SU(6), triquark states, and the pentaquark

Abstract

The purported observation of a state Θ⁺ with strangeness S=+1 led to its quark model interpretation in terms of a pentaquark combination involving a triquark-diquark structure-the Karliner-Lipkin model. In this work, the proper color-spin symmetry properties for the qqq̅ triquark are elucidated by calculating the SU(6) unitary scalar factors and Racah coefficients. Using these results, the color-spin hyperfine interactions, including flavor symmetry breaking therein, become straightforward to incorporate and the pentaquark masses are readily obtained. We examine the effect on the pentaquark mass of (a) deviations from the flavor symmetric limit and (b) different strengths of the doublet and triplet hyperfine interactions. Reference values of these parameters yield a Θ⁺ mass prediction of 1601 MeV but it can comfortably accommodate 1540 MeV for alternate choices. In the same framework, other pentaquark states Ξ(S=−2) and Θ^c (with charm C=−1) are expected at 1783 MeV and 2757 MeV, respectively.