Meson baryon components in the states of the baryon decuplet

Abstract

We apply an extension of the Weinberg compositeness condition on partial waves of $L=1$ and resonant states to determine the weight of meson-baryon component in the $\Delta (1232)$ resonance and the other members of the $J^P={\frac{3}{2}}^{+}$ baryon decuplet. We obtain an appreciable weight of $\pi N$ in the $\Delta (1232)$ wave function, of the order of 60 \%, which looks more natural when one recalls that experiments on deep inelastic and Drell Yan give a fraction of $\pi N$ component of 34 \% for the nucleon. We also show that, as we go to higher energies in the members of the decuplet, the weights of meson-baryon component decrease and they already show a dominant part for a genuine, non meson-baryon, component in the wave function. We write a section to interpret the meaning of the Weinberg sum-rule when it is extended to complex energies and another one for the case of an energy dependent potential.