Effects of hybrid confinement potential on predictable hadronic highly resonance states

Document Type : Research Article

Authors

1 Department of Physics and Engineering Sciences, Buein Zahra Technical University, Qazvin, Iran

2 Department of Physics, University of Agriculture and Environmental Sciences Umuagwo, Imo State, Nigeria

Abstract

Unlike light quarkonium bound states, the relativistic effects in highly massive quarkonium states, such as Bottomia, in the large radial excitation states, cause Bottomia to have a strong reaction and sensitivity to relativistic corrections. Highly excited states have a larger separation distance between the constituent quark-antiquark pair in the bound state. Therefore, they will have a relatively high velocity, which makes the relativistic kinetic energy and relativistic mass of quarks non-negligible. Notably, in this study, one of the important behaviors of relativistic effects of predicted highly excited hadronic bound states of Bottomia within the hybrid confinement potential is obtained. The high-energy refinement and relativistic effect modification of mass and kinematic energy are defined within the formalism of quantum oscillator principles and quantum field theory, utilizing the auxiliary variational method. Relativistic corrections and effects on the shape of the potential due to relativistic mass are plotted and compared to the calculated non-relativistic plots. The values of the mass spectra of Bottomia used in the potential plot are consistent with predictions from other theoretical approaches and explain the behavior of the results obtained by the used method.

Graphical Abstract

Effects of hybrid confinement potential on predictable hadronic highly resonance states

Highlights

  • Mass spectra of highly excited states of Bottomia are calculated.
  • Relativistic correction on mass is defined.
  • Relativistic correction effect on the shape of the hybrid potential is plotted. 

Keywords

Main Subjects

Copyright © 2025 The Author(s). Published by IROST.

