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Mass Spectra and Decay Constants of Heavy-Light Axial Quarkonia in the Framework of Bethe-Salpeter Equation

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Abstract

In this work we calculate the mass spectrum and decay constants of ground and excited states of heavy-light P-wave mesons such as 1++ and 1+−, with quark composition, \(c\overline {u}, c\overline {s}, b\overline {u}, b\overline {s}\), and \(b\overline {c}\) in the framework of a QCD motivated Bethe-Salpeter equation (BSE) by making use of the exact treatment of the spin structure \((\gamma _{\mu }\bigotimes \gamma _{\mu })\) in the interaction kernel, In this 4 × 4 BSE framework, the coupled Salpeter equations for \(Q\overline {q}\) are first solved for the confining part of interaction, and are shown to decouple under heavy-quark approximation. Then the one-gluon-exchange interaction is perturbatively incorporated, leading to their mass spectral equations. The analytic forms of wave functions obtained from these equations are then used for calculation of leptonic decay constants of ground and excited states of 1++, and 1+− as a test of these wave functions and the over all framework.

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References

  1. Brambilla, N., Pineda, A., Soto, J., Vairo, A.: . Rev. Mod. Phys. 77, 1423 (2005)

    Article  ADS  Google Scholar 

  2. Shifman, M.A., Vainshtein, A.I., Zakharov, V.I.: . Nucl. Phys. B 147, 385,448 (1979)

    Google Scholar 

  3. Eichten, E.J., Quigg, C.: . Phys. Rev. D99, 054025 (2019)

    ADS  Google Scholar 

  4. Godfrey, S., Isgur, N.: . Phys. Rev. D32, 189 (1985)

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Colquhoun, B., Davies, C.T.S., Dowdall, R.J., Kettle, J., Koponen, J., Lepage, G.P., Lytle, A.T.: (HPQCD collaboration). Phys. Rev. D91, 114509 (2015)

    ADS  Google Scholar 

  7. Bali, G.S., Schiling, K., Wachter, A.: . Phys. Rev. D56, 2566 (1997)

    ADS  Google Scholar 

  8. Burch, T., et al.: (Fermilab and MILC Collaboration). Phys. Rev. D81, 034508 (2010)

    ADS  Google Scholar 

  9. Mitra, A.N., Sodermark, B.M.: . Nucl. Phys. A 695, 328 (2001)

    Article  ADS  Google Scholar 

  10. Mitra, A.N., Bhatnagar, S.: . Intl. J. Mod. Phys. A07, 121 (1992)

    Article  ADS  Google Scholar 

  11. Munczek, H.J., Jain, P.: . Phys. Rev. D 46, 438 (1992)

    Article  ADS  Google Scholar 

  12. Jain, P., Munczek, H.J.: . Phys. Rev. D 48, 5403 (1993)

    Article  ADS  Google Scholar 

  13. Bhatnagar, S., Li, S.-Y.: . J. Phys. G 32, 949 (2006)

    Article  ADS  Google Scholar 

  14. Bhatnagar, S., Li, S-Y., Mahecha, J.: . Intl. J. Mod. Phys. E 20, 1437 (2011)

    Article  ADS  Google Scholar 

  15. Bhatnagar, S., Mahecha, J., Mengesha, Y.: . Phys.Rev. D90, 014034 (2014)

    ADS  Google Scholar 

  16. Wang, G.L.: . Phys. Lett. B633, 492 (2006)

    Article  ADS  Google Scholar 

  17. Neubert, M.: . Phys. Rep. bf 245, 259 (1994)

    Article  ADS  Google Scholar 

  18. Ebert, D., Faustov, R.N., Galkin, V.O.: . Phys. At. Nucl. 76, 1554 (2013)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Gasser, J., Leutwyler, H.: . Ann. Phys. 158, 142 (1984)

