Skip to main content
SpringerLink
Log in

Bottomonium spectroscopy using Coulomb plus linear (Cornell) potential

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

The Coulomb plus linear (Cornell) potential is used to investigate the mass spectrum of bottomonium. Gaussian wave function is used in position and momentum space to estimate values of potential and kinetic energies, respectively. Based on our calculations, we study newly observed \({\varUpsilon {(10860)}}\) as an admixture of \(4^{3}S_{1}\) with \(4^{3}D_{1}\) and \({\varUpsilon {(10753)}}\) as an admixture of \(6^{3}S_{1}\) with \(4^{3}D_{1}\); also, we try to assign \({{\varvec{\Upsilon }}{(11020)}}\) as a pure \(4^{3}D_{1}\) bottomonium state. We also study the Regge trajectories in the \((J,M^{2})\) and \((n_r,M^{2})\) planes to help prove our association. We estimate the pseudoscalar and vector decay constants, the radiative (electric and magnetic dipole) transition rates, and the annihilation decay width for bottomonium states.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: There are no associated data available.]

References

  1. P.A. Zyla et al., PTEP 2020(8), 083C01 (2020)

    Google Scholar 

  2. W.R. Innes et al., Phys. Rev. Lett. 39, 1240 (1977)

    Article  ADS  Google Scholar 

  3. K. Han et al., Phys. Rev. Lett. 49, 1612 (1982)

    Article  ADS  Google Scholar 

  4. G. Eigen et al., Phys. Rev. Lett. 49, 1616 (1982)

    Article  ADS  Google Scholar 

  5. C. Klopfenstein et al., Phys. Rev. Lett. 51, 160 (1983)

    Article  ADS  Google Scholar 

  6. F. Pauss et al., Phys. Lett. 130B, 439 (1983)

    Article  ADS  Google Scholar 

  7. D. Besson et al., Phys. Rev. Lett. 54, 381 (1985)

    Article  ADS  Google Scholar 

  8. D.M.J. Lovelock et al., Phys. Rev. Lett. 54, 377 (1985)

    Article  ADS  Google Scholar 

  9. B. Aubert et al., Phys. Rev. Lett. 101, 071801 (2008)

    Article  ADS  Google Scholar 

  10. R. Mizuk et al., Phys. Rev. Lett. 109, 232002 (2012)

    Article  ADS  Google Scholar 

  11. G. Bonvicini et al., Phys. Rev. D 70, 032001 (2004)

    Article  ADS  Google Scholar 

  12. P. del Amo Sanchez et al., Phys. Rev. D 82, 111102 (2010)

    Article  ADS  Google Scholar 

  13. I. Adachi et al., Phys. Rev. Lett. 108, 032001 (2012)

    Article  ADS  Google Scholar 

  14. G. Aad et al., Phys. Rev. Lett. 108, 152001 (2012)

    Article  ADS  Google Scholar 

  15. R. Aaij et al., JHEP 10, 088 (2014)

    Article  ADS  Google Scholar 

  16. A. Bondar et al., Phys. Rev. Lett. 108, 122001 (2012)

    Article  ADS  Google Scholar 

  17. A.E. Bondar et al., Phys. Rev. D 84, 054010 (2011)

    Article  ADS  Google Scholar 

  18. R. Mizuk et al., JHEP 10, 220 (2019)

    ADS  Google Scholar 

  19. B. Chen, A. Zhang, J. He, Phys. Rev. D 101(1), 014020 (2020)

    Article  ADS  Google Scholar 

  20. A. Ali, C. Hambrock, M.J. Aslam, Phys. Rev. Lett. 104, 162001 (2010). [Erratum: Phys. Rev. Lett. 107, 049903 (2011)]

  21. M. Alberti et al., Phys. Rev. D 95(7), 074501 (2017)

    Article  ADS  Google Scholar 

  22. D. Molina, M. De Sanctis, C. Fernández-Ramírez, E. Santopinto, Eur. Phys. J. C 80(6), 526 (2020)

    Article  ADS  Google Scholar 

  23. B. Pandya, M. Shah, P.C. Vinodkumar, Eur. Phys. J. C 81(2), 116 (2021)

    Article  ADS  Google Scholar 

  24. R. Chaturvedi, A.K. Rai, N.R. Soni, J.N. Pandya, J. Phys. G47(11), 115003 (2020)

    Article  ADS  Google Scholar 

  25. J.F. Liu, G.J. Ding, Eur. Phys. J. C 72, 1981 (2012)

    Article  ADS  Google Scholar 

  26. E. Eichten, S. Godfrey, H. Mahlke, J.L. Rosner, Rev. Mod. Phys. 80, 1161 (2008)

    Article  ADS  Google Scholar 

  27. N. Brambilla et al., Eur. Phys. J. C 71, 1534 (2011)

    Article  ADS  Google Scholar 

  28. N. Brambilla et al., Eur. Phys. J. C 74(10), 2981 (2014)

    Article  Google Scholar 

  29. C. McNeile, C.T.H. Davies, E. Follana, K. Hornbostel, G.P. Lepage, Phys. Rev. D 86, 074503 (2012)

    Article  ADS  Google Scholar 

  30. M. Neubert, Phys. Rept. 245, 259 (1994)

    Article  ADS  Google Scholar 

  31. M. Pentia et al., Nucl. Instrum. Meth. A 603, 309 (2009)

    Article  ADS  Google Scholar 

  32. R. Ricken et al., Eur. Phys. J. A 9, 221 (2000)

    Article  ADS  Google Scholar 

  33. A.N. Mitra, S. Bhatnagar, Int. J. Mod. Phys. A 7, 121 (1992)

    Article  ADS  Google Scholar 

  34. T. Otsuka et al., Rev. Mod. Phys. 92(1), 015002 (2020)

    Article  ADS  Google Scholar 

  35. V. Mateu, P.G. Ortega, D.R. Entem, F. Fernández, Eur. Phys. J. C 79(4), 323 (2019)

    Article  ADS  Google Scholar 

  36. N. Brambilla, W.K. Lai, J. Segovia, J. Tarrús Castellà, Phys. Rev. D 101(5), 054040 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  37. M. Nielsen, S.J. Brodsky, Phys. Rev. D 97(11), 114001 (2018)

