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

TL;DR

This study compares two lattice QCD methods for calculating topological susceptibility, finding spectral projectors more accurate with smaller errors than gradient flow, and discusses potential for eliminating discretization effects.

Contribution

It introduces a comparative analysis of gluonic and fermionic definitions of topological susceptibility using twisted mass fermions, highlighting the advantages of spectral projectors.

Findings

Spectral projector results have smaller total errors than gluonic ones.

Both methods agree in the continuum limit after fitting to chiral perturbation theory.

Discretization effects can be potentially eliminated at a specific spectral cutoff.

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.