References

  1. Yoh, J. (1998). The Discovery of the b Qquark at Fermilab in 1977: The Experiment Coordinator’s Story. AIP Conference Proceedinds, 424(1), 29-42. https://doi.org/10.1063/1.55114
  2. Asner, D. M., Atmacan, H., Banerjee, Sw., Bennett, J. V., Bertemes, M., & Bessner, M. et al. (2022). Belle II Executive Summary, arXiv:2203.10203v2[hep-ex]. https://doi.org/10.48550/arXiv.2203.10203
  3. Brambilla, N., Eidelman, S., Hanhart, C., Nefediev, A., Shen, C., & Thomas, C. E. et al. (2020). The xyz States: Experimental and Theoretical Status and Perspectives, Physics Reports, 873, 1-154. https://doi.org/10.1016/j.physrep.2020.05.001
  4. Bokade, C. A., & Bhaghyesh (2025). Predictions for Bottomonium from a Relativistic Screened Potential Model, arXiv: 2501.03147v1[hep-ph]. https://arxiv.org/pdf/2501.03147v1
  5. Tang, Z., Wu, B., Hanlon, A., Mukherjee, S., Petreczky, P., & Rapp, R. (2025). Quarkonium Spectroscopy in the Quark-Gluon Plasma, arXiv:2502.09044v1[nucl-th]. https://doi.org/10.48550/arXiv.2502.09044
  6. Fujiwara, D. (2017). Rigorous Time Slicing Approach to Feynman Path Integrals (1st). Springer. https://doi.org/10.1007/978-4-431-56553-6
  7. Struckmeier, J. (2024). Relativistic Generalization of Feynman’s Path Integral Based on Extended Lagrangians. arXiv:2406.06530v1[quant-ph]. https://doi.org/10.48550/arXiv.2406.06530
  8. Semenoff, G. W. (2023). Quantum Field Theory: An Introduction (1st). Springer Singapore. https://doi.org/10.1007/978-981-99-5410-0
  9. Dienykhan, M., Efimov, G. V., Ganbold, G., & Nedelko, S. N. (1995). Oscillator Representation in Quantum Physics. In Lecture Notes in Physics Monographs (1st). Springer Berlin. https://doi.org/10.1007/978-3-540-49186-6
  10. Greiner, W., Schramm, S., & Steinm W. (2007). Quantum Chromodynamics (3rd). Springer Berlin. https://doi.org/10.1007/978-3-540-48535-3
  11. Gould, R., (2020). Quantum Electrodynamics. Electromagnetic Processes (1st). Springer-Verleg.
  12. Albeverio, S., Høegh-Krohn, R., & Mazzucchi, S. (2008). Mathematical Theory of Feynman Path Integrals: An Introduction (1st). Springer Berlin. https://doi.org/10.1007/978-3-540-76956-9
  13. Copson, E. T. (2009). Asymptotic Expansions: The Saddle-Point Method (1st). Cambridge University Press. https://doi.org/10.1017/CBO9780511526121
  14. Barley, K., Vega-Guzm, J., Ruffing, A., & Suslov, S. K. (2022). Discovery of the Relativistic Schrödinger Equation. Journal of Experimental and Theoretical Physics, Russian Academy of Sciences, 65(1), 90-103. https://doi.org/10.3367/ufne.2021.06.039000
  15. Badalov, V., & Badalov, S. (2023). Generalised Tanh-Shaped Hyperbolic Potential: Klein–Gordon Equation's Bound State Solution. Communications in Theoretical Physics, 75(7), 075003. https://doi.org/10.1088/1572-9494/acd441
  16. Kher, V., Chaturvedi, R., Devlani, N., & Rai, A. K. (2022). Bottomonium Spectroscopy Using Coulomb Plus Linear (Cornell) Potential. The European Physical Journal Plus, 137, 357. https://doi.org/10.1140/epjp/s13360-022-02538-5
  17. Kutzelnigg, W. (1994). Theory of the Expansion of Wave Functions in a Gaussian Basis. Quantum Chemistry Journal, 51(6), 447-463. https://doi.org/10.1002/qua.560510612
  18. Rushka, M., & Freericks, J. K. (2019). A Completely Algebraic Solution of the Simple Harmonic Oscillator. American Journal of Physics, 88(11), 976-985. https://doi.org/10.1119/10.0001702
  19. Kelley, J. D., & Leventhal, J. J. (2017). Ladder Operators for the Harmonic Oscillator. In Problems in Classical and Quantum Mechanics. Springer. https://doi.org/10.1007/978-3-319-46664-4_7
  20. Lehmer, D. H. (1940). On the Maxima and Minima of Bernoulli Polynomials. American Mathematical Monthly, 47(8), 533-538. https://doi.org/10.2307/2303833
  21. Sun, Z.-W., & Pan, H. (2006). Identities Concerning Bernoulli and Euler Polynomials. Acta Arithmetica. 125(1), 21-39. http://eudml.org/doc/278468
  22. Shafie, A., Naji, J., Jahanshir, A., & Heshmatian, S. (2023). Approximation and Analytical Study of the Relativistic Confined Two Particles State within the Complex Potential in the Isotropic Medium. Journal of Particle Science and Technology, 9(2), 85-101. https://doi.org/10.22104/jpst.2024.6528.1243
  23. Ahmadov, A. I., Abasova, K. H., Orucova, M. Sh. (2021). Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature. Advances in High Energy Physics, 2021, 1861946. https://doi.org/10.1155/2021/1861946
  24. Particle Data  Group  (2020). Review  of  Particle Physics. Progress  of   Theoretical   and   Experimental Physics, 2020(8), 083C01. https://doi.org/10.1093/ptep/ptaa104
  25. Badalov, V., Ahmadov, A. I., Dadashov, E. A., & Badalov, S. V.. (2025). Dirac Equation Solution with Generalized Tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra. arXiv:2409.15538v3[hep-ph]. https://doi.org/10.48550/arXiv.2409.15538
  26. Abu-Shady, M. (2016). Heavy Quarkonia and bc* Mesons in the Cornell Potential with Harmonic Oscillator Potential in the N-Dimensional. International Journal of Applied Mathematics and Theoretical Physics, 2(2), 16-20. https://doi.org/10.11648/j.ijamtp.20160202.11
  27. Bukor, B., & Tekel, J. (2023). On Quarkonium Masses in 3D Non-Commutative Space. The European Physical Journal Plus, 138, 499. https://doi.org/10.1140/epjp/s13360-023-04049-3
  28. Purohit, K. R., Jakhad, P., & Rai, A. K. (2022). Quarkonium Spectroscopy of the Linear Plus Modified Yukawa Potential. Physica Scripta, 97(4), 044002. https://doi.org/10.1088/1402-4896/ac5bc2
  29. Li, Q., Liu, M.-S., Lü, Q.-F., Gui, L. C. & Zhong, X.-H.(2020). Canonical Interpretation of Y(10750) and ϒ(10860) in the ϒ Family. The European Physical Journal C, 80(1), 59. https://doi.org/10.1140/epjc/s10052-020-7626-2
  30. Wang, J., & Liu, X. (2024). Identifying a Characterized Energy Level Structure of Highly Charmonium Well Matched to the Peak Structures in e+e− → π+ D0D∗−. Physics Letters B, 849(8), 138456. https://doi.org/10.1016/j.physletb.2024.138456
Journal of Particle Science and Technology
Volume 11, Issue 1
June 2025
Pages 1-10

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History

  • Receive Date: 11 May 2025
  • Revise Date: 11 June 2025
  • Accept Date: 25 June 2025

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