Improving the topological charge density operator on the lattice

TL;DR

This paper introduces improved lattice topological charge density operators using a smearing-like procedure, resulting in more accurate, less noisy estimators with reduced renormalization and suppression of perturbative artifacts.

Contribution

The authors develop and optimize a class of smearing-based operators that enhance the statistical and renormalization properties of lattice topological charge measurements.

Findings

Operators exhibit significantly reduced noise in topological charge estimation.

Renormalization factors are closer to unity, improving measurement accuracy.

Perturbative tail in topological susceptibility is substantially suppressed.

Abstract

We analyze the properties of a class of improved lattice topological charge density operators, constructed by a smearing-like procedure. By optimizing the choice of the parameters introduced in their definition, we find operators having (i) a much better statistical behavior as estimators of the topological charge density on the lattice, i.e. much less noisy; (ii) a multiplicative renormalization much closer to one; (iii) a large suppression of the perturbative tail in the corresponding lattice topological susceptibility.