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Study of the Generalized Isotonic Oscillators Interaction in Semileptonic Decays of Bottom Mesons and Baryons

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Abstract

We have used mesonic and baryonic wave functions in the presence of the modified quantum isotonic oscillator interaction to compute the parameters of the Isgur–Wise function. Thereby we have presented branching ratios for mesons B and \(B_{s}\), decay widths of baryons \(\Lambda _b \), \(\Omega _b\), \({\vert }V_{cb}{\vert }\) for B and \(B_{s}\) semileptonic decays by using of differential decay width and Isgur–Wise functions. The results are in good agreement with experimental data and the other theoretical values.

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References

  1. B. Aubert, et al. (The BABAR Collaboration), Measurements of the semileptonic decays \(\bar{B}\longrightarrow D\ell \bar{v}\) and \(\bar{B}\longrightarrow D^{*}\ell \bar{v}\) using a global fit to \(DX\ell \bar{v}\) final states. Phys. Rev. D 79, 012002 (2009)

  2. S.S. Gershtein, M. Yu. Khlopov, On the lepton decays of heavy pseudoscalar mesons. Pis’ma v ZhETF 23, 374–377 (1976) [English translation: JETP Lett. 23 (1976) 338–340]

  3. M. Yu. Khlopov, Effects of symmetry breaking in semileptonic decays of mesons. Yadernaya Fizika 28, 1134–1137 (1978) [English translation: Sov. J. Nucl. Phys. 28 (1978) 583–584]

  4. S. Faller, A. Khodjamirian, C. Klein, Th Mannel, \(B\longrightarrow D(*)\) form factors from QCD light-cone sum rules. Eur. Phys. J. C 60, 603–615 (2009)

    Article  ADS  Google Scholar 

  5. B. Aubert, et al. (The BABAR Collaboration), Measurement of \(|V_{cb}|\) and the form-factor slope in \(\bar{B}\longrightarrow D\bar{\ell }\bar{v}_{\ell }\) decays in events tagged by a fully Reconstructed B meson. Phys. Rev. Lett. 104, 011802 (2010)

  6. R.N. Faustov, V.O. Galkin, Weak decays of \(B_s\) mesons to \(D_s\) mesons in the relativistic quark model. Phys. Rev. D 87, 034033 (2013)

    Article  ADS  Google Scholar 

  7. M.A. Ivanov, J.G. Körner, V.E. Lyubovitskij, A.G. Rusetsky, Charm and bottom baryon decays in the Bethe-Salpeter approach: heavy to heavy semileptonic transitions. Phys. Rev. D 59, 074016 (1999)

    Article  ADS  Google Scholar 

  8. S.W. Qiu, C. DeTar, A.X. El-Khadra, A.S. Kronfeld, J. Laiho, R.S. Van de Water, Semileptonic decays \(B \rightarrow D^{(*)}l\nu \) at nonzero recoil. arXiv:1312.0155 [hep-lat]

  9. H.W. Ke, X.H. Yuan, X.Q. Li, Z.T. Wei, Y.X. Zhang, \(\Sigma _b\rightarrow \Sigma _c\) and \(\Omega _b\rightarrow \Omega _c\) weak decays in the light-front quark model. Phys. Rev. D 86, 114005 (2012)

    Article  ADS  Google Scholar 

  10. T.D. Cohen, P.M. Hohler, Heavy baryons in the Skyrme model: the role of highly anharmonic collective motion. Phys. Rev. D 75, 094007 (2007)

    Article  ADS  Google Scholar 

  11. S.H. Dong, G.H. San, Quantum spectrum of some anharmonic central potentials: wave functions ansatz. Found. Phys. Lett. 16, 357 (2003)

    Article  MathSciNet  Google Scholar 

  12. S.H. Dong, On the solutions of the Schrodinger equation with some anharmonic potentials: wave function ansatz. Phys. Scr. 65, 289 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. S.H. Dong, A new approach to the relativistic Schrödinger equation with central potential: ansatz method. Int. J. Theor. Phys. 40, 559 (2001)

