Effects of Gravitational Field of a Topological Defect on Heavy Quarkonia Spectra in a Non-relativistic Quark Model

Abstract

In this paper, we analyze the properties of heavy quarkonia in a curved space-time with conical geometry induced by a topological defect, namely a cosmic string. The particles moving within the latter space are under the influence of an extended version of the Cornell potential. Assuming that the cosmic string space time is torsion free, the full spectrum of each particle is obtained by solving the Schrödinger equation using the extended Nikiforov–Uvarov method. It is observed that the gravitational field of the topological defect acts on the energy levels in a manner similar to the Zeeman effect due to the magnetic field. However, in the limit of the flat Minkowski space-time \((\alpha \rightarrow 1)\), we recover the classical mass spectra of heavy quarkonia for the extended Cornell potential. The numerical outcomes of this study are overall found in good agreement with experimental data and other relevant theoretical works. Thus, to illustrate the effect of the topological defect graphically, mass spectra, wave functions and radial probability densities are plotted for \(P-\)states at different values of \(\alpha \). It is found that, at large values of the quantum number n, the mass spectra of heavy quarkonia exhibit saturation effect governed by the topological parameter.