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

TL;DR

This paper analyzes the quantum numbers of pentaquark states using symmetry and geometric considerations, proposing specific $J^{P}$ assignments for low-lying states based on their nodal structure.

Contribution

It introduces a symmetry-based approach to determine pentaquark quantum numbers, independent of dynamical models, by analyzing their inherent nodal structures.

Findings

Proposes specific $J^{P}$ quantum numbers for low-lying pentaquark states.

Shows that quantum numbers depend only on geometric symmetry, not on dynamics.

Identifies accessible low-lying states with orbital angular momentum $L \,\leq\, 3$.

Abstract

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.