Quantum numbers of the pentaquark states $P_c^{+}$ via symmetry analysis

We investigate the quantum numbers of the pentaquark states $P_c^{+}$, which are composed of 4 (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 is at the ground state, we determine the nodeless structure of the states with orbital angular moment L ≤ 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 $P_c^{+}$ may be ${\frac{3}{2}}^{-}$, ${\frac{5}{2}}^{-}$, ${\frac{3}{2}}^{+}$and ${\frac{5}{2}}^{+}$, independent of dynamical models. (paper)