On the microscopic structure of $\pi NN$, $\pi N\Delta$ and $\pi \Delta \Delta$ vertices

Abstract

We use a hybrid constituent-quark model for the microscopic description of $\pi NN$, $\pi N\Delta$ and $\pi \Delta \Delta$ vertices. In this model quarks are confined by an instantaneous potential and are allowed to emit and absorb a pion, which is also treated as dynamical degree of freedom. The point form of relativistic quantum mechanics is employed to achieve a relativistically invariant description of this system. Starting with an $SU(6)$ spin-flavor symmetric wave function for $N_0$ and ${\Delta }_0$, i.e. the eigenstates of the pure confinement problem, we calculate the strength of the $\pi N_0{N}_0$, $\pi N_0{\Delta }_0$ and $\pi {\Delta }_0{\Delta }_0$ couplings and the corresponding vertex form factors. Interestingly the ratios of the resulting couplings resemble strongly those needed in purely hadronic coupled-channel models, but deviate significantly from the ratios following from SU(6) spin-flavor symmetry in the non-relativistic constituent-quark model.

Comments: Talk presented by J.-H. Jung at "The 23rd European Conference on Few-Body Problems in Physics", Aarhus, Denmark, 8-12 August 2016; 4 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1610.09242