Lorentz Multiplet Structure of Baryon Spectra and Relativistic Description

Abstract

The pole positions of the various baryon resonances are known to reveal well-pronounced clustering, so-called Hoehler clusters. For nonstrange baryons the Hoehler 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 Lambda hyperons below 1800 MeV these clusters are shown to be of the type [(1,0)+ (0,1)]*[(1/2,0)+(0,1/2)] while above 1800 MeV they are parity duplicated (J,0)+(0,J) (Weinberg-Ahluwalia) states. Therefore, for Lambda hyperons the restoration of chiral symmetry takes place above 1800 MeV. Finally, it is demonstrated that the description of spin-3/2 particles in terms of a 2nd 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 upon a 4-vector with Dirac spinor components.