On the Microscopic Structure of πNN, πNΔ and πΔΔ Vertices

We use a hybrid constituent-quark model for the microscopic description of πNN, πNΔ and πΔΔ 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 N₀ and Δ₀, i.e. the eigenstates of the pure confinement problem, we calculate the strength of the πN₀N₀, πN₀Δ₀ and πΔ₀Δ₀ 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. (author)