Even-wave harmonic oscillator theory of baryonic states: a new classification

Abstract

An even-wave harmonic oscillator (h.o.) model for the quark-quark interaction proposed recently for the baryon spectrum is described with a detailed mathematical formulation. The mechanism, which formally admits of a relativistic extension of the Feynman-Kislinger-Ravndal type, leaves unchanged the usual h.o. predictions for 56 states (symmetric) for all L values even and odd, but totally keeps out the 20 states (antisymmetric). It changes the structure of the 70 states considerably, while retaining the principal feature of linear rise of (mass)² with J through the interplay of two reduced slopes of magnitudes ½ α and ½ √ 3α , compared to a for the 56 spectrum. The new features of the 70 states are (i) a dual spectrum leading to considerable mass splitting compared to the usual h.o. model without SU(6)-breaking effects, (ii) prediction of a unique (70, 0⁺) supermultiplet lower than the (70, 1^-), and (iii) the prediction of low radial excitations because of the reduced slopes. The immediate experimental successes are (i) an understanding of P₁₁(1470) together with possible Δ, Σ, Λ counterparts, (ii) two distinct mass groupings manifest in (70, 1^-) states, and (iii) plausible explanation of P₁₁'(1750) as a radial excitation of P₁₁(1470). The mass splittings of Δ, Σ, Λ from their N counterparts, compared for 56 and 70 states, conform extremely well to the ratio of the average slope δ=1/4α(1+√3)≈ 0.68 a for 70 states to that (a) for the 56, thus facilitating the prediction of Δ, Σ, Λ positions from those of N states for different quantum numbers. Extra predictions of states are discussed in terms of an extended classification scheme given by an ordered set of four quantum numbers (n_xl_xn_yl_y) defined in the text.