Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility

TL;DR

This paper calculates topological charge moments in lattice QCD using Chiral Perturbation Theory to better determine the three-flavour quark condensate and understand chiral symmetry breaking.

Contribution

It provides next-to-leading order formulas for topological susceptibility and the fourth cumulant, highlighting the fourth cumulant's enhanced sensitivity to the quark condensate.

Findings

The fourth cumulant is more sensitive than the susceptibility to the quark condensate.

A combination of both observables can precisely determine the three-flavour condensate.

Predictions are made for recent lattice QCD analysis by RBC/UKQCD.

Abstract

The first two non-trivial moments of the distribution of the topological charge (or gluonic winding number), i.e., the topological susceptibility and the fourth cumulant, can be computed in lattice QCD simulations and exploited to constrain the pattern of chiral symmetry breaking. We compute these two topological observables at next-to-leading order in three-flavour Chiral Perturbation Theory, and we discuss the role played by the eta propagation in these expressions. For hierarchies of light-quark masses close to the physical situation, we show that the fourth cumulant has a much better sensitivity than the topological susceptibility to the three-flavour quark condensate, and thus constitutes a relevant tool to determine the pattern of chiral symmetry breaking in the limit of three massless flavours. We provide the complete formulae for the two topological observables in the isospin limit, and predict their values in the particular setting of the recent analysis of the RBC/UKQCD collaboration. We show that a combination of the topological susceptibility and the fourth cumulant is able to pin down the three-flavour condensate in a particularly clean way in the case of three degenerate quarks.