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.

中文翻译：

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五夸克态的量子数 ${{\rm{P}}}_{{\rm{c}}}^{+}$ 通过对称分析

我们研究了五夸克态 $\textrm{P}_{\textrm{c}}^{+}$ 的量子数，它由四种（三种风味）夸克和一个反夸克组成，通过分析它们在这篇报告。假设四个夸克形成一个四面体或一个正方形，反夸克位于四夸克簇的中心，我们确定轨道角矩为$L\leq 3$的态的无节点结构，进而得到可及地势低洼的州。由于固有节点结构仅取决于固有几何对称性，我们提出低位五夸克态 $\textrm{P}_{c}^{+}$ 的量子数 $J^{P}$ 可能是 $ {\frac{3}{2}}^{-}$, ${\frac{5}{2}}^{-} $, ${\frac{3}{2}}^{+}$, ${\frac{5}{2}}^{+} $，独立于动力学模型。