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

We investigate the quantum numbers of the pentaquark states $textrm{P}_{textrm{c}}^{+}$, 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 $L leq 3$, 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 $textrm{P}_{c}^{+}$ may be ${frac{3}{2}}^{-}$, ${frac{5}{2}}^{-} $, ${frac{3}{2}}^{+}$, ${frac{5}{2}}^{+} $, independent of dynamical models.