πN and ππN Couplings of the Δ(1232) and Its Chiral Partners

We investigate the interactions and chiral properties of the four spin-3/2 baryons N^-(D₁₃), N⁺(P₁₃), Δ⁺(P₃₃), and Δ^-(D₃₃) together with the nucleon. We construct the SU(2)_R×SU(2)_L invariant interactions between the spin-1/2 and spin-3/2 baryons with the aid of a new, specially developed spin and isospin projection technique for these baryon fields, where the chiral invariant interactions contain one- and two-pion couplings. We obtain simple relations for the coupling constants of the one- and two-pion spin–1/2-3/2 transitions terms. The relation for the one-pion interactions reasonably agrees with the experiments, which suggests that these spin-3/2 baryons are chiral partners.