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

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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 Schrodinger equation using the extended Nikiforov-Uvarov method; the wave functions and the radial probability densities of charmonium and bottomonium mesons are derived using the bi-confluent Heun functions. It it observed that the presence of the topological defect, produces a splitting between nP and nD states. The latter states are separated into 2l + 1 components, implying that the gravitational field of a topological defect acts on energy levels like in a way similar to the Zeeman effect due to the magnetic field. However, inthe limit α → 1, which correspond to the usual flat Minkowski space-time, we recover the classical mass spectrum of heavy quarkonia for the extended Cornell potential. The numerical results obtained in 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 α. 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. PACS numbers: 21.60.Fw, 21.10.Re, 70.25.+k, 04.10.Mn

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