    Article  ADS  Google Scholar 

  38. Q. Li et al., Phys. Rev. D 99(9), 096020 (2019)

    Article  ADS  Google Scholar 

  39. D. Ebert, R.N. Faustov, V.O. Galkin, Eur. Phys. J. C 71, 1825 (2011)

    Article  ADS  Google Scholar 

  40. E. Eichten et al., Phys. Rev. D 17(11), 3090 (1978)

    Article  ADS  Google Scholar 

  41. E. Eichten, K. Gottfried, T. Kinoshita, K.D. Lane, T.M. Yan, Phys. Rev. D 21, 203 (1980)

    Article  ADS  Google Scholar 

  42. W. Lucha, F.F. Schöberl, Int. J. Mod. Phys. C 10(04), 607–619 (1999)

    Article  ADS  Google Scholar 

  43. R.L. Hall, Phys. Rev. D 30, 433 (1984)

    Article  ADS  Google Scholar 

  44. A. Vega, J. Flores Pramana 87, 73 (2016)

    Article  ADS  Google Scholar 

  45. S. Jacobs, M.G. Olsson, C. Suchyta, Phys. Rev. D 33, 3338 (1986)

    Article  ADS  Google Scholar 

  46. V. Kher, A.K. Rai, Chin. Phys. C 42(8), 083101 (2018)

    Article  ADS  Google Scholar 

  47. Y. Koma, M. Koma, H. Wittig, Phys. Rev. Lett. 97, 122003 (2006)

    Article  ADS  Google Scholar 

  48. S.N. Gupta, J.M. Johnson, Phys. Rev. D 51(1), 168 (1995)

    Article  ADS  Google Scholar 

  49. D.S. Hwang, C. Kim, W. Namgung, Phys. Lett. B 406, 117 (1997)

    Article  ADS  Google Scholar 

  50. N. Devlani, V. Kher, A.K. Rai, Eur. Phys. J. A 50(10), 154 (2014)

    Article  ADS  Google Scholar 

  51. V. Kher, N. Devlani, A.K. Rai, Chin. Phys. C 41(9), 093101 (2017)

    Article  ADS  Google Scholar 

  52. V. Kher, N. Devlani, A.K. Rai, Chin. Phys. C 41(7), 073101 (2017)

    Article  ADS  Google Scholar 

  53. A.K. Rai, B. Patel, P.C. Vinodkumar, Phys. Rev. C 78(5), 055202 (2008)

    Article  ADS  Google Scholar 

  54. T. Barnes, S. Godfrey, E.S. Swanson, Phys. Rev. D 72, 054026 (2005)

    Article  ADS  Google Scholar 

  55. M.B. Voloshin, Prog. Part. Nucl. Phys. 61, 455 (2008)

    Article  ADS  Google Scholar 

  56. O. Lakhina, E.S. Swanson, Phys. Rev. D 74, 014012 (2006)

    Article  ADS  Google Scholar 

  57. A.M. Badalian, B.L.G. Bakker, I.V. Danilkin, Phys. At. Nucl. 73(1), 138–149 (2010)

    Article  Google Scholar 

  58. M. Shah, A. Parmar, P.C. Vinodkumar, Phys. Rev. D 86, 3 (2012)

    Google Scholar 

  59. S.F. Radford, W.W. Repko, Nucl. Phys. A 865(1), 69–75 (2011)

    Article  ADS  Google Scholar 

