Expectation values and Fisher information theoretic measures of heavy flavoured mesons

Authors

  • E. Omugbe
    Department of Physics, University of Agriculture and Environmental Sciences, Umuagwo, P.M.B. 1038, Imo State, Nigeria
  • E. P. Inyang
    Department of Physics, National Open University of Nigeria, Abuja, Nigeria
  • A. Jahanshir
    Department of Physics and Engineering Sciences, Buein Zahra Technical University, Buein Zahra, Iran
  • C. A. Onate
    Physics Department, Bowen University, Iwo, Osun State, Nigeria
  • C. N. Isonguyo
    Theoretical Physics Group, Department of Physics, University of Uyo, Uyo, Nigeria
  • E. S. Eyube
    Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
  • U. S. Okorie
    Department of Physics, Akwa Ibom State University, Ikot Akpaden, Uyo, Nigeria
  • R. Horchani
    Department of Physics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman
  • A. N. Ikot
    Theoretical Physics Group, Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria

Keywords:

Mesons spectroscopy, Hellmann-Feynman theorem, Expectation values, Fisher information

Abstract

The expectation values play important role in atomic physics and quantum mechanics. They are vital to obtaining the quantum information theoretic measures, Compton profile, electronic kinetic energy, Langevin-Pauli diamagnetic susceptibility, Dirac exchange energy and so on. In this work, however, we utilized the bound state solutions of the non-relativistic Schrödinger equation under the Cornell potential to obtain the expectation values using two analytical methods such as the integral approach and the Hellmann-Feynman theorem method. We applied the mean values to obtain the Fisher information theoretic measures for the Charmonium and Bottomonium mesons. We found that the mean values and probability densities are sensitive to the meson masses and the principal quantum number for fixed orbital quantum states. The Dirac exchange and the kinetic energies obey the lowest bound inequalities for 3D atomic systems. Also, the results obey the Fisher uncertainty product, Cramer-Rao and the Heisenberg uncertainty inequalities for 3D quantum systems.

Dimensions

H. Mutuk, “Mass spectra and decay constants of heavy?light mesons: a case study of QCD sum rules and quark model”, Advances in High Energy Physics 1 (2018) 8095653. https://doi.org/10.1155/2018/8095653.

W. Chen, Y. Chen, T. Chiu, H. Chou, T. Guu & T. Hsieh, “Decay constants of pseudoscalar D-mesons in lattice QCD with domain-wall fermion”, Physics Letters B 736 (2014) 236. https://doi.org/10.1016/j.physletb.2014.07.025.

E. Omugbe, E. P. Inyang, I. J. Njoku, C. Mart??nez-Flores, A. Jahanshir, I. B. Okon, E. S. Eyube, R. Horchani & C. A. Onate, “Approximate mass spectra and root mean square radii of quarkonia using Cornell potential plus spin?spin interactions”, Nuclear Physics A 1034 (2023) 122653. https://doi.org/10.1016/j.nuclphysa.2023.122653.

E. P. Inyang, E. O. Obisung, P. C. Iwuji, J. E. Ntibi, J. Amajama & E. S. William, “Masses and thermal properties of Charmonium and Bottomonium Mesons”, Journal of the Nigerian Society of Physical Sciences 4 (2022) 884. https://doi.org/10.46481/jnsps.2022.884.

E. P. Inyang, A. N. Ikot, E. P. Inyang, I. O. Akpan, J. E. Ntibi, E. Omugbe & E. S. William, “Analytic study of thermal properties and masses of heavy mesons with quarkonium potential”, Results in Physics 39 (2022) 105754. https://doi.org/10.1016/j.rinp.2022.105754.

R. L. Hall & N. Saad, “Schrödinger spectrum generated by the Cornell potential”, Open Physics 13 (2015) 83. https://inspirehep.net/files/0dd5c1297b5b564364fee48eadec646b.

