Masses and thermal properties of a Charmonium and Bottomonium Mesons

Authors

  • E. P. Inyang
    Department of Physics, National Open University of Nigeria, Jabi, Abuja, Nigeria
    https://orcid.org/0000-0002-5031-3297
  • E. O. Obisung
    Department of Physics, University of Calabar, PMB 1115, Calabar, Nigeria
  • P. C. Iwuji
    Department of Physics, University of Calabar, PMB 1115, Calabar, Nigeria
  • J. E. Ntibi
    Theoretical Physics Group, Department of Physics, University of Calabar, PMB 1115, Calabar, Nigeria
  • J. Amajama
    Department of Physics, University of Calabar, PMB 1115, Calabar, Nigeria
  • E. S. William
    Theoretical Physics Group, Department of Physics, University of Calabar, PMB 1115, Calabar, Nigeria

Keywords:

Schrödinger equation, Nikiforov-Uvarov method, heavy mesons, Thermal properties

Abstract

In this research, we model Hulthén plus generalized inverse quadratic Yukawa potential to interact in a quark-antiquark system. The solutions of the Schrödinger equation are obtained using the Nikiforov-Uvarov method. The energy spectrum and normalized wave function were obtained. The masses of the heavy mesons for different quantum states such as 1S, 2S , 1P, 2P 3S, 4S, 1D, and 2D were predicted as 3.096 GeV, 3.686 GeV, 3.327 GeV, 3.774GeV, 4.040 GeV, 4.364GeV, 3.761 GeV, and 4.058 GeV respectively for charmonium (cc). Also, for bottomonium (bb) we obtained 9.460 GeV, 10.023 GeV, 9.841 GeV, 10.160 GeV, 10.345 GeV, 10.522 GeV, and 10.142GeV for different states of 1S , 2S , 1P , 2P , 3S , 4S , 1D respectively. The partition function was calculated from the energy spectrum, thereafter other thermal properties were obtained. The results obtained showed an improvement when compared with the work of other researchers and excellently agreed with experimental data with a percentage error of 1.60 % and 0.46 % for (cc) and (bb), respectively.

Author Biography

J. Amajama

Department of Physics

Dimensions

H. Ciftci & H.F. Kisoglu, “Nonrelativistic-Arbitrary l-states of quarkonium through Asymptotic Iteration method”, Advances in High Energy Physics 45 (2018) 49705.

E. Omugbe, O.E. Osafile, I. B. Okon, E.S. Eyube, E.P. Inyang, U.S. Okorie, A. Jahanshir, & C.A. Onate, “Non- relativistic bound state solutions with l-deformed Kratzer-type potential using the super-symmetric WKB method: application to theoretic-information measures”, European Physical Journal D 76 (2022) 11.

C.O.Edet, E.B.Ettah, S.A.Aljunid, R.Endut,N.Ali,A.N.Ikot, & M.Asjad, “Global Quantum information-Theoretic measures in the presence of Magnetic and Aharanov-Bohm(AB)fields”, Symmetry 14 (2022) 976. doi.org/10.3390/sym14050976.2022.105749

E.Omugbe, O.E. Osafile, I.B. Okon, E.P. Inyang, E.S. William, & A. Jahanshir, “Any L-state energy of the spinlessSalpeter equation under the Cornell potential by the WKB Approximation method: An Application to mass spectra of mesons”, Few-Body Systems 63 (2022) 7.

M. Allosh,Y. Mustafa, N.K. Ahmed & A.S. Mustafa, “Ground and Excited state mass spectra and properties of heavy-light mesons”, Few-Body System 62 (2021) 26.

E. S. William, E. P. Inyang, & E. A. Thompson, “Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén-Hellmann potential model”, Revista Mexicana Fisica 66 (2020) 730. https://doi.org/10.31349/RevMexFis.66.730.

