Higher Symmetries for Vector-Meson—Baryon Couplings from Superconvergence Relations

Superconvergence relations for vector-meson—baryon scattering are saturated with the baryon octet ($B$) and decuplet ($B^{*}$). The sum rules were selected by the infinite-momentum limit and evaluated at zero momentum transfer. Using $\mathrm{SU}\left(3\right)\mathrm{}$ invariance at the vertices and retaining terms to all orders in $\frac{{\mu }^2}{M^2}$ ($\mu$ is the vector-meson mass and $M$ is the baryon mass), a nontrivial solution is obtained for all vector-meson—baryon couplings. For degenerate octet and decuplet masses, this solution is consistent with collinear $U\left(6\right)\mathrm{}$ symmetry for the vertices and agrees with the corresponding result previously obtained by Oehme on neglecting corrections of order $\frac{{\mu }^2}{M^2}$ at the 8-10 and 10-10 vertices. If the octet and decuplet mass splittings are retained in a subset of our relations, the deviations from collinear $U\left(6\right)\mathrm{}$ invariance at the vertices are obtained. Consideration of the $\rho B$ scattering processes using only isospin invariance at the vertices and $\rho$ dominance of the isovector form factors leads to broken collinear $U\left(6\right)\mathrm{}$ relations between the magnetic moments of the baryons. The question of higher intermediate states in the saturation is discussed briefly.