    Article  MATH  Google Scholar 

  14. D. Agboola, J. Links, I. Marquette, Y.Z. Zhang, New quasi-exactly solvable class of generalized isotonic oscillators. J. Phys. A: Math. Theor. 47, 395305 (2014), arXiv:1401.6565 [math-ph]

  15. N. Saad, R.L. Hall, H. Ciftci, O. Yesiltas, Study of the generalized quantum isotonic nonlinear oscillator potential. Adv. Math. Phys. 2011, 750168 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Sesma, The generalized quantum isotonic oscillator. J. Phys. A Math. Theor. 43, 185303 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. R. Kumar, F. Chand, Asymptotic study to the N-dimensional radial Schrödinger equation for the quark-antiquark system. Commun. Theor. Phys. 59, 528–532 (2013)

    Article  MathSciNet  Google Scholar 

  18. R. Kumar, F. Chand, Series solutions to the \(N\)-dimensional radial Schrödinger equation for the quark–antiquark interaction potential. Phys. Scr. 85, 055008 (2012)

    Article  ADS  MATH  Google Scholar 

  19. I. D’Souza, C.S. Kalman, P.Y. Kulikov, I.M. Narodetskii, The Kalman-Tran-D’Souza model and the semileptonic decay rates of heavy baryons. Nucl. Phys. B 93, 3–8 (2001)

    Article  Google Scholar 

  20. H. Hassanabadi, S. Rahmani, S. Zarrinkamar, Study of heavy-baryon transitions. Phys. Rev. D 90, 074024 (2014)

    Article  ADS  Google Scholar 

  21. T. Coleman, M.G. Olsson, S. Veseli, Semileptonic form factors: a model-independent approach. Phys. Rev. D 63, 032006 (2001)

    Article  ADS  Google Scholar 

  22. F.U. Bernlochner, Z. Ligeti, S. Turczyk, A proposal to solve some puzzles in semileptonic B decays. Phys. Rev. D 85, 094033 (2012)

    Article  ADS  Google Scholar 

  23. K.A. Olive et al. (Particle Data Group), Review of particle physics. Chin. Phys. C 38, 090001 (2014)

  24. T. Gutsche, M.A. Ivanov, J.G. Korner, V.E. Lyubovitskij, P. Santorelli, N. Habyl, Semileptonic decay \(\Lambda _{b} \rightarrow \Lambda _{c} + \bar{\tau }+ \bar{v}_{\tau }\) in the covariant confined quark model. Phys. Rev. D 91, 074001 (2015)

  25. K. C. Bowler et al., (UKQCD collaboration), First lattice study of semileptonic decays of \(\Lambda _b\) and \(\Xi _b\) baryons. Phys. Rev. D 57, 6948 (1998)

  26. B. Holdom, M. Sutherland, J. Mureika, Comparison of \(\frac{1}{m_{Q}^{2}}\) corrections in mesons and baryons. Phys. Rev. D 49, 2359 (1994)

    Article  ADS  Google Scholar 

  27. T.E. Browder, K. Honscheid, B Mesons. Prog. Part. Nucl. Phys. 35, 81–219 (1995). arXiv:hep-ph/9503414

  28. K.C. Bowler, G. Douglas, R.D. Kenway, G.N. Lacagnina, C.M. Maynard, Semi-leptonic decays of heavy mesons and the Isgur-Wise function in quenched lattice QCD. Nucl. Phys. B 637, 293–310 (2002)

    Article  ADS  Google Scholar 

  29. E. Jenkins, A. Manohar, M.B. Wise, The Baryon Isgur-Wise Function in the Large \(N_c\) Limit. Nucl. Phys. B 396, 38 (1993)

    Article  ADS  Google Scholar 

  30. M.A. Ivanov, V.E. Lyubovitskij, J.G. Körner, P. Kroll, Heavy baryon transitions in a relativistic three-quark model. Phys. Rev. D 56, 348 (1997)

    Article  ADS  Google Scholar 

  31. M.Q. Huang, H.Y. Jin, J.G. Körner, C. Liu, Note on the slope parameter of the baryonic \(\Lambda _b\rightarrow \Lambda _c\) Isgur-Wise function. Phys. Lett. B 629, 27–32 (2005)

