Abstract
We compare lattice QCD determinations of topological susceptibility using a gluonic definition from the gradient flow and a fermionic definition from the spectral projector method. We use ensembles with dynamical light, strange and charm flavors of maximally twisted mass fermions. For both definitions of the susceptibility we employ ensembles at three values of the lattice spacing and several quark masses at each spacing. The data are fitted to chiral perturbation theory predictions with a discretization term to determine the continuum chiral condensate in the massless limit and estimate the overall discretization errors. We find that both approaches lead to compatible results in the continuum limit, but the gluonic ones are much more affected by cut-off effects. This finally yields a much smaller total error in the spectral projector results. We show that there exists, in principle, a value of the spectral cutoff which would completely eliminate discretization effects in the topological susceptibility.
Highlights
Topology is essential in understanding the physics of QCD
We have compared the calculation of the topological susceptibility and the chiral condensate using the spectral-projector method to an Oða2Þ-improved gluonic definition using the gradient flow
That in the case of the gradient flow an improved definition could be derived which reduces cutoff effects significantly [63,64]. It would be interesting whether such an improved definition can be found for the here considered topological susceptibility
Summary
Topology is essential in understanding the physics of QCD. Due to the fact that the lattice inherently has different topology from the continuum, an accurate and precise measurement of topological charge is a difficult task in lattice QCD, with a long history of failed attempts and practical and theoretical issues to overcome [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]. In this paper we focus on a fermionic definition using the method of spectral projectors [16,17], but we compare the results to ones from a GF-smeared gluonic definition. Q, on every gauge field configuration, the topological susceptibility, χ, is given by the ensemble average hQ2i, divided by the lattice volume V. It is essentially a quantity which provides a measure of topological charge fluctuations. The coefficient of the mass term, which is a low energy constant (LEC) known as the chiral condensate, Σ, is extracted, from both the spectral-projector definition and the GF-smeared gluonic definition.
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