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.

Comments: 5 pages, 3 figures, Proceedings of the Mini-Workshop in Bled 2016