H. S. Chung, J. Lee & D. K. Chung, “Cornell potential parameters for S-wave heavy quarkonia”, Journal of the Korean Physical Society 52 (2008) 1154. https://doi.org/10.3938/jkps.52.1151.

H. Mutuk, “Cornell potential: a neural network approach”, Advances in High Energy Physics 2019 (2019) 3105373. https://doi.org/10.1155/2019/3105373.

E. P. Inyang, N. Ali, R. Endut, N. Rusli, S. A. Aljunid, N. R. Ali & M. Asjad, “Thermal properties and mass spectra of heavy mesons in the presence of a point-like defect”, East European Journal of Physics 1 (2024) 166. https://doi.org/10.26565/2312-4334-2024-1-13.

E. Omugbe, “Non-relativistic eigensolutions of molecular and heavy quarkonia interacting potentials via the Nikiforov-Uvarov method”, Canadian Journal of Physics 98 (2020) 1132. https://doi.org/10.1139/cjp-2020-0039.

E. Omugbe, O. E. Osafile, I. B. Okon, E. P. Inyang & A. Jahanshir, “Any l-state energy of the spinless Salpeter equation under the Cornell potential by the WKB Approximation method: An application to mass spectra of mesons”, Few-Body Syst. 63 (2022) 7. https://doi.org/10.1007/s00601-021-01705-1.

R. Rani, S. B. Bhardwaj & F. Chand, “Mass spectra of heavy and light mesons using asymptotic iteration method”, Communications in Theoretical Physics 70 (2018) 179. https://doi.org/10.1088/0253-6102/70/2/179.

E. Omugbe, O. E. Osafile & M. C. Onyeaju, “Mass spectrum of mesons via the WKB approximation method”, Advances in High Energy Physics 2020 (2020) 5901464. https://doi.org/10.1155/2020/5901464.

P. Gupta & I. Mehrotra, “Study of heavy quarkonium with energy-dependent potential”, Journal of Modern Physics 3 (2012) 1530. https://doi.org/10.4236/jmp.2012.310189.

G. R. Boroum & H. Abdolmalki, “Variational and exact solutions of the wavefunction at origin (WFO) for heavy quarkonium by using a global potential”, Physica Scripta 80 (2009) 065003. https://doi.org/10.1088/0031-8949/80/06/065003.

M. Abu-Shady, E. Omugbe & E. P. Inyang, “Approximate bound state solutions of the fractional Schrödinger equation under the spin?spin-dependent Cornell potential”, Journal of Nigerian Society of Physical Sciences 6 (2024) 1771. https://doi.org/10.46481/jnsps.2024.1771.

N. V. Maksimenko & S. M. Kuchin, “Theoretical estimations of the spin-averaged mass spectra of heavy quarkonia and Bc mesons”, Universal Journal of Physics and Application 7 (2013) 298. https://doi.org/10.13189/ujpa.2013.010310.

R. J. Lombard, J. Mars & C. Volpe, “Wave equation with energy-dependent potentials for confined systems”, Journal of Physics G: Nuclear and Particle Physics 34 (2007) 1879. https://doi.org/10.1088/0954-3899/34/9/002.

M. Abu-Shady & E. P. Inyang, “Heavy and heavy-light meson masses in the framework of trigonometric Rosen-Morse potential using the generalized fractional derivative”, East European Journal of Physics 4 (2022) 80. https://doi.org/10.26565/2312-4334-2022-4-06.

M. Abu-Shady & S. Y. Ezz-Alarab, “Conformable fractional of the analytical exact iteration method for heavy quarkonium masses spectra”, Few-Body Systems 62 (2021) 13. https://doi.org/10.1007/s00601-021-01591-7.

M. Abu-Shady & E. M. Khokha, “Bound state solutions of the Dirac equation for the generalized Cornell potential model”, International Journal of Modern Physics A 36 (2021) 2150195. https://doi.org/10.1142/S0217751X21501955.

M. Coppola, D. Gomez Dumm, S. Noguera & N. N. Scoccola, “Masses of magnetized pseudoscalar and vector mesons in an extended NJL model: The role of axial vector mesons”, Physical Review D 109 (2024) 054014. https://doi.org/10.1103/PhysRevD.109.054014.

