Predicting New Bc Mesons' Excited States: The Tridiagonal Matrix-Numerov Approach

doi:10.26565/2312-4334-2025-4-05

Ali A. Alkathiri Department of Physics, College of Science, Taif University, Taif, Saudi Arabia https://orcid.org/0000-0001-9096-3270
S.A. Abd El-Azeem Physics Department, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia; Physics Department, Faculty of Women for Arts, Science and Education, Ain Shams University, Cairo, Egypt https://orcid.org/0000-0003-4434-9004
Weeam S. Albaltan Department of Physics, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia https://orcid.org/0009-0000-4314-6956
R.F. Alnahdi Physics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia https://orcid.org/0000-0002-1034-1322
Atef Ismail Department of Physics, Al–Azhar University, Assiut, Egypt https://orcid.org/0000-0002-2669-0914
M. Allosh Department of Physics, Faculty of Science, South Valley University, Qena, Egypt https://orcid.org/0000-0001-8389-7076
M.S. Ali African Institute for Mathematical Sciences, Mbour city, Senegal https://orcid.org/0000-0002-0250-438X
Tarek A. Nahool Physics Department, Faculty of Science, Aswan University, Egypt https://orcid.org/0000-0002-3967-0103

DOI: https://doi.org/10.26565/2312-4334-2025-4-05

Keywords: Bottom-charmed meson, Numerov's tridiagonal matrix, β coefficient, Root-mean-square radii

Abstract

The properties of Bottom-charmed meson states were extensively investigated using Numerov's tridiagonal matrix approach to predicting the radial wavefunctions. Based on the resulted values, we predicted the β anharmonicity values and root mean square radii for different excited states of B_c mesons. A comprehensive comparison between the estimated results and recently published theoretical and experimental data was conducted, exhibiting a comparable product with a high degree of accuracy.

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References

M.S. Ali, Spectra of quarkonium, (LAP LAMBERT Academic Publishing, Germany, 2015). http://dx.doi.org/10.13140/2.1.4598.8166

D. Griffiths, Introduction to elementary particles, (John Wiley & Sons, 2020).

M. Thomson, Modern particle physics, (Cambridge University Press, 2013).

G. Kane, Modern elementary particle physics: explaining and extending the standard model, (Cambridge University Press, 2017).

L. Apolinário, Y.-J. Lee, and M. Winn, “Heavy quarks and jets as probes of the QGP,” Progress in Particle and Nuclear Physics, 127, 103990 (2022). https://doi.org/10.1016/j.ppnp.2022.103990

M. Mai, Ulf-G. Meißner, and C. Urbach, “Towards a theory of hadron resonances,” Physics Reports, 1001, 1-66 (2023). https://doi.org/10.1016/j.physrep.2022.11.005

N. Akbar, F. Akram, B. Masud, and M.A. Sultan, “Conventional and hybrid Bc mesons in an extended potential model,” The European Physical Journal A, 55(5), 82 (2019). https://doi.org/10.1140/epja/i2019-12735-1

K.K. Pathak, S. Bhattacharya, and T. Das, “Weak decays of Bc meson in a QCD potential model,” Indian Journal of Physics, 97, 3685–3689 (2023). https://doi.org/10.1007/s12648-023-02716-w

P. Gambino, S. Hashimoto, S. Mächler, M. Panero, F. Sanfilippo, S. Simula, A. Smecca, and N. Tantalo, “On the study of inclusive semileptonic decays of Bs-meson from lattice QCD,” arXiv preprint arXiv:2311.09892 (2023). https://doi.org/10.48550/arXiv.2311.09892

A.M. Yasser, G.S. Hassan, and T.A. Nahool, “A study of some properties of bottomonium,” Journal of Modern Physics, 5(17), 1938 (2014). http://dx.doi.org/10.4236/jmp.2014.517188

M.A. Nobes, and R.M. Woloshyn, “Decays of the Bc meson in a relativistic quark-meson model,” Journal of Physics G: Nuclear and Particle Physics, 26(7), 1079 (2000). https://doi.org/10.1088/0954-3899/26/7/308

M.S. Ali, G.S. Hassan, A.M. Abdelmonem, S.K. Elshamndy, F. Elmasry, and A.M. Yasser, “The spectrum of charmed quarkonium in non-relativistic quark model using matrix Numerov’s method,” Journal of Radiation Research and Applied Sciences, 13(1), 226-233 (2020). https://doi.org/10.1080/16878507.2020.1723949

A.M. Yasser, and T.A. Nahool, “A new gate to Numerov’s method,” Open Access Journal of Physics, 2(3), (2018). https://doi.org/10.22259/2637-5826.0203001

