The Spectrum of the Nucleons and the Strange Hyperons and Chiral Dynamics

Abstract

The spectra of the nucleons, $Δ$ resonances and the strange hyperons are well described by the constituent quark model if in addition to the harmonic confinement potential the quarks are assumed to interact by exchange of the $SU(3)_F$ octet of pseudoscalar mesons, which are the Goldstone bosons associated with the hidden approximate chiral symmetry of QCD. In its $SU(3)_F$ invariant approximation the pseudoscalar exchange interaction splits the multiplets of $SU(6)_{FS}\times U(6)_{conf}$ in the spectrum to multiplets of $SU(3)_F\times SU(2)_S\times U(6)_{conf}$. The position of these multiplets differ in the baryon sectors with different strangeness because of the mass splitting of the pseudoscalar octet and the different constituent masses of the u,d and s quarks that breaks $SU(3)_F$ flavor symmetry. A description of the whole spectrum, to an accuracy of $\simeq$ 4\% or better, is achieved if one matrix element of the boson interaction for each oscillator shell is extracted from the empirical mass splittings. The ordering of the positive and negative parity states moreover agrees with the empirical one in all sectors of the spectrum. A discussion of the conceptual basis of the model and its various phenomenological ramifications is presented.