Systematic study of pentaquark states: $qqq-q\bar{q}$ configuration
  Group theoretic method for the systematic study of five-quark states with meson-baryon ($q\bar{q}-q^3$) configuration is developed. The calculation of matrix elements of many body Hamiltonian is simplified by transforming the physical bases (meson-baryon quark cluster bases) to symmetry bases (group chain classified bases), where the fractional parentage expansion method can be used. Three quark models, the naive Glashow-Isgur model, Salamanca chiral quark model and quark delocalization color screening model, are used to show the general applicability of the method and general results of constituent quark models for five-quark states are given. The method can also be useful in the calculation of meson-baryon scattering and the study of the five-quark components effect in baryon structure. The physical contents of different model configurations for the same multi-quark system can also be compared through the transformation between different physical bases to the same set of symmetry bases. 
Jialun Ping, Hongxia Huang, Chengrong Deng, Fan Wang, T. Goldman