SU(6), Triquark states, and the pentaquark

TL;DR

This paper analyzes the structure and mass predictions of pentaquark states, especially the $ heta^+$, using SU(6) symmetry and hyperfine interactions within a triquark-diquark model, providing refined mass estimates.

Contribution

It elucidates the colour-spin symmetry properties of the triquark and incorporates these into mass calculations, improving understanding of pentaquark structures and predictions.

Findings

Predicted $ heta^+$ mass of 1601 MeV with parameter variations.

Accommodates experimental $ heta^+$ mass of 1540 MeV.

Forecasts masses for other pentaquarks like $\\Xi$ and $\\Theta^c$.

Abstract

The purported observation of a state $\Theta^+$ 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 colour-spin symmetry properties for the $q q \bar{q}$ triquark are elucidated by calculating the SU(6) unitary scalar factors and Racah coefficients. Using these results, the colour-spin hyperfine interactions, including flavour symmetry breaking therein, become straight-forward to incorporate and the pentaquark masses are readily obtained. We examine the effect on the pentaquark mass of (a) deviations from the flavour symmetric limit and (b) different strengths of the doublet and triplet hyperfine interactions. Reference values of these parameters yield a $\Theta^+$ mass prediction of 1601 MeV but it can comfortably accommodate 1540 MeV for alternate choices. In the same framework, other pentaquark states $\Xi$ (S=--2) and $\Theta^c $ (with charm C=--1) are expected at 1783 MeV and 2757 MeV, respectively.