Abstract
We compute the topological susceptibility Xt of 2+1-flavor lattice QCD with dynamical Möbius domain-wall fermions, whose residual mass is kept at 1 MeV or smaller. In our analysis, we focus on the fluctuation of the topological charge density in a “slab” sub-volume of the simulated lattice, as proposed by Bietenholz et al. The quark mass dependence of our results agrees well with the prediction of the chiral perturbation theory, from which the chiral condensate is extracted. Combining the results for the pion mass Mπ and decay constant Fπ, we obtain Xt = 0.227(02)(11)M2πF2π at the physical point, where the first error is statistical and the second is systematic.
Highlights
Computing the topological susceptibility, χt, has been a challenging task for lattice QCD
Σ denotes the chiral condensate, l = l3r − l7r + hr1 − hr3 is a combination of the low-energy constants at next-to-leading order (NLO) [8], and Mphys and Fphys are the physical values of the pion mass and decay constant, respectively
We observe the consistency between the L = 32 and L = 48 data, which suggests that the systematics due to the finite volume is well under control
Summary
Χt, has been a challenging task for lattice QCD. Simulating QCD on a sufficiently fine lattice is another challenge, as the global topological charge tends to be frozen along the Monte Carlo history [1] Due to these difficulties, the study of the quark mass dependence of χt and its comparison with the ChPT formula [2,3,4], χt. We employ the Yang-Mills (YM) gradient flow [16,17,18] in order to make the global topological charge close to integers, to remove the UV divergences, and to reduce the statistical noise With these improvements, we achieve good enough statistical precision to investigate the dependence of χt on the sea quark mass. Further details of this work may be found in [20]
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