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

Details $πN$ and $ππN$ Couplings of the $Δ(1232)$ and its Chiral Partners $πN$ and $ππN$ Couplings of the $Δ(1232)$ and its Chiral Partners

2008-04-20

arxiv.org/abs/0804.3185v1

Phys.Rev.Lett.101:092001,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

Scientific paper

10.1103/PhysRevLett.101.092001

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.

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