Meson baryon components in the states of the baryon decuplet

TL;DR

This paper extends the Weinberg compositeness condition to analyze meson-baryon components in the baryon decuplet, revealing significant meson-baryon contributions in the $ riangle(1232)$ and their decrease at higher energies.

Contribution

It introduces an extension of the Weinberg sum-rule to complex energies and energy-dependent potentials for studying baryon resonances.

Findings

$ riangle(1232)$ has about 60% $ ext{π}N$ component.

Higher decuplet members show decreasing meson-baryon weights.

The approach clarifies the nature of baryon resonances in terms of meson-baryon components.

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.