  60. R. Van Royen, V. Weisskopf, Nuovo Cim. A 50, 617 (1967)

    Article  ADS  Google Scholar 

  61. E. Braaten, S. Fleming, Phys. Rev. D 52(1), 181 (1995)

    Article  ADS  Google Scholar 

  62. D.S. Hwang, G.H. Kim, Phys. Rev. D 55(11), 6944 (1997)

    Article  ADS  Google Scholar 

  63. G.J. Ding, J.J. Zhu, M.L. Yan, Phys. Rev. D 77, 014033 (2008)

    Article  ADS  Google Scholar 

  64. Q.F. Lu, T.T. Pan, Y.Y. Wang, E. Wang, D.M. Li, Phys. Rev. D 94(7), 074012 (2016)

    Article  ADS  Google Scholar 

  65. F.K. Guo, C. Hanhart, G. Li, U.G. Meissner, Q. Zhao, Phys. Rev. D 82, 034025 (2010)

    Article  ADS  Google Scholar 

  66. S.F. Radford, W.W. Repko, M.J. Saelim, Phys. Rev. D 80(3), 034012 (2009)

    Article  ADS  Google Scholar 

  67. D.M. Li, P.F. Ji, B. Ma, Eur. Phys. J. C 71, 1582 (2011)

    Article  ADS  Google Scholar 

  68. W.A. Bardeen, E.J. Eichten, C.T. Hill, Phys. Rev. D 68(5), 054024 (2003)

    Article  ADS  Google Scholar 

  69. W. Kwong, P.B. Mackenzie, R. Rosenfeld, J.L. Rosner, Phys. Rev. D 37, 3210 (1988)

    Article  ADS  Google Scholar 

  70. W. Kwong, J.L. Rosner, Phys. Rev. D 38, 279 (1988)

    Article  ADS  Google Scholar 

  71. J. Segovia, P.G. Ortega, D.R. Entem, F. Fernández, Phys. Rev. D 93(7), 074027 (2016)

    Article  ADS  Google Scholar 

  72. A. Bradley, A. Khare, Z. Phys. C 8, 131 (1981)

    Article  ADS  Google Scholar 

  73. G. Belanger, P. Moxhay, Phys. Lett. B 199, 575 (1987)

    Article  ADS  Google Scholar 

  74. J.Z. Wang, Z.F. Sun, X. Liu, T. Matsuki, Eur. Phys. J. C 78(11), 915 (2018)

    Article  ADS  Google Scholar 

  75. M. Bhat, A.P. Monteiro, K.B. Vijaya Kumar, arXiv:1702.06774v2 (2017)

  76. W.J. Deng, H. Liu, L.C. Gui, X.H. Zhong, Phys. Rev. D 95(7), 074002 (2017)

    Article  ADS  Google Scholar 

  77. Y. Lu, M.N. Anwar, B.S. Zou, Phys. Rev. D 94(3), 034021 (2016)

    Article  ADS  Google Scholar 

  78. S. Godfrey, K. Moats, Phys. Rev. D 92(5), 054034 (2015)

    Article  ADS  Google Scholar 

  79. M. Wurtz, R. Lewis, R.M. Woloshyn, PoS LATTICE2015, 097 (2016)

    Google Scholar 

  80. B.Q. Li, K.T. Chao, Commun. Theor. Phys. 52, 653 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  81. N.R. Soni, B.R. Joshi, R.P. Shah, H.R. Chauhan, J.N. Pandya, Eur. Phys. J. C 78(7), 592 (2018)

