Quartet of spin-3/2 baryons in chiral multiplet $(1, 1/2) \oplus (1/2, 1) $ with mirror assignment

TL;DR

This paper investigates the existence of chiral partner quartets of spin-3/2 baryons within a specific chiral multiplet structure, deriving constraints and identifying candidate baryons that fit the theoretical framework.

Contribution

It introduces a quartet scheme for spin-3/2 baryons with mirror assignment in chiral multiplets and analyzes their mass patterns using an effective Lagrangian.

Findings

Two baryon sets reasonably match the predicted mass pattern.

Derived constraints from chiral symmetry on masses and couplings.

Identified candidate baryons for the chiral quartet.

Abstract

We study the possible existence of chiral partners in the spin-$\thalf$ sector of the baryon spectrum. We consider a quartet scheme where four spin-3/2 baryons, $P_{33}$, $D_{33}$, $D_{13}$ and $P_{13}$, group into higher-dimensional chiral multiplets $(1, \half)\oplus (\half,1)$ with a mirror assignment. With an effective $SU(2)_R\times SU(2)_L$ Lagrangian, we derive constraints imposed by chiral symmetry together with the mirror assignment on the masses and coupling constants of the quartet. Using the effective Lagrangian, we try to find a set of baryons suitable for the chiral quartet. It turns out that two cases reasonably agree with the mass pattern of the quartet: ($\Delta(1600)$, $\Delta(1940)$, $N(1520)$, $N(1720)$) and ($\Delta(1920)$, $\Delta(1940)$, $N(2080)$, $N(1900)$).