S.M. Ryan, D.J. Wilson, and Hadron Spectrum Collaboration, “Excited and exotic bottomonium spectroscopy from lattice QCD,” Journal of High Energy Physics, 2021(2), 1-23 (2021). https://doi.org/10.1007/JHEP02(2021)214

J. Killingbeck, “Shooting methods for the Schrodinger equation,” Journal of Physics A: Mathematical and General, 20(6), 1411 (1987). https://doi.org/10.1088/0305-4470/20/6/024

V. Kumar, R.M. Singh, S.B. Bhardwaj, R. Rani, and F. Chand, “Analytical solutions to the Schrodinger equation for generalized Cornell potential and its applications to diatomic molecules and heavy mesons,” Modern Physics Letters A, 37(02), 2250010 (2022). https://doi.org/10.1142/S0217732322500109

F.J. Ynduráin, The theory of quark and gluon interactions, (Springer Science & Business Media, 2007).

M.A. Ivanov, Yu.L. Kalinovsky, and C.D. Roberts, “Survey of heavy-meson observables.” Physical Review D, 60(3), 034018 (1999). https://doi.org/10.1103/PhysRevD.60.034018

J. Ahmed, R. Manzoor, L. Chang, A. Raya, and K. Raya, “Heavy Quark Mesons: Mass Spectrum and Mass Relations,” Few-Body Systems, 62(3), 39 (2021). https://doi.org/10.1007/s00601-021-01624-1

A.M. Yasser, G.S. Hassan, S.K. Elshamndy, and M.S. Ali, “Comparison Between Two Numerical Schemes to Study the Spectra of Charmed Quarkonium,” arXiv preprint arXiv:2010.07436 (2020). https://doi.org/10.48550/arXiv.2010.07436

M. Allosh, M.S. Abdelaal, F. Alshowaikh, and A. Ismail, “Numerical Solutions of a Three-Dimensional Schrodinger Equation for a Non–Relativistic Quark Model,” Applied Mathematics & Information Sciences, 17(3), 447-452 (2023). http://dx.doi.org/10.18576/amis/170306

M.S. Ali, and A.M. Yasser, “Spectra of quark-antiquark bound states via two derived QCD potential,” arXiv preprint arXiv:1502.06569 (2015). https://arxiv.org/abs/1502.06569

T.A. Nahool, M. Yasser, M. Anwar, and G.A. Yahya, “Charmonium properties,” East European Journal of Physics, (3) 31-38 (2020). https://doi.org/10.26565/2312-4334-2020-3-04

T. Barnes, S. Godfrey, and E.S. Swanson, “Higher charmonia,” Physical Review D, 72(5), 054026 (2005). https://doi.org/10.1103/PhysRevD.72.054026

Semay, Claude, and B. Silvestre-Brac. "Potential models and meson spectra." Nuclear Physics A 618, no. 4 (1997): 455-482.

M. Allosh, Y. Mustafa, N. Khalifa Ahmed, A. Sayed Mustafa, Few-Body Syst (2021) 62:26 https://doi.org/10.1007/s00601-021-01608-1

M.I. Hapareer, M. Allosh, G.S. Hassan, and A.M. Yasser, “Bottomonia Under Effect Three Inspired QCD Potentials in the Framework of Non-Relativistic Quark Model,” East Eur. J. Phys. (2), 348 (2023). https://doi.org/10.26565/2312-4334-2023-2-41

T. Das, and D.K. Choudhury, “Root mean square radii of heavy flavoured mesons in a quantum chromodynamics potential model,” Pramana, 87, 1-7 (2016). https://doi.org/10.1007/s12043-016-1242-6

C.-Y. Wong, “Molecular states of heavy quark mesons,” Physical Review C, 69(5), 055202 (2004). https://doi.org/10.1103/PhysRevC.69.055202

P.A. Zyla, and Particle Data Group, “Review of Particle Physics,” PTEP, 2020, 083C01 (2020). https://doi.org/10.1093/ptep/ptaa104

I. Asghar, F. Akram, B. Masud, and M.A. Sultan, “Properties of excited charmed-bottom mesons,” Physical Review D, 100(9), 096002 (2019). https://doi.org/10.1103/PhysRevD.100.096002

Q. Li, M.-S. Liu, L.-S. Lu, Q.-F. Lü, L.-C. Gui, and X.-H. Zhong, “Excited bottom-charmed mesons in a nonrelativistic quark model,” Physical Review D, 99(9), 096020 (2019). https://doi.org/10.1103/PhysRevD.99.096020

A.A. Aly, “Heavy meson spectra in the non-relativistic quark model,” M. Sc. Thesis, South Valley University, Egypt, 2012.