E. Omugbe, “Non-relativistic eigensolutions of molecular and heavy quarkonia interacting potentials via the Nikiforov-Uvarov method”, Canadian Journal of Physics 98 (2020)1125.

E.S. William, E.P. Inyang, I.O. Akpan, J.A. Obu, A.N. Nwachukwu, & E.P. Inyang, “Ro-vibrational energies and expectation values of selected diatomic molecules via Varshni plus modified Kratzer potential model”, Indian Journal of Physics (2022). https://doi.org/10.1007/s12648-0222-02308-0

E.P. Inyang & E.O. Obisung, “The study of electronic states of NI and ScI molecules with screened Kratzer Potential”, East European Journal of Physics 3 (2022) 32. https://doi.org/10.26565/2312-4334-2022-3-04.

M.C.Zhang, G.H.Sun & S.H.Dong.“Exactly complete solutions of the Schrodinger equation with a spherically harmonic oscillatory ring-shaped potential”, Physics Letters A 374 (2010) 708.

E. S. William, E. P. Inyang, J. E. Ntibi, J.A. Obu & E. P. Inyang, “Solutions of the Non-relativistic Equation Interacting with the Varshni-Hellmann potential model with some selected Diatomic molecules”, Jordan Journal of Physics 15 (2022) 193.

M.G. Miranga, G.H. Sun & S.H. Dong, “The Solution of the second Poschl-Teller like potential by Nikiforov-Uvarov method”, International Journal of Modern Physics E 19 (2010) 129.

E.P. Inyang, E.S. William, E. Omugbe, E.P. Inyang, E.A. Ibanga, F. Ayedun,I.O. Akpan & J.E. Ntibi, “Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional analysis method”, Revista Mexicana de Fisica 68 (2022) 14.

A.N. Ikot, U.S. Okorie, P.O. Amadi, C.O. Edet, G.J. Rampho, & R. Sever, “The Nikiforov-Uvarov-Functional Analysis (NUFA) Method: A new approach for solving exponential-Type potentials”, Few-Body System 62 (2021) 9. https://doi.org/10.1007/s00601-021-021-01593-5

E. P. Inyang, E.S. William , J.E. Ntibi, J.A. Obu, P.C. Iwuji, & E.P. Inyang, “Approximate solutions of the Schrodinger equation with Hulthén plus screened Kratzer potential using the Nikiforov-Uvarov-Functional analysis method: An Application to diatomic molecules”, Canadian Journal of Physics (2022). https://doi.org/10.1139/cjp-2022-0030

I.B. Okon, C.A. Onate, E. Omugbe, U.S. Okorie, C.O. Edet, A.D. Antia, J.P. Araujo, C.N. Isonguyo, M.C. Onyeaju, E.S William, R. Horchani, & A. N. Ikot, “Aharonov-Bohm(AB) flux and thermomagnetic properties of Hellmann plus screened Kratzer potential as applied to diatomic molecules using Nikiforov-Uvarov-Functional analysis method”, Molecular Physics (2022) e2046295.

E. P. Inyang, E. P. Inyang, I. O. Akpan, J. E. Ntibi, & E. S.William, “Analytical solutions of the Schrödinger equation with class of Yukawa potential for a quarkonium system via series expansion method”, European Journal of Applied Physics 2 (2020) 36. http://dx.doi.org/10.24018/ejphysics.2020.2.6.26

E.P. Inyang, P.C. Iwuji, J.E. Ntibi ,E.S. William & E.A. Ibanga, “Solutions of the Schrodinger equation with Hulthén-screened Kratzer potential : Application to diatomic molecules”, East European Journal of Physics 1 (2022)11. https://doi.org/10.26565/2312-4334-2022-2-02

M. Abu-Shady, & H.M. Fath-Allah, “The effect of extended Cornell potential on heavy and heavy-light meson masses using series method”, Journal of the Egyptian mathematical society 23 (2019) 156.

