Abstract
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 Delta(1232) resonance and the other members of the 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 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.
Highlights
An interesting challenge in the study of the hadron spectrum, is understanding whether a resonance can be considered as a composite state of other hadrons or else a “genuine” state
We obtain an appreciable weight of N in the (1232) wave function, of the order of 60 % and we 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 component in the wave function
For complex values of the energies this interpretation is not possible and this is related to the fact that the modulus square of the wave function is substituted in Eq (1) by the square of the wave function, chosen the stardand phase convention of
Summary
An interesting challenge in the study of the hadron spectrum, is understanding whether a resonance can be considered as a composite state of other hadrons or else a “genuine” state. The work was generalized to higher partial waves [2] and the results obtained were used to justify the commonly accepted idea that the meson is not a composite state but a genuine one. No attempt was done to apply the method to baryonic resonances. We use it here to investigate the nature of the baryons of the J P.
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