The $\eta$ and $\eta^\prime$ mesons from Lattice QCD

TL;DR

This paper presents a lattice QCD calculation of the $\, ext{eta}$ and $ ext{eta}^\prime$ meson masses and mixing, confirming the role of the axial anomaly and topology in their large mass, with results consistent with experimental data.

Contribution

It provides a realistic 2+1 flavor lattice QCD computation of the $\, ext{eta}$ and $ ext{eta}^\prime$ masses and mixing angles, supporting theoretical explanations of their mass origin.

Findings

Masses consistent with experimental values

Small octet-singlet mixing angle measured

Supports axial anomaly and topology effects in mass generation

Abstract

The large mass of the ninth pseudoscalar meson, the $\eta^\prime$, is believed to arise from the combined effects of the axial anomaly and the gauge field topology present in QCD. We report a realistic, 2+1 flavor, lattice QCD calculation of the $\eta$ and $\eta^\prime$ masses and mixing which confirms this picture. The physical eigenstates show small octet-singlet mixing with a mixing angle of $\theta = -14.1(2.8)^\circ$. Extrapolation to physical light quark mass gives, with statistical errors only, $m_\eta=573(6)$ MeV and $m_{\eta^\prime}=947(142)$ MeV, consistent with the experimental values of 548 MeV and 958 MeV.