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

TL;DR

This paper explores the chiral interactions of spin-3/2 baryons and nucleons, developing a new projection technique to analyze their couplings, and finds that the results support the idea that these baryons are chiral partners.

Contribution

It introduces a novel spin and isospin projection method to analyze chiral interactions of spin-3/2 baryons and derives relations for their pion couplings, supporting their status as chiral partners.

Findings

One-pion coupling relations agree with experimental data.

The study supports the chiral partner hypothesis for these baryons.

Develops a new technique for spin and isospin projection in baryon interactions.

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.