General SU(3) Particle Mixing Among Mesons in SU(3) Sum Rules

The features of general SU(3) particle mixing among mesons are studied in the framework of asymptotic SU(3), chiral SU(3) ⊗ SU(3) charge algebra, and the hypothesis of asymptotic level realization of SU(3) in the algebra $[A_i, A_j]=i{f}_{\mathrm{ijk}}{V}_k$. In the level scheme of a simple quark model, our framework requires that the mixings between the corresponding members of two nonets with the same $J^{\mathrm{PC}}$ but different $L$ excitations should take place in such a way that their net effect disappears from the SU(3) sum rules, leaving the previously obtained nonet structure of bosons intact. We thus need to consider, in effect, only the usual mixings between the $I=Y=0\mathrm{}$ members of each nonet (with the same $L$) and also, less importantly, the mixings between the $I=\frac{1}{2}$ members of two nonets with the same $J^P$ and $L$ but opposite $C$. These mixing parameters are fixed in our theoretical framework.