Range of topological fluctuations in the three-flavor linear sigma model

TL;DR

This paper calculates the topological charge density correlations in a three-flavor linear sigma model, revealing a large scale for topological fluctuations and suggesting dominance of higher topological sectors in the ground state.

Contribution

It introduces a method to compute topological charge correlations in a three-flavor linear sigma model, including arbitrary topological sectors, and connects these to QCD estimates.

Findings

Large topological fluctuation scale inferred

Dominance of higher topological charge configurations suggested

Accurate eta-eta' sector spectroscopy achieved

Abstract

The topological charge density two-point function is computed in a three-flavor effective linear meson model, including contributions from topological sectors with arbitrary charge. A corresponding composite field is introduced via a Hubbard-Stratonovich transformation. In the $\eta$-$\eta$' sector, the model yields very accurate spectroscopy with negligible mixing with the composite field. The resulting topological susceptibility allows for the extraction of a surprisingly large absolute scale for the range of topological fluctuations. When compared with various QCD-based estimates, this indirectly suggests the dominance of higher topologically charged configurations in the ground state.