A group theoretical study of the harmonic oscillator quark model and its implications for baryon spectroscopy

• Main Author: Corvi, Peter John
• Published: University of Edinburgh 1981
• Subjects: 531.16
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.645011

We undertake a group-theoretical study of the specific form of the harmonic oscillator quark model proposed by Isgur and Karl, restricting our attention to the non-strange sector of the baryon spectrum. In particular, we consider the spectrum-generating group, Sp(12,R), appropriate to the study of the 3-quark problem and demonstrate how it may be used to label the oscillator eigenstates and to provide a new and direct means of constructing wave functions of definite orbital angular momentum and permutation - symmetry type. We indicate how Sp(12,R) provides the most appropriate means of classifying the symmetry-breaking induced by an enharmonic perturbation and we derive an algebraic mass formula, involving the quadratic Casimir invariant operators of Sp(12,R) and its relevant subgroups, plus one non-subgroup invariant operator, which successfully reproduces the splitting pattern of the N = 2 supermultiplets originally derived in the literature by straightforward perturbative techniques. Some results for the N = 3 level are also given together with an outline of the method for generalisation to any degree of excitation of the system. Much of our understanding of the role of the spectrum-generating group in this context derives from a parallel study of the simpler case of a 2-particle bound system, which we also describe. We examine the implications of our results for baryon spectroscopy: in particular, we discuss in some detail the possibility that the AD35(1940) resonance is evidence for an N = 3 [56,1 ] supermultiplet corresponding to excitation of new gluonic degrees of freedom. After inclusion of hyperfine effects, and with reasonable values of the parameters in the model, we recover the pertinent features appropriate to the D35, G37 and G39 sectors of a recent preliminary phase-shift analysis by Cutkosky et al.