Paraquark dynamics of baryons and resonances

Abstract

A three-body formalism, within a non-relativistic quark ( Q) model, is developed for a dynamical treatment of baryons and their resonances as bound 3 Q-systems, via Q- Q interactions operating through a Schrödinger equation, with all degrees of freedom (space, spin and unitary spin) taken into account. The main assumptions are (i) parastatistics and (ii) operation of Q- Q forces in s- and p-waves only. A detailed classification of the various 3 Q-states of the correct symmetry is obtained in terms of (LSJ) assignments as well as SU(3) multiplet structures, using the symmetric ( S), antisymmetric ( A), and mixed ( M) representations of the permutation group of three objects. The Schrödinger equations for the spatial parts of the 3 Q-wavefunctions are found to separate into those for S, M, and A types for different values of L, in the limit of “full degeneracy” represented by spin and SU (3)-spin-independent Q- Q potentials in s- and p-waves. The group structures generated by these equations are precisely those of SU(6) ⊗ O(3). The further assumption of separable forms for the potentials, leads to coupled one-dimensional equations for certain “spectator functions” associated with the spatial wavefunctions. For the s-wave force which strongly generates even-parity ( L = 0) states, and only weak L P = 1 − states, these kernels are attractive for S, but repulsive for M functions of L P = 0 +. The p-wave interaction, on the other hand, strongly generates both even- and odd-parity states. For L P = 1 − states, M and A functions have attractive and repulsive kernels, respectively. The opposite holds for even-parity states, with A functions of L P = 1 +and 0 + having attractive and repulsive kernels, respectively. A p-wave spin-orbit force is incorporated in the formalism and shown to break up the supermultiplets into SU(3) multiplets for which approximate but explicit mass formulas are derived. The main results of experimental interest are the following: 1. (i) A dynamical realization of the 56 states of baryons via S-functions of L P = 0 +. 2. (ii) A ( 70, 3) representation of SU(6) ⊗ (3), via M-functions of L P = 1 − of the negative parity baryon states whose SU(3) multiplet structure is in qualitative accord with Dalitz' analysis of experimental data. 3. (iii) A ( 20, 3) representation for L P = 1 + states of which the lowest lying ones are an octet and a singlet, each of J P = 1 2 + , thus providing a dynamical explanation of the “Roper” resonance and predicting a new singlet in the “low”-mass region.