M. Abu-Shady, T. A. Abdel-Karim , & E. M. Khokha, “Exact solution of the N-dimensional Radial Schrödinger Equation via Laplace Transformation method with the Generalized Cornell potential”, Journal of Quantum Physics 45 (2018) 587.

C.O. Edet, S. Mahmoud, E.P. Inyang, N. Ali, S. A. Aljunid, R. Endut, A.N. Ikot & M. Asjad, “Non-Relativistic Treatment of the 2D Electron System Interacting via Varshni-Shukla Potential Using the Asymptoptic Iteration Method”, Mathematics 10 (2022) 2824. https://doi.org/10.3390/math10152824.

E. Omugbe, O.E.Osafile, & M.C. Onyeajh, “Mass spectrum of mesons via WKB Approximation method”, Advances in High Energy Physics 10 (2020)1143.

E.Omugbe,O.E.Osafile,,E.P.Inyang & A.Jahanshir, “Bound state solutions of the hyper-radial Klein-Gordon equation under the Deng-Fan potential by WKB and SWKB methods”, Physica Scripta 96 (2021) 125408

E. Omugbe, “Non-relativistic energy spectrum of the Deng-Fan Oscillator via the WKB Approximation method”, Asian Journal of Physics and Chemistry 26 (2020) 36.

C.A. Onate, I.B. Okon, M.C. Onyeaju & A.D. Antia, “Approximate solutions of the Schrodinger Equation for a Momentum-Dependent potential ”,Journal of Nigeria Society Physical Science 4 (2022) 250. DOI:10.46481/jnsps.2021.209

C.A. Onate, G.O. Egharerba, & D.T. Bankole, “Eigensolution to Morse potential for Scandium and Nitrogen monoiodides ”,Journal of Nigeria Society Physical Science 3 (2021) 286. Doi: 10.46481/jnsps/2021.407

W.C. Qiang & S.H. Dong, “Proper quantization rule”, Europhysics Letters 89 (2010) 10003.

C.A.Onate, & M.C. Onyeaju, “Entropic system in the relativistic Klein-Gordon Particle ”, Journal of Nigeria Society Physical Science 3 (2021) 171. DOI:10.46481/jnsps.2021.209

S.H. Dong & M. Cruz-Irisson,“Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties”,Journal of Mathematical Chemistry 50 (2012) 892.

S. H. Dong, M. Lozada-Casson, J. Yu, F.J. Angeles & A.L. Rivera, “Hidden symmetries and thermodynamic properties for a harmonic oscillator plus an inverse square potential”, International Journal of Quantum Chemistry 107 (2007) 371.

S. H. Dong, “Group theory approach to the Dirac equation with a Coulomb plus Scalar potential in D+1dimensions”, Journal of Mathematical Physics 44 (2003) 4479.

M. Abu-shady, C.O.Edet & A.N.Ikot, “Non-relativistic Quark model under external magnetic and Aharanov-Bohm (AB) fields in the presence of Temperature-Dependent confined Cornell potential”, Canadian Journal of Physics (2021) 10.11139/cjp-2020-0101

R. Kumar & F. Chand, “Asymptotic study to the N-dimensional Radial Schrodinder Equation for the quark-antiquark system”, Communication in Theoretical Physics 59 (2013) 467.

J.P. Prasanth , K. Sebastian & V. M. Bannur, “Revisiting Cornell potential model of the Quark-Gluon plasma”, Physica A 558 (2020) 124921.

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 20 (2018) 653.

H. Mutuk, “Cornell Potential: A Neural Network Approach”, Advances in High Energy Physics 22 (2019) 65.

A. Vega & J. Flores, “Heavy quarkonium properties from Cornell potential using variational method and supersymmetric quantum mechanics”, Pramana-Journal of Physics 87 (2016)111.

R. Kumar, R.M.Singh,S.B.Bhahardivaj,R.Rani & F. Chand, “Analytical solutions to the Schrodinger equation for generalized Cornell potential and its application to diatomic molecules and heavy mesons”, Modern Physics Letter A 37 (2022) 2250010.