    Article  ADS  Google Scholar 

  32. H.W. Ke, X.Q. Li, Z.T. Wei, Diquarks and \(\Lambda _b\rightarrow \Lambda _c\) weak decays. Phys. Rev. D 77, 014020 (2008)

    Article  ADS  Google Scholar 

  33. S. Eidelman et al., Review of particle physics. Phys. Lett. B 592, 1 (2004)

    Article  ADS  Google Scholar 

  34. P. Blasi, P. Colangelo, G. Nardulli, N. Paver, Phenomenology of \(B_s\) decays. Phys. Rev. D 49, 238 (1994)

    Article  ADS  Google Scholar 

  35. R.H. Li, C.D. Lu, Y.M. Wang, Exclusive \(B_s\) decays to the charmed mesons \(D_s^+\) (1968,2317) in the standard model. Phys. Rev. D 80, 014005 (2009)

    Article  ADS  Google Scholar 

  36. S.M. Zhao, X. Liu, S.J. Li, Study on \(B_s\rightarrow D_sJ\)(2317,2460)\(lv^{-}\) semileptonic decays in the CQM model. Eur. Phys. J. C 51, 601 (2007)

    Article  ADS  Google Scholar 

  37. X.J. Chen, H.F. Fu, C.S. Kim, G.L. Wang, Estimating form factors of \(B_s\rightarrow D_s^{(*)}\) and their applications to semi-leptonic and non-leptonic decays. J. Phys. G 39, 045002 (2012)

    Article  ADS  Google Scholar 

  38. Z.J. Xiao, Y. Ying Fan, W.F. Wang, S. Cheng, The semileptonic decays of \(B/Bs\) meson in the perturbative QCD approach: a short review. Chin. Sci. Bull. 59, 3787 (2014)

    Article  Google Scholar 

  39. F. Palombo, “B Decays and CP Violation from BaBar”. Invited talk presented at the 8th Latin American Symposium on High Energy Physics, Valparaiso, Chile (2010). arXiv:1104.1420 [hep-ex]

  40. N.E. Adam et al. (CLEO collaboration), Determination of the \(B \rightarrow D l \bar{\nu }\) decay width and \(|V_{cb}|\). Phys. Rev. D 67, 032001 (2003)

  41. R. Singleton Jr., Semileptonic baryon decays with a heavy quark. Phys. Rev. D 43, 2939 (1991)

    Article  ADS  Google Scholar 

  42. H. Hassanabadi, S. Rahmani, Decay Rates and Branching Ratios of \(\Xi _{b} \rightarrow \Xi {c}\) and \(\Lambda _{b} \rightarrow \Lambda _{c}\) Modes. Eur. Phys. J. Plus 131, 34 (2016)

  43. H.Y. Cheng, B. Tseng, \(1/M\) corrections to baryonic form factors in the quark model. Phys. Rev. D 53, 1457 (1996)

    Article  ADS  Google Scholar 

  44. C. Albertus, E. Herna’ndez, J. Nieves, Combined nonrelativistic constituent quark model and heavy quark effective theory study of semileptonic of \(\Lambda _{b}\) and \(\Xi _{b}\) baryons. Phys. Rev. D 71, 014012 (2005)

  45. J.G. Körner, D. Pirjol, M. Kramer, Heavy baryons. Prog. Part. Nucl. Phys. 33, 787 (1994)

    Article  ADS  Google Scholar 

  46. D. Ebert, R.N. Faustov, V.O. Galkin, Semileptonic decays of heavy baryons in the relativistic quark model. Phys. Rev. D 73, 094002 (2006)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Physics Department, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran

    S. Rahmani & H. Hassanabadi

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  1. S. Rahmani
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Rahmani, S., Hassanabadi, H. Study of the Generalized Isotonic Oscillators Interaction in Semileptonic Decays of Bottom Mesons and Baryons. Few-Body Syst 58, 150 (2017). https://doi.org/10.1007/s00601-017-1311-5

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