Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow

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. *

Comparison of topological charge definitions in Lattice QCD

“…A warning about the usage of field theoretic definitions is provided by our follow-up analysis [92], where we compared the GF definition with the spectral projector one on a wide range of ETMC's N f = 2 + 1 + 1 large-volume ensembles. We found that cut-off effects in the topological susceptibility from the GF are much larger than in the susceptibility from spectral projectors and can be up to 500% at the coarsest lattice spacing of around 0.09 fm.…”

“…However, the cost of this method is significantly larger than the one of the gradient flow. Nevertheless, it might be the method of choice for some applications, since it yields much smaller cut-off effects than the GF, at least in the setup of our follow-up work [92]. Concerning other fermionic definitions, such as the index of the overlap Dirac operator or the spectral flow of the Wilson-Dirac operator, they are theoretically very clean and provide integer values of the topological charge, but their cost is prohibitive for large-scale analyses.…”

Spectral Projectors Method for Staggered Fermions

“…In that case, since non-zerocharge configurations are not efficiently suppressed in the path integral because of the presence of large would-be-zero-modes, topological observables suffer for larger discretization effects compared to the quenched case. Results obtained in [8], instead, show that a spectral fermionic definition of χ, matching the same discretization adopted for the Monte Carlo evolution, can strongly reduce such discretization errors and greatly improve the accuracy of the continuum extrapolation.…”

“…Instead, a theoretically better founded solution could be to use a fermionic definition of the topological charge matching the same discretization of the sea quarks. This possibility is supported by a recent study [8], where the topological susceptibility of QCD with twisted mass Wilson fermions is measured through twisted mass spectral projectors, resulting in an improved scaling towards the continuum compared to the standard gluonic measure.…”

“…The spectral projectors method, which relies on the latter strategy, has been used to obtain a theoretically well-posed definition of the continuum topological susceptibility χ = Q 2 /V [4,5] which is also easily adaptable for numerical simulations on the lattice. Up to now, this method has been defined for Dirac-Wilson fermions and successfully tested in pure Yang-Mills theories [6,7] and in full QCD [8].…”