Colour?Spin Matrix Elements for Multiquark Systems

Abstract

Tensor operator methods have been developed for calculating the matrix elements of the two-particle colour-spin operator that arises in the calculation of the quark-gluon interaction in the MIT bagmodel treatment of the S-wave colour singlet states of multiquark hadrons. A group classification scheme for multi quark states which distinguishes the nonstrange and strange quarks, and thus avoids the occurrence of hidden strangeness ss pairs, is constructed. This scheme has the added advantage of avoiding any need to approximate the strangeness dependence of the relevant interaction integrals. The colour-spin matrix elements for all the q4 if colour singlet states and for the strangeness - 2 states of q6 are given by way of examples. A number of checking procedures have been developed to ensure the correctness of the calculated matrix elements.