Meson-baryon components in the states of the baryon decuplet

We apply an extension of the Weinberg compositeness condition on partial waves of L = 1 and resonant states to determine the weight of the meson-baryon component in the Δ(1232) resonance and the other members of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ J^P= \frac{3}{2}^{+}$\end{document} baryon decuplet. We obtain an appreciable weight of πN in the Δ(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 πN 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 the 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.