S. Yang, M. Jin & D. Hou, “Mass spectra and decay of mesons under strong external magnetic field”, Chinese Physics C 46 (2022) 043107. https://doi.org/10.1088/1674-1137/ac4694.

N. Mukherjee & A. K. Roy, “Energy and information analysis for confined H atom in harmonic environment”, Journal of Physics: Conference Series 1850 (2021) 012013. https://doi.org/10.1088/1751-8113/1850/1/012013.

C. R. Estañón, N. Aquino, D. Puertas-Centeno & J. S. Dehesa, “Two?dimensional confined hydrogen: An entropy and complexity approach”, International Journal of Quantum Chemistry 120 (2020) e26192. https://doi.org/10.1002/qua.26192.

C. R. Estañón, N. Aquino, D. Puertas-Centeno & J. S. Dehesa, “Crámer?Rao complexity of the confined two-dimensional hydrogen”, International Journal of Quantum Chemistry 121 (2021) e26424. https://doi.org/10.1002/qua.26424.

N. Mukherjee, N. P. Chandra & A. K. Roy, “Confined hydrogenlike ions in plasma environments”, Physical Review A 104 (2021) 012803. https://doi.org/10.1103/PhysRevA.104.012803.

K. Kumar & V. Prasad, “Entropic measures of an atom confined in modified Hulthen potential”, Results in Physics 21 (2021) 103796. https://doi.org/10.1016/j.rinp.2020.103796.

J. S. Dehesa, S. Lopez-Rosa & D. Manzano, “Entropy and complexity analyses of D-dimensional quantum systems”, in Statistical Complexity, K. Sen (Ed.), Springer, Dordrecht, 2011. https://doi.org/10.1007/978-90-481-3890-6_5.

N. Mukherjee & A. K. Roy, “Some complexity measures in confined isotropic harmonic oscillator”, Journal of Mathematical Chemistry 57 (2019) 1821. https://doi.org/10.1007/s10910-019-01039-8.

J. C. Angulo, E. Romera & J. S. Dehesa, “Inverse atomic densities and inequalities among density functional”, Journal of Mathematical Physics 41 (2000) 7917. https://doi.org/10.1063/1.1320857.

M. B. Pintarelli & F. Vericat, “Generalized Hausdorff inverse moment problem”, Physica A: Statistical Mechanics and its Applications 324 (2003) 588. https://doi.org/10.1016/S0378-4371(03)00066-9.

N. Mukherjee & A. K. Roy, “Analysis of Compton profile through information theory in H-like atoms inside impenetrable sphere”, Journal of Physics B: Atomic, Molecular and Optical Physics 53 (2020) 235002. https://doi.org/10.1088/1361-6455/abbe28.

C. A. S. Almeida, C. O. Edet, F. C. E. Lima, N. Ali & M. Asjad, “Quantum information entropy of heavy mesons in the presence of point-like defect”, Results in Physics 47 (2023) 106343. https://doi.org/10.1016/j.rinp.2023.106343.

E. Omugbe, E. P. Inyang, R. Horchani, E. S. Eyube, C. A. Onate, T. V. Targema, C. A. Obikee & S. O. Ogundeji, “The correspondences between variance and information entropies of a particle confined by q-deformed hyperbolic potential”, Modern Physics Letters A 39 (2024) 2450151. https://doi.org/10.1142/S0217732324501517.

R. P. Feynman, “Forces in molecules”, Physical Review 56 (1939) 340. https://doi.org/10.1103/PhysRev.56.340.

H. Hellmann, “Zur Rolle der kinetischen Elektronenenergie für die zwischenatomaren Kräfte”, Zeitschrift für Physik 85 (1933) 190. https://doi.org/10.1007/BF01342053.

P. C. W. Davies & D. S. Betts, Introduction to quantum mechanics, Chapman and Hall, London 1994. https://doi.org/10.1201/9780203741481.

