https://doi.org/10.1140/epja/s10050-023-01216-z
Regular Article - Theoretical Physics
Spin averaged mass spectra and decay constants of heavy quarkonia and heavy-light mesons using bi-confluent heun equation
1
Laboratory of Atomic, Molecular and Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
2
Department of Physics, Bertoua Higher Teachers’ Training College, University of Bertoua, P.O. Box 55, Bertoua, Cameroon
3
The Nuclear Technology Section (NTS), Institute of Geological and Mining Research, P.O. Box 4110, Yaoundé, Cameroon
Received:
2
August
2023
Accepted:
11
December
2023
Published online:
1
March
2024
In this paper, we study the mass spectra of heavy quarkonia and heavy-light mesons in a curved space-time with conical geometry induced by a topological defect. The interactions between particles are modeled by an extended version of the Cornell potential, namely the singularized harmonic potential. To compute energy levels as well as the corresponding wave functions, the Hamiltonian operator is constructed within a torsion free space-time with a point-like global monopole. Then the full spectrum is obtained by solving the Schrödinger equation using the bi-confluent Heun equation. It is found that the energy spectra and wave functions of each meson differ from their flat Minkowski space-time counterparts. To check the efficiency of our model, we use the results of calculation to reproduce the mass spectra of heavy quarkonia such as 
, 
and some heavy-light mesons such as 
and 
. The mass spectra are calculated up to 4 S state at different values of the topological defect, then compared with experimental data and some relevant theoretical works. Decay constants are also computed for the selected mesons. The effect of the topological defect is also analyzed in details. It is observed that, for small values of the parameter 
, our predictions approach the experimental data, especially when 
. Whereas for close to unity, the mass spectrum of the system gives values quite far from the experiment.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