H. Hassanabadi, M. Ghafourian & S. Rahmani,“ Study of the Heavy-Light mesons properties via the Variational method for Cornell interaction”, Few-Body System 15 (2016) 1040. DOI: 10.1007/s00601-015-1040-6

M. Abu-Shady, & S.Y. Ezz-Alarab, “Trigonometric Rosen-Morse Potential as a Quark-Antiquark Interaction Potential for Meson Properties in the Non-relativistic Quark Model Using EAIM”, Few-Body Systems 60 (2019) 66. https://doi.org/10.1007/s00601-019-1531-y

M. Abu-shady, H.M. Mansour & A. I. Ahmador, “Dissociation of Quarkonium in Hot and Dense media in an Anisotropic plasma in the Non-relativistic Quark model”, Advances in High Energy Physics 22 (2019) 615.

E.P. Inyang , E.P. Inyang, J. E. Ntibi, E. E. Ibekwe, & E. S. William, “Approximate solutions of D-dimensional Klein-Gordon equation with Yukawa potential via Nikiforov-Uvarov method”, Indian Journal of Physics 95 (2021) 2739. https://doi.org/10.1007/s12648-020-01933-x

E.P. Inyang, E.P. Inyang, E. S. William & E.E. Ibekwe, “Study on the applicability of Varshni potential to predict the mass-spectra of the Quark-Antiquark systems in a non-relativistic framework”, Jordan Journal of Physics 14 (2021) 345.

E.E. Ibekwe, U.S. Okorie, J.B. Emah, E.P. Inyang & S.A. Ekong, “Mass spectrum of heavy quarkonium for screened Kratzer potential(SKP) using series expansion method”, European Physical Journal Plus 87 (2021) 11. https://doi.org/10.1140/epjp/s13360-021-01090-y

K. R. Purohit, P. Jakhad & A.K. Rai, “Quarkonium spectroscopy of the linear plus modified Yukawa potential”, Physica Scripta 97 (2022) 044002.

S. Patel, P.C. Vinodkumar & S. Bhatnagar, “Decay rates of charmonia within a quark-antiquark confining potential”, Chinese Physics C 40 (2016) 053102

V. Mateu, P.G. Ortega, D.R. Entem & F. Fernadez,“ Calibrating the nave Cornell model with nrqcd”, The European Physical Journal C 79 (2019) 323.

F. Brau & C. Sernay, “The three-dimensional Fourier grid Hamiltonian method”, Journal of computational physics 139 (1998) 136.

A. Bhaghyesh, “Charmonium properties using the Discrete variable representation (DVR)method”, Advances in High Energy Physics (2021)7. Doi.org/10.1155/2021/9991152

S. Jacobs, M.G. Olsson & C. Suchyta, “Comparing the Schrodinger and Spinless Salpeter equations for heavy-quark bound states”, Physical Review D 33 (1986) 3348.

B. Grinstein, “A modern introduction to quarkonium theory”, International Journal of Modern Physics 15 (2000) 461.

W. Lucha, F. Schoberl & D. Gromes. “Bound states of quarks”, Physics Reports 200 (1991)240.

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

M. Abu-Shady , T. A. Abdel-Karim & Y. Ezz-Alarab, “Masses and thermodynamic properties of heavy mesons in the non-relativistic quark model using the Nikiforov-Uvarov method”, Journal of Egyptian Mathematical Society 23 (2019)155.

E.P.Inyang,E.P.Inyang, I.O.Akpan, J.E.Ntibi, & E.S.William, “Masses and thermodynamic properties of a Quarkonium system”, Canadian Journal Physics 99 (2021) 990.https://doi.org/10.1139/cjp-2020-0578.

