# Improved lattice operators: the case of the topological charge density

## 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 unphysical contributions.

## Contribution

The paper develops optimized improved lattice operators for topological charge density with enhanced statistical and physical properties compared to previous methods.

## Key findings

- Operators exhibit less noise in topological charge estimation
- Renormalization factors are closer to unity
- Suppression of perturbative tail and unphysical mixings

## 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 better statistical behavior as estimators of the topological charge density on the lattice, i.e. less noisy; (ii) a multiplicative renormalization much closer to one; (iii) a large suppression of the perturbative tail (and other unphysical mixings) in the corresponding lattice topological susceptibility.