Improving the topological charge density operator on the lattice

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.