Lorentz multiplet structure of baryon spectra and relativistic description

The pole positions of the various baryon resonances are known to reveal well-pronounced clustering, so-called Höhler clusters. For nonstrange baryons, the Höhler clusters are shown to be identical to Lorentz multiplets of the type {j, j} ⊗ [{1/2, 0} ⊕ {0, 1/2}] with j being a half-integer. For the Λ hyperons below 1,800 MeV, these clusters are shown to be of the type {1, 0} ⊕ {0, 1} ⊗ [{1/2, 0} ⊕ {0, 1/2}] while above 1,800 MeV they are parity duplicated {J, 0} ⊕ {0, J} higher-spin (Weinberg-Ahluwalia) states. Therefore, for Λ hyperons the restoration of chiral symmetry takes place above 1,800 MeV. Finally, it is demonstrated that the description of spin-3/2 particles in terms of a second rank antisymmetric Lorentz tensor with Dirac spinor components does not contain any off-shell parameters and avoids the main difficulties of the Rarita-Schwinger description based on a four-vector with Dirac spinor components.

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