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

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: ($Δ(1600)$, $Δ(1940)$, $N(1520)$, $N(1720)$) and ($Δ(1920)$, $Δ(1940)$, $N(2080)$, $N(1900)$).