Quantum Numbers of the Pentaquark States $P_c^{+}$ via Symmetry Analysis

Abstract

We investigate the quantum numbers of the pentaquark states ${\text{P}}_{\text{c}}^{+}$, which are composed of four (three flavors) quarks and an antiquark, by analyzing their inherent nodal structure in this paper. Assuming that the four quarks form a tetrahedron or a square, and the antiquark locates at the center of the four quark cluster, we determine the nodeless structure of the states with orbital angular moment $L\le 3$, and in turn, the accessible low-lying states. Since the inherent nodal structure depends only on the inherent geometric symmetry, we propose the quantum numbers $J^P$ of the low-lying pentaquark states ${\text{P}}_c^{+}$ may be ${\frac{3}{2}}^{-}$, ${\frac{5}{2}}^{-}$, ${\frac{3}{2}}^{+}$, ${\frac{5}{2}}^{+}$, independent of dynamical models.

Comments: 17 pages. 2 figures, 7 tables