Group theoretical methods and multiquark hadrons

Abstract

Tensor operator techniques are used to evaluate the colour-spin matrix elements of multiquark hadrons in the static spherical cavity approximation to the M.I.T. bag model, thereby obviating the necessity for the Jaffe approximation, which creates isospin degeneracies. All q⁴q, q²q² and q⁶ isospin multiplet masses are tabulated and are to be regarded as Jaffe-Low primitives. The dissociation of multiquark bag model eigenstates is shown to be related to a basis transformation and techniques for performing this transformation are described. Tables of 3jm factors and 6j symbols, adequate to calculate dissociations for all q²q² and q⁴q primitives and q⁶ primitives for strangeness ⩽ -2, are provided. The generalized Wigner-Racah algebra is reviewed with emphasis on phase freedom. A method of choosing phases is described and the simplifications due to certain canonical choices are noted. This leads naturally onto a discussion of Butler's method for calculating 3jm factors and 6j symbols for arbitrary compact group chains. The 6j symbols and 3jm factors required for the multiquark calculations are used as examples