Flavour symmetry breaking and meson masses

TL;DR

This paper derives mass formulas for neutral pseudoscalar mesons using the axial-vector Ward-Takahashi identity, linking flavor symmetry breaking, topological susceptibility, and meson masses, supported by a simple dynamical model.

Contribution

It develops exact chiral-limit relations connecting the dressed-quark propagator to topological susceptibility and applies a dynamical model to analyze meson spectra and mixing angles.

Findings

b7 a0Mass formulas relate meson masses to topological susceptibility.

b7 a0Model predicts e9ta-e9ta' mixing angles of about -15 degrees.

b7 a0Model successfully describes pseudoscalar and vector meson spectra.

Abstract

The axial-vector Ward-Takahashi identity is used to derive mass formulae for neutral pseudoscalar mesons. Flavour symmetry breaking entails non-ideal flavour content for these states. Adding that the \eta^\prime is not a Goldstone mode, exact chiral-limit relations are developed from the identity. They connect the dressed-quark propagator to the topological susceptibility. It is confirmed that in the chiral limit the \eta^\prime mass is proportional to the matrix element which connects this state to the vacuum via the topological susceptibility. The implications of the mass formulae are illustrated using an elementary dynamical model, which includes an Ansatz for that part of the Bethe-Salpeter kernel related to the non-Abelian anomaly. In addition to the current-quark masses, the model involves two parameters, one of which is a mass-scale. It is employed in an analysis of pseudoscalar- and vector-meson bound-states. While the effects of SU(N_f=2) and SU(N_f=3) flavour symmetry breaking are emphasised, the five-flavour spectra are described. Despite its simplicity, the model is elucidative and phenomenologically efficacious; e.g., it predicts \eta-\eta^\prime mixing angles of ~ (-15 degrees) and \pi^0-\eta angles of ~ 1 degree.