The microscopic structure of $\pi NN$, $\pi N\Delta$ and $\pi\Delta\Delta$ vertices in a hybrid constituent quark model

Abstract

We present a microscopic description of the strong $\pi NN$, $\pi N\Delta$ and $\pi\Delta\Delta$ vertices. Our starting point is a constituent-quark model supplemented by an additional $3q\pi$ non-valence component. In the spirit of chiral constituent-quark models, quarks are allowed to emit and reabsorb a pion. This multichannel system is treated in a relativistically invariant way within the framework of point-form quantum mechanics. Starting with a common $SU(6)$ spin-flavor-symmetric wave function for $N$ and $\Delta$, we calculate the strength of the $\pi NN$, $\pi N\Delta$ and $\pi\Delta\Delta$ couplings and the corresponding vertex form factors. Our results are in accordance with phenomenological fits of these quantities that have been obtained within purely hadronic multichannel models for baryon resonances.