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

TL;DR

This work develops a three-flavor linear sigma model that includes a composite topological-density field q_M(x) via a Hubbard–Stratonovich construction to study the range of topological fluctuations. By analyzing the η–η′ sector and solving the extended mass matrix, it finds a suppressed topological mass μ_c^2 ≈ 0.029 m_c^2, yielding a topological susceptibility χ_top ≈ 34 m_c^4, and reproduces the physical η, η′ spectrum (m_η ≈ 538 MeV, m_{η′} ≈ 964 MeV) with negligible q_M–η mixing. The results indicate dominance of higher-topological-charge configurations at T=0 and demonstrate that the topological fluctuations extend over a range several times larger than the HS compositeness scale, aligning with lattice QCD insights and the Witten–Veneziano framework. The paper also sketches directions for including two-loop correlators, finite-temperature effects, and FRG approaches to further illuminate the role of the anomaly in the QCD vacuum.

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 $η$-$η$' 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.