}) = [274(13)(29)\mbox{MeV}]^3$, where the first error is statistical and the second one is systematic. Combining the results for the pion mass $M_\pi$ and decay constant $F_\pi$, we obtain $\chi_t = 0.229(03)(13)M_\pi^2F_\pi^2$ at the physical point.
Highlights
The topological susceptibility χt is an interesting quantity that characterizes how many topological excitations are created in the QCD vacuum
the new method using a sub-volume of the simulated lattice
we have computed the topological susceptibility of QCD
Summary
The topological susceptibility χt is an interesting quantity that characterizes how many topological excitations are created in the QCD vacuum. Even if we could simulate QCD on a sufficiently fine lattice, the global topological charge would become frozen along the Monte Carlo history [10] Due to these difficulties, the study of the quark mass dependence and its comparison with the ChPT formula of χt has been very limited, and only some pilot works with dynamical chiral fermions on rather small or coarse lattices [11,12,13,14,15,16,17,18,19] are available. Details of the computation are presented in a separate article [46]
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