Systematic study of multi-quark states I. qq-qq-\bar{q} configuration

TL;DR

This paper develops a group theoretic method for systematically studying multi-quark states, simplifying calculations by transforming bases and applying it to five-quark systems with various models.

Contribution

It introduces a new group representation approach for multi-quark calculations, including transformation coefficients and isoscalar factors, applicable across different quark models.

Findings

Transformation coefficients relate to SU groups and are tabulated.

The method is demonstrated on five-quark systems with multiple models.

Results provide general insights into five-quark state properties.

Abstract

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 $qq-qq-\bar{q}$ 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 ${SU}_{mn}\supset{SU}_m\times{SU}_n$ 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.