Systematic study of multi-quark states I. qq-qq-q configuration

الأصل · EN

Group theoretic method for the systematic study of multi-quark states is developed. The calculation of matrix elements of many body Hamiltonian is simplified by transforming the physical bases (quark cluster bases) to symmetry bases (group chain classified bases), where the fractional parentage expansion method can be used. Five quark system is taken as example in this study. The Jaffe-Wilczek qq-qq-q configuration is chosen as one of examples to construct the physical bases and the transformation coefficients between physical bases and symmetry ones are shown to be related to the SUmn⊃SUₘ×SUₙ isoscalar factors and a complete transformation coefficients table is given. The needed isoscalar factors and fractional parentage coefficients had been calculated with our new group representation theory and published before. Three quark models, the naive Glashow-Isgur, Salamanca and quark delocalization color screening, are used to show the general applicability of the new multi-quark calculation method and general results of constituent quark models for five-quark states are given.