Mass formula for nonets

Abstract

The relation between the masses and mixing angle in a nonet of mesons is studied in a simple quark-gluon picture. We find that both the splitting of ${{\mu }_{\eta }}^2$ from ${{\mu }_{\pi }}^2$ and the departure of ${\theta }_P$ from ${\theta }_{\mathrm{ideal}}$ are due to annihilation forces. Mass formulas which describe the masses in a nonet in terms of two parameters are derived and found to be in good agreement with observed masses for the $0^{-+}$, $1^{--}$, and $2^{++}$ nonets.