Saturation of current algebra equations with higher baryonic resonances

The saturation of the commutation relations of the chiral $U(3)\otimes U(3)$ algebra with supermultiplets of $S{U}_6$ or $S{U}_6\otimes O_3$ is considered. The general helicity dependence of the matrix elements of axial charges at $\mathbf{p}=\infty$ is calculated. A continuity postulate is introduced to select the physically significant solutions from the multiplicity of solutions of the non-linear set of saturated commutator equations. A linearized approach is developed to derive criteria of "connection" between two supermultiplets with respect to the chiral algebra and to calculate the renormalizatioris (at second order) of the couplings. The possible relevance of the connection criteria and of the compatibility with data of the coupling renormalizations to discriminate among various possibilities of classification of higher resonances is pointed out. Special cases discussed are classifications of negative parity resonances according to the representations and 56 of $S{U}_6$ and (20, $L=\mathit{1}$) of $S{U}_6\otimes O_3$. Only the last one gives consistent predictions.