Birleştirilmiş Cornell ve Kuadratik Potansiyeller ile Sinir Ağı Kullanarak bc ̅ Mezon Kütle Spektrumlarının Tahmini

Öz

Bu makale, Cornell potansiyelini ek bir kuadratik potansiyel ile harmanlayan bir sinir ağı (NN) yöntemi kullanarak bc ̅ mezon kütle spektrumlarını incelemektedir. Teorik ve deneysel referanslarla karşılaştırılan sonuçlarımız, bc ̅ mezonlarının özelliklerini tanımlamak için birleşik potansiyel modelinin geçerliliğini doğrulamaktadır. Ayrıca, ek boyutların kuarkonyum sistemleri üzerindeki etkisinin tanımlanması için teorik bir çerçeve vermek üzere yöntemi varsayımsal dört boyutlu bir uzaya uyguluyoruz. Sonuçlar, karmaşık potansiyel modellemesi ile geliştirilmiş NN yönteminin ağır mezon spektroskopisi çalışmalarına uygulanabilirliği ile tutarlıdır.

Anahtar Kelimeler

• Hadronlar
• Makine Öğrenmesi
• QCD

Predicting bc ̅ Meson Mass Spectra Using Neural Network with Combined Cornell and Quadratic Potentials

Öz

This paper examines the bc ̅ meson mass spectra employing a neural network (NN) method which blends Cornell potential with an additional quadratic potential. Our results, which were compared with theoretical and experimental references, confirm the validity of the combined potential model for the description of the properties of bc ̅ mesons. We further apply the method to a hypothetical four-dimensional space to give a theoretical framework for the description of the effect of additional dimensions on quarkonium systems. The results are consistent with the applicability of the NN method, enhanced with the modeling of complex potential, to the study of heavy meson spectroscopy

Anahtar Kelimeler

• Hadrons
• Machine Learning
• QCD

Kaynakça

1. [1] Kuchin, S., Maksimenko, N. 2013. Theoretical estimations of the spin-averaged mass spectra of heavy quarkonia and Bc mesons. Universal Journal of Physics and Application, 7(3), 295-298.
2. [2] Kumar, R., Chand, F. 2013. Asymptotic study to the N-dimensional radial Schrödinger equation for the quark-antiquark system. Communications in Theoretical Physics, 59(5), 528.
3. [3] Dib, C. O., Neill, N. A. 2012. χ b (3 P) splitting predictions in potential models. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 86(9), 094011.
4. [4] Evans, P., Allton, C., Skullerud, J. I. 2014. Ab initio calculation of finite-temperature charmonium potentials. Physical Review D, 89(7), 071502.
5. [5] Hall, R. L. 1984. Simple eigenvalue formula for the Coulomb-plus-linear potential. Physical Review D, 30(2), 433.
6. [6] Thacker, B. A., Lepage, G. P. 1991. Heavy-quark bound states in lattice QCD. Physical Review D, 43(1), 196.
7. [7] Godfrey, S., Isgur, N. 1985. Mesons in a relativized quark model with chromodynamics. Physical Review D, 32(1), 189.
8. [8] Lepage, G. P., Magnea, L., Nakhleh, C., Magnea, U., Hornbostel, K. 1992. Improved nonrelativistic QCD for heavy-quark physics. Physical Review D, 46(9), 4052.

