Symmetry Predictions from Sum Rules without Saturation

The application of sum rules derived from current commutation relations to give $\mathrm{SU}\left(6\right)\mathrm{}$-like results is developed without the assumption of saturation. We first derive a consistency condition by comparing sum rules, and then study the sum rules for $\frac{1}{g_A^{}{}_{}{}^2}$ and the isovector charge radii, replacing the assumption of saturation with a simple dynamical model for the remaining continuuum contribution. This results in several $\mathrm{SU}\left(6\right)\mathrm{}$-like predictions which contain important correction factors to the results previously derived assuming saturation. We have also re-examined the experimental data for the sum rule for $\frac{{〈r_N^{}{}_{}{}^2〉}^V}{6}$, and find that it converges below 1 GeV like the sum rule for $\frac{1}{g_A^{}{}_{}{}^2}$ when account is taken of the contribution to the sum rule of the large resonant $M_{1+}$ and nonresonant ${\mathrm{E}}_{0+}$ multipoles in pion photoproduction, and of the $N^{**}\mathrm{}\left(1520\right)\mathrm{}$.