    Article  ADS  Google Scholar 

  21. Olive, K.A., et al.: . Chin. Phys. C 38, 090001 (2014)

    Article  ADS  Google Scholar 

  22. Patrignani, C., et al.: [Particle Data Group]. Chin. Phys. C40, 100001 (2016)

    ADS  Google Scholar 

  23. Zyla, P.A., et al.: (Particle Data Group). Prog. Theo. Expt. Phys. 2020, 083C01 (2020)

    Article  Google Scholar 

  24. Baglin, C., et al.: . Phys. Lett. B171, 135 (1986)

    Article  ADS  Google Scholar 

  25. Andreotti, M., et al.: . Phys. Rev. D72, 032001 (2005)

    ADS  Google Scholar 

  26. Ablikim, M., et al.: [BESIII Collaboration]. Phys. Rev. Lett. 118, 092002 (2017)

    Article  ADS  Google Scholar 

  27. Deng, W.J., Liu, H., Gui, L.C., Zhong, X.H.: . Phys. Rev. D95, 034026 (2017)

    ADS  Google Scholar 

  28. Bhatnagar, S., Gebrehana, E.: . Phys. Rev. D102, 094024 (2020)

    ADS  Google Scholar 

  29. Bhatnagar, S., Alemu, L.: . Phys. Rev. D 97, 034021 (2018)

    Article  ADS  Google Scholar 

  30. Gebrehana, E., Bhatnagar, S., Negash, H.: . Phys. Rev. D100, 054034 (2019)

    ADS  Google Scholar 

  31. Smith, C.H.L.: . Ann. Phys. (N.Y.) 53, 521 (1969)

    Article  ADS  Google Scholar 

  32. Alkofer, R., Von Smekal, L.: . Phys. Rep. 353, 281 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  33. Karmanov, V.A., Karbonell, J., Sazdjian, H.: . EPJ Web of Conferences 204, 01014 (2019)

    Article  Google Scholar 

  34. Fredrico, T., Salme, G., Viviani, M.: . Phys. Rev. D89, 016010 (2014)

    ADS  Google Scholar 

  35. He, J.: . Phys. Eur. J. C79, 393 (2019)

    Article  ADS  Google Scholar 

  36. Wang, Z.Y., Qi, J.J., Guo, X.H.: . Adv. High Energy Phys. 2019, 7576254 (2019)

    Google Scholar 

  37. Yang, C.B., Cai, X.: . Phys. Rev. D51, 6332 (1995)

    ADS  Google Scholar 

  38. Negash, H., Bhatnagar, S.: . Intl. J. Mod. Phys. E25, 1650059 (2016)

    Article  ADS  Google Scholar 

  39. Azizi, K., Sungu, J.Y.: . J.Phys. G46, 035001 (2019)

    Article  ADS  Google Scholar 

  40. Souza, P.P.D., Monterio, A.P., Vijaya Kumar, K.B.: . Comm. Theor. Phys. 71, 192 (2019)

    Article  ADS  Google Scholar 

  41. Kawanai, T., Sasaki, S.: . AIP Conf. Proc. 1701, 050022 (2016)

    Article  Google Scholar 

  42. Verma, R.C.: . J.Phys. G39, 025005 (2012)

    Article  ADS  Google Scholar 

  43. Wang, Z.G.: . Eur. Phys. J. C 73(8), 2533 (2013)

    Article  ADS  Google Scholar 

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Acknowledgments

This work was done at the Department of Physics, Chandigarh University. We are thankful for the facilities provided to us during the course of work. VG would like to thank Chandigarh University for support for her Doctoral programme. SB would like to thank Prof. K.B. Vijaya Kumar for discussions, and his classmate, Dr. Deept Khanna, for inspiration, due to her selfless service to mankind, even during corona pandemic.

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Authors and Affiliations

  1. Department of Physics, University Institute of Sciences, Chandigarh University, Mohali, 140413, India

    Vaishali Guleria & Shashank Bhatnagar

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  1. Vaishali Guleria
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  2. Shashank Bhatnagar
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Correspondence to Shashank Bhatnagar.

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Guleria, V., Bhatnagar, S. Mass Spectra and Decay Constants of Heavy-Light Axial Quarkonia in the Framework of Bethe-Salpeter Equation. Int J Theor Phys 60, 3143–3160 (2021). https://doi.org/10.1007/s10773-021-04870-5

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