9. [9] Soto, J. 2007. Overview of non-relativistic QCD. The European Physical Journal A, 31, 705-710.
10. [10] Ciftci, H., Hall, R. L., Saad, N. 2003. Asymptotic iteration method for eigenvalue problems. Journal of Physics A: Mathematical and General, 36(47), 11807.
11. [11] Gönül, B., Köksal, K., Bakir, E. 2006. An alternative treatment for Yukawa-type potentials. Physica Scripta, 73(3), 279.
12. [12] Patrignani, C., Agashe, K., Aielli, G., Amsler, C., Antonelli, M., Asner, D., Baer, H., Banerjee, S., Barnett, R., Basaglia, T. 2016. Review of particle physics.
13. [13] Nikiforov, A.F., Uvarov, V.B. 1988. Special functions of mathematical physics (Vol. 205). Springer.
14. [14] Abu-Shady, M. 2016. Heavy quarkonia and Bc-mesons in the cornell potential with harmonic oscillator potential in the N-dimensional Schrodinger equation. International Journal of Applied Mathematics Physics, 2(2), 16-20.
15. [15] Vigo‐Aguiar, J., Simos, T. 2005. Review of multistep methods for the numerical solution of the radial Schrödinger equation. International journal of quantum chemistry, 103(3), 278-290.
16. [16] Gupta, P., Mehrotra, I. 2012. Study of heavy quarkonium with energy dependent potential. Journal of Modern Physics, 3(10), 1530.
17. [17] Kumar, R., Chand, F. 2012. Series solutions to the N-dimensional radial Schrödinger equation for the quark–antiquark interaction potential. Physica Scripta, 85(5), 055008.
18. [18] Eichten, E.J., Quigg, C. 1994. Mesons with beauty and charm: Spectroscopy. Physical Review D, 49(11), 5845.
19. [19] Ebert, D., Faustov, R., Galkin, V. 2003. Properties of heavy quarkonia and B c mesons in the relativistic quark model. Physical Review D, 67(1), 014027.
20. [20] Abou-Salem, L. 2005. A systematic study on nonrelativistic quark–antiquark interactions. International Journal of Modern Physics A, 20(17), 4113-4122.
21. [21] Eichten, E., Gottfried, K., Kinoshita, T., Kogut, J., Lane, K., Yan, T.-M. 1976. Spectrum of Charmed Quark-Antiquark Bound States. Physical Review Letters, 36(21), 1276.
22. [22] Quigg, C., Rosner, J.L. 1979. Quantum mechanics with applications to quarkonium. Physics Reports, 56(4), 167-235.
23. [23] Alford, J., Strickland, M. 2013. Charmonia and bottomonia in a magnetic field. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 88(10), 105017.
24. [24] Barnes, T., Godfrey, S., Swanson, E. 2005. Higher charmonia. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 72(5), 054026.
25. [25] Mutuk, H. 2019. Cornell potential: a neural network approach. Advances in High Energy Physics, 2019(1), 3105373.
26. [26] Lagaris, I.E., Likas, A., Fotiadis, D.I. 1997. Artificial neural network methods in quantum mechanics. Computer Physics Communications, 104(1-3), 1-14.
27. [27] Haykin, S. 1994. Neural networks: a comprehensive foundation. Prentice Hall PTR.
28. [28] Yadav, N., Yadav, A., Kumar, M. 2015. An introduction to neural network methods for differential equations. SpringerBriefs in Applied Sciences and Technology.
29. [29] Spining, M., Darsey, J., Sumpter, B., Nold, D. 1994. Opening up the black box of artificial neural networks. Journal of chemical education, 71(5), 406.
30. [30] Darsey, J., Noid, D., Upadhyaya, B. 1991. Application of neural network computing to the solution for the ground-state eigenenergy of two-dimensional harmonic oscillators. Chemical physics letters, 177(2), 189-194.
31. [31] Barron, A. R. 1993. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information theory, 39(3), 930-945.
32. [32] Karakoc, M., Boztosun, I. 2006. Accurate iterative and perturbative solutions of the Yukawa potential. International Journal of Modern Physics E, 15(06), 1253-1262.
33. [33] Gönül, B., Cançelik, Y. 2017. Remarks on the treatments of nonsolvable potentials. Turkish Journal of Physics, 41(4), 326-336.
34. [34] Chen, J. K. 2013. Spectral method for the Cornell and screened Cornell potentials in momentum space. Physical Review D—Particles, Fields, Gravitation, and Cosmology, 88(7), 076006.
35. [35] Chung, H.S., Lee, J., Kang, D. 2008. Cornell potential parameters for S-wave heavy quarkonia. arXiv preprint arXiv:0803.3116.
36. [36] Eichten, E., Gottfried, K., Kinoshita, T., Lane, K., Yan, T.-M. 1980. Charmonium: comparison with experiment. Physical review D, 21(1), 203.
37. [37] Fulcher, L.P. 1994. Matrix representation of the nonlocal kinetic energy operator, the spinless Salpeter equation and the Cornell potential. Physical Review D, 50(1), 447.
38. [38] Vega, A., Flores, J. 2016. Heavy quarkonium properties from Cornell potential using variational method and supersymmetric quantum mechanics. Pramana, 87, 1-7.
39. [39] Brambilla, N., Eidelman, S., Heltsley, B., Vogt, R., Bodwin, G., Eichten, E., Frawley, A., Meyer, A., Mitchell, R., Papadimitriou, V. 2011. Heavy quarkonium: progress, puzzles, and opportunities. The European Physical Journal C, 71, 1-178.
40. [40] Lichtenberg, D. 1987. Energy levels of quarkonia in potential models. International Journal of Modern Physics A, 2(06), 1669-1705.
41. [41] Akan, T. 2024. Exploring machine learning models for predicting meson mass and width. Physica Scripta, 99(2), 125305.
42. [42] Assi, B., Wagman, M. L. 2023. Baryons, multihadron sytstems, and composite dark matter in nonrelativistic QCD. Physical Review D, 108(9), 096004.