Calculation of Binding Energy and Wave Function for Exotic Hidden-Charm Pentaquark

Abstract

In this study, pentaquark $P_c\left(4380\right)$ composed of a baryon ${\Sigma }_c$ , and a ${\overline{D}}^{\ast }$ meson is considered. Pentaquark is as a bound state of two-body systems composed of a baryon and a meson. The calculated potential will be expanded and replaced in the Schrödinger equation until tenth sentences of expansion. Solving the Schrödinger equation with the expanded potential of Pentaquark leads to an analytically complete approach. As a consequence, the binding energy $E_B$ of pentaquark $P_c$ and wave function is obtained. The results $E_B$ will be presented in the form of tables so that we can review the existence of pentaquark $P_c$ . Then, the wave function will be shown on diagrams. Finally, the calculated results are compared with the other obtained results, and the mass of observing pentaquark $P_c$ and the radius of pentaquark are estimated.