Quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$ via symmetry analysis

We investigate the quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$, 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 ${{\rm{P}}}_{c}^{+}$ may be ${\tfrac{3}{2}}^{-}$, ${\tfrac{5}{2}}^{-}$, ${\tfrac{3}{2}}^{+}$and ${\tfrac{5}{2}}^{+}$, independent of dynamical models.