Systematic study of multi-quark states: Aqq−qq−q¯configuration

Abstract

A group theoretic method for the systematic study of multiquark states is developed. The calculation of matrix elements of many-body Hamiltonians 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. A five-quark system is taken as the example in this study. The Jaffe--Wilczek $\mathit{qq}\text{\ensuremath{-}}\mathit{qq}\text{\ensuremath{-}}\overline{q}$ configuration is chosen as one of the examples to construct the physical bases and the transformation coefficients between physical bases and symmetry ones are shown to be related to the ${\mathrm{SU}}_{\mathit{mn}}\ensuremath{\supset}{\mathrm{SU}}_{m}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}}_{n}$ isoscalar factors. A complete transformation coefficient table is obtained. The needed isoscalar factors and fractional parentage coefficients have been calculated with our new group representation theory and published before. Three quark models, the naive Glashow-Isgur model, the Salamanca chiral quark model, and quark delocalization color screening model, are used to show the general applicability of the new multiquark calculation method and general results of constituent quark models for five-quark states are given.