Low-lying $s=+1$ Pentaquark states in the Inherent Nodal Structure Analysis

Abstract

The strangeness $s=+1$ pentaquark states as $qqqq\bar{q}$ clusters are investigated in this letter. Starting from the inherent geometric symmetry, we analyzed the inherent nodal structure of the system. As the nodeless states, the low-lying states are picked out. Then the S-wave state $(J^P,T)=({1/2}^{-},0)$ and P-wave state $(J^P,T)=({1/2}^{+},0)$ may be the candidates of low-lying pentaquark states. By comparing the accessibility of the two states and referring the presently obtained K-N interaction potential, we propose that the quantum numbers of the observed pentaquark state ${\Theta }^{+}$ may be $(J^P,T)=({1/2}^{+},0)$ and L=1.

Comments: 15 pages, 2 figures, 4 tables. Revised version with detailed description, expanded discussion and reference for the geometric configuration to be proposed being added