    Article  ADS  Google Scholar 

  82. K.B. Bhaghyesh, A.P. Vijaya Kumar, Monteiro J. Phys. G38, 085001 (2011)

    Article  ADS  Google Scholar 

  83. G.L. Wang, Phys. Lett. B 633, 492 (2006)

    Article  ADS  Google Scholar 

  84. D. Ebert, R. Faustov, V. Galkin, Phys. Rev. D 67, 014027 (2003)

    Article  ADS  Google Scholar 

  85. N. Akbar, M.A. Sultan, B. Masud, F. Akram, Phys. Rev. D 95, 074018 (2017)

    Article  ADS  Google Scholar 

  86. N. Brambilla, et al., CERN-2005-005 (2004)

  87. F. Giannuzzi, Phys. Rev. D 78, 117501 (2008)

    Article  ADS  Google Scholar 

  88. S.F. Radford, W.W. Repko, Phys. Rev. D 75, 074031 (2007)

    Article  ADS  Google Scholar 

  89. P. Gonzalez, A. Valcarce, J. Vijande, H. Garcilazo, Int. J. Mod. Phys. A 20, 1842 (2005)

    Article  ADS  Google Scholar 

  90. V.V. Anisovich et al., Phys. Atom. Nucl. 70, 63 (2007)

    Article  ADS  Google Scholar 

  91. C.R. Munz, Nucl. Phys. A 609, 364 (1996)

    Article  ADS  Google Scholar 

  92. D. Ebert, R.N. Faustov, V.O. Galkin, Mod. Phys. Lett. A 18, 601 (2003)

    Article  ADS  Google Scholar 

  93. J.T. Laverty, S.F. Radford, W.W. Repko. arXiv:0901.3917 (2009)

  94. H. Negash, S. Bhatnagar, Int. J. Mod. Phys. E 25(08), 1650059 (2016)

    Article  ADS  Google Scholar 

  95. R. Bruschini, P. González, Phys. Lett. B 791, 409–413 (2019)

    Article  ADS  Google Scholar 

  96. P. Bicudo, M. Cardoso, N. Cardoso, M. Wagner, Phys. Rev. D 101(3), 034503 (2020)

    Article  ADS  Google Scholar 

  97. V.M. Abazov et al., Phys. Rev. D 86, 031103 (2012)

    Article  ADS  Google Scholar 

  98. R. Aaij et al., Eur. Phys. J. C 74(10), 3092 (2014)

    Article  Google Scholar 

  99. D. Ebert, R.N. Faustov, V.O. Galkin, Phys. Rev. D 67, 014027 (2003)

    Article  ADS  Google Scholar 

  100. S.N. Gupta, J.M. Johnson, W.W. Repko, Phys. Rev. D D54, 2075 (1996)

    Article  ADS  Google Scholar 

  101. M. Kruczenski, L.A. Pando Zayas, J. Sonnenschein, D. Vaman, JHEP 06, 046 (2005)

    Article  ADS  Google Scholar 

  102. S.S. Afonin, I.V. Pusenkov, EPJ Web Conf. 125, 04006 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

A. K. Rai acknowledges the financial support extended by the Department of Science of Technology, India, under the SERB fast track scheme SR/FTP /PS-152/2012.

Author information

Authors and Affiliations

  1. Applied Physics Department, Polytechnic, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, 390002, India

    Virendrasinh Kher & Nayneshkumar Devlani

  2. Ministry of Education, Abu Dhabi, UAE

    Raghav Chaturvedi

  3. Department of Physics, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat, 395007, India

    A. K. Rai

Authors
  1. Virendrasinh Kher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raghav Chaturvedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nayneshkumar Devlani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. K. Rai
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kher, V., Chaturvedi, R., Devlani, N. et al. Bottomonium spectroscopy using Coulomb plus linear (Cornell) potential. Eur. Phys. J. Plus 137, 357 (2022). https://doi.org/10.1140/epjp/s13360-022-02538-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-02538-5

Search

Navigation