Superconvergence Relations for Mesons and Higher Symmetries

Superconvergence relations for meson-meson scattering are obtained on the basis of locality and unitarity, and they are selected using the infinite-momentum limit. Complete saturation of these superconvergence relations with nonets of pseudoscalar and vector mesons gives rise to a consistent set of relations between coupling constants. These equations have a unique solution which is consistent with collinear $U\left(6\right)\mathrm{}$ symmetry for the vertices. It is proposed that this result remains unchanged if additional intermediate states are introduced in sets corresponding to higher representations of $U\left(6\right)\mathrm{}\otimes U\left(6\right)\mathrm{}\otimes O\left(3\right)\mathrm{}$ which separately satisfy the relations.