$\pi N$ 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.

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Cited by in corpus (6)

• Baryon Fields with U_L(3) times U_R(3) Chiral Symmetry III: Interactions with Chiral (3,3_bar)+(3_bar,3) Spinless Mesons
• Chiral partner structure of light nucleons in an extended parity doublet model
• Baryon fields with $U_L(3)\times U_R(3)$ chiral symmetry V: Pion-Nucleon and Kaon-Nucleon $\Sigma$ Terms
• Nucleon axial couplings and [(1/2,0) + (0,1/2)]-[(1,1/2) + (1/2,1)] chiral multiplet mixing
• Bi-local baryon interpolating fields with two flavours
• Quartet of spin-3/2 baryons in chiral multiplet $(1,1/2)\oplus (1/2,1)$ with mirror assignment