Topological susceptibility on the lattice and the three-flavour quark condensate

TL;DR

This paper reanalyzes the topological susceptibility in lattice QCD to better understand the three-flavour quark condensate, highlighting the importance of simulation conditions and providing updated quantitative estimates.

Contribution

It introduces a combined fit approach using resummed ChPT to extract the three-flavour quark condensate from lattice data, considering the effects of quark mass hierarchy and vacuum fluctuations.

Findings

The three-flavour quark condensate is approximately 243 MeV.

Simulations with equal light quark masses are more effective for disentangling condensate contributions.

There is a significant suppression of the three-flavour condensate compared to the two-flavour case.

Abstract

We reanalyse the topological susceptibility assuming the possibility of a significant paramagnetic suppression of the three-flavour quark condensate and a correlated enhancement of vacuum fluctuations of $s\bar{s}$ pairs. Using the framework of resummed ChPT, we point out that simulations performed near the physical point, with a significant mass hierarchy between u,d and s dynamical quarks, are not able to disentangle the contributions from the quark condensate and sea $s\bar{s}$-pair fluctuations, and that simulations with three light quark masses of the same order are better suited for this purpose. We perform a combined fit of recent RBC/UKQCD data on pseudoscalar masses and decay constants as well as the topological susceptibility, and we reconsider the determination of lattice spacings in our framework, working out the consequences on the parameters of the chiral Lagrangian. We obtain Sigma(3;2 GeV)^1/3=243 \pm 12 MeV for the three-flavour quark condensate in the chiral limit. We notice a significant suppression compared to the two-flavour quark condensate Sigma(2;2 GeV)/Sigma(3;2 GeV)=1.51\pm 0.11 and we confirm previous findings of a competition between leading order and next-to-leading order contributions in three-flavour chiral series.