X. Cao, S. Qiu, H. Liu & D. Li, “Thermal properties of light mesons from holography” 8 (2021) 005.

E.P. Inyang, E.S. William, J.O. Obu, B. I. Ita , E.P. Inyang & I.O. Akpan, “Energy spectra and expectation values of selected diatomic molecules through the solutions of Klein-Gordon equation with Eckart-Hellmann potential model”, Molecular Physics 119 (2021) e1956615 https://doi.org/10.1080/00268976.2021.1956615

I.B Okon,E. Omugbe, A.D. Antia, C. A. Onate, L.E. Akpabio, & O.E. Osafile, “Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthén plus hyperbolic exponential inversely quadratic potential”, Scientific Reports 11 (2021)21.

P.O. Okoi, C.O. Edet, T.O. Magu & E.P. Inyang, “Eigensolution and Expectation values of the Hulthén and Generalized Inverse Quadratic Yukawa potential”, Jordan Journal of Physics 15 (2022) 148.

L. Hulthén ,“Über die eigenlosunger der Schro¨dinger-Gleichung des deuterons”, Ark. Mat. Astron. Fys. A 28 (1942) 5 .

O. Oluwadare & K. Oyewumi “Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential”, Chinese Physics Letters 34 (2017) 110301.

S.K. Nikiforov, & V.B. Uvarov. Special functions of Mathematical Physics (Birkhauser, Basel, 1988).

E. P. Inyang, E. S. William & J.A.Obu, “Eigensolutions of the N-dimensional Schrödinger equation interacting with Varshni-Hulthén potential model”, Revista Mexicana de Fisica 67 (2021) 193. https://doi.org/10.31349/RevMexFis.67.193

M. Abu-Shady, “N-dimensional Schrödinger equation at finite temperature using the Nikiforov-Uvarov method”, Journal of Egyptian Mathematical Society 21 (2016) 4.

I.S. Gradshteyn & I.M. Ryzhik, Tables of integrals, series and product, 7th ed. Academic Press, Boston (2007).

I.O. Akpan, E.P. Inyang, E.P. Inyang & E.S. William, “Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system”, Revista Mexica De Fisica 67 (2021) 490.

E. P. Inyang, J. E. Ntibi, E.A. Ibanga, F. Ayedun, E. P. Inyang, E.E. Ibekwe, E. S. William & I.O. Akpan, “Thermodynamic properties and mass spectra of a quarkonium system with Ultra Generalized Exponential- Hyperbolic potential”, Communication in Physical Science 7 (2021)114.

R. Olive, D. E. Groom & T.G. Trippe, “Particle Data Group”, Chinese Journal of Physics C 38 (2014) 60.

M. Tanabashi , C. D. Carone,T.G.Trippe, & C.G. Wohl, “Particle Data Group”, Physical Review D 98 (2018) 546.

E.P. Inyang, P.C. Iwuji, J.E. Ntibi, E. Omugbe, E.A. Ibanga & E.S. William, “Quark-antiquark study with inversely quadratic Yukawa potential using Nikiforov-Uvarov-Functional analysis method”, East European Journal of Physics 2 (2022) 51. https://doi.org/10.26565/2312-4334-2022-2-05

Published

2022-08-19

How to Cite

Masses and thermal properties of a Charmonium and Bottomonium Mesons. (2022). Journal of the Nigerian Society of Physical Sciences, 4(3), 884. https://doi.org/10.46481/jnsps.2022.884

Issue

Volume 4, Issue 3, August 2022

Section

Special Issue : "Recent Advances in Applications of Potential Models ... "
Copyright & Licensing

Copyright (c) 2022 E. P. Inyang, E. O. Obisung, P. C. Iwuji, J. E. Ntibi, J. Amajama, E. S. William

Creative Commons License

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

How to Cite

Masses and thermal properties of a Charmonium and Bottomonium Mesons. (2022). Journal of the Nigerian Society of Physical Sciences, 4(3), 884. https://doi.org/10.46481/jnsps.2022.884

Similar Articles

31-40 of 273

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)