ShouldSU(3)Mass Formulas for Mesons Use the Masses of the Mesons or Their Squares?

Abstract

The practice of using squares of masses in mass formulas for $S{U}_3$ meson multiplets, which arose originally in order to bring the Gell-Mann-Okubo mass formula for the $0^{-}$ meson octet more nearly into agreement with experiment, is criticized. The basis of the criticism is that $X^0-\eta$ mixing can make the Gell-Mann-Okubo formula compatible with the observed $0^{-}$ meson spectrum not only when one applies it to the squares of the masses, but also when one applies it to the masses themselves. Of course, the degree of the mixing is different in the two cases and this affects the prediction of decay rates. Accordingly, the decays of $2^{+}$ mesons into two $0^{-}$ mesons are discussed in considerable detail as an example of a situation where experimental measurements may discriminate between the values of the mixing angle corresponding to linear and quadratic mass formulas.