$\pi N$ and $\pi \pi N$ Couplings of the $\Delta (1232)$ and its Chiral Partners

Abstract

We investigate the interactions and chiral properties of the four spin-$\thalf$-baryons : $N^{-}(D_{13})$, $N^{+}(P_{13})$, ${\Delta }^{+}(P_{33})$ and ${\Delta }^{-}(D_{33})$ together with the nucleon. We construct the $SU(2{)}_R\times SU(2{)}_L$ invariant interactions between the spin-$\half$ and -$\thalf$ 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 $\half-\thalf$ transitions terms. The relation for the one-pion interactions reasonably agrees with the experiments, which suggests that these spin-$\thalf$ baryons are chiral partners.