M. N. Berberan-Santos, E. N. Bodunov & L. Pogliani, “Classical and quantum study of the motion of a particle in a gravitational field”, Journal of Mathematical Chemistry 37 (2005) 115. https://doi.org/10.1007/s10910-004-1443-y.

V. V. Nesvizhevsky, A. K. Petukhov, H. G. Borner, T. A. Baranova, A. M. Gagarski, M. G. & A. Petrov, “Study of the neutron quantum states in the gravity field”, The European Physical Journal C 40 (2005) 491. https://doi.org/10.1140/epjc/s2005-02135-y.

J. S. Dehesa, R. Gonzalez-Ferez & P. Sanchez-Moreno, “The Fisher-information-based uncertainty relation, Cramer?Rao inequality & kinetic energy for the D-dimensional central problem”, Journal of Physics A: Mathematical and Theoretical 40 (2007) 1845. https://doi.org/10.1088/1751-8113/40/8/011.

E. Omugbe, O. E. Osafile, M. C. Onyeaju, I. B. Okon & C. A. Onate, “The unified treatment of the non-relativistic bound state solutions, thermodynamic properties & expectation values of exponential-type potentials”, Canadian Journal of Physics 99 (2021) 532. https://doi.org/10.1139/cjp-2020-0368.

E. Omugbe, O. E. Osafile, I. B. Okon, E. A. Enaibe & M. C. Onyeaju, “Bound state solutions, Fisher information measures, expectation values & transmission coefficient of the Varshni potential”, Molecular Physics 119 (2021) e1909163. https://doi.org/10.1080/00268976.2021.1909163.

B. R. Frieden, “Science from Fisher information: A unification”, Cambridge University Press, Cambridge, 2004. https://doi.org/10.1017/CBO9780511616907.

B. R. Frieden, A. Plastino, A. R. Plastino & B. H. Soffer, “Fisher-based thermodynamics: Its Legendre transform and concavity properties”, Physical Review E 60 (1999) 48. https://doi.org/10.1103/PhysRevE.60.48.

M. Costa, A. L. Goldberg & C. K. Peng, “Multiscale entropy analysis of biological signals”, Physical Review E 71 (2005) 021906. https://doi.org/10.1103/PhysRevE.71.021906.

P. Jizba, H. Kleinert & M. Shefaat, “Rényi?s information transfer between financial time series”, Physica A: Statistical Mechanics and its Applications 391 (2012) 2989. https://doi.org/10.1016/j.physa.2011.12.064.

C. Ansler, et al., “Particle Data Group”, Physics Letters B 667 (2008) 010001. http://pdg.lbl.gov.

E. Omugbe, R. Horchani, N. J. Okoro, E. S. Eyube, C. A. Onate, E. P. Inyang, V. C. Eze & E. Feddi, “Non-relativistic energy spectra of spectra of O2+ (X 2 ?g ) and N2 (X 1 ?+g ) diatomic molecules confined in a modified Scarf potential via supersymmetric WKB approach”, Molecular Physics 2024 (2024) e2390591. https://doi.org/10.1080/00268976.2024.2390591.

Published

2025-02-01

How to Cite

Expectation values and Fisher information theoretic measures of heavy flavoured mesons. (2025). Journal of the Nigerian Society of Physical Sciences, 7(1), 2350. https://doi.org/10.46481/jnsps.2025.2350

Issue

Volume 7, Issue 1, February 2025

Section

Physics & Astronomy
Copyright & Licensing

Copyright (c) 2024 E. Omugbe, E. P. Inyang, A. Jahanshir, C. A. Onate, C. N. Isonguyo, E. S. Eyube, U. S. Okorie, R. Horchani, A. N. Ikot

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Expectation values and Fisher information theoretic measures of heavy flavoured mesons. (2025). Journal of the Nigerian Society of Physical Sciences, 7(1), 2350. https://doi.org/10.46481/jnsps.2025.2350

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