Semileptonic Decay of Bc Meson into S Wave Charmonium in a QCD Potential Model with Coulombic Part as Perturbation

Abstract

We present the semileptonic decay of Bc meson in a QCD potential model with the coulombic part of the Cornell potential -4αs/3r+br+c as perturbation. Computing the slope and curvature of Isgur Wise function in this approach, we study the pseudoscalar and vector form factors for the transition of Bc meson to its S wave charmonium states. Numerical estimates of widths for the transitions of Bc→J|ψ(ηc)lv1 are presented.

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K. Pathak and D. Choudhury, "Semileptonic Decay of Bc Meson into S Wave Charmonium in a QCD Potential Model with Coulombic Part as Perturbation," Journal of Modern Physics, Vol. 3 No. 8, 2012, pp. 821-826. doi: 10.4236/jmp.2012.38107.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] F. Abe, et al., “Observation of Bc Mesons in pp Collisions at = 1.8 TeV,” Physical Review D, Vol. 58, No. 11, 1998, Article ID 112004. doi:10.1103/PhysRevD.58.112004
[2] I. P. Gouz, V. V. Kiselev, A. K. Likhoded, V. I. Romanovsky and O. P. Yushchenko, “Prospects for the Bc Studies at LHCb,” Physics of Atomic Nuclei, Vol. 67, No. 8, 2004, pp. 1559-1570. doi:10.1134/1.1788046
[3] V. V. Kiselev, A. E. Kovalsky and A. K. Likhoded, “Bc Decays and Lifetime in QCD Sum Rules,” Nuclear Phy- sics B, Vol. 585, No. 1, 2000, pp. 353-382.
[4] T. Huang and F. Zuo, “Semileptonic Bc Decays and Char- monium Distribution Amplitude,” The European Physical Journal C, Vol. 51, No. 4, 2007, pp. 833-839. doi:10.1140/epjc/s10052-007-0333-4
[5] M. A. Ivanov, J. G. K?rner and P. Santorelli, “Semileptonic Decays of the Bc Meson,” Physical Review D, Vol. 63, No. 7, 2001, Article ID 074010. doi:10.1103/PhysRevD.63.074010
[6] M. A. Ivanov, J. G K?rner and P. Santorelli, “Semilep- tonic Decays of Bc Mesons into Charmonium States in a Relativistic Quark Model,” Physical Review D, Vol. 71, No. 9, 2005, Article ID 094006. doi:10.1103/PhysRevD.71.094006
[7] M. A. Ivanov, J. G K?rner and P. Santorelli, “Exclusive Semileptonic and Nonleptonic Decays of the Bc Meson,” Physical Review D, Vol. 73, No. 5, 2006, Article ID 054024. doi:10.1103/PhysRevD.73.054024
[8] D. Ebert, R. N. Faustov and V. O. Galkin, “Properties of Heavy Quarkonia and Bc Mesons in the Relativistic Quark Model,” Physical Review D, Vol. 67, No. 1, 2003, Article ID 014027. doi:10.1103/PhysRevD.67.014027
[9] D. Ebert, R. N. Faustov and V. O. Galkin, “Weak Decays of the Bc Meson to Charmonium and D Mesons in the Relativistic Quark Model,” Physical Review D, Vol. 68, No. 9, 2003, Article ID 094020. doi:10.1103/PhysRevD.68.094020
[10] D. Ebert, R. N. Faustov and V. O. Galkin, “Weak Decays of the Bc Meson to Bs and B Mesonsin the Relativistic Quark Model,” The European Physical Journal C, Vol. 32, No. 1, 2003, pp. 29-43. doi:10.1140/epjc/s2003-01347-5
[11] C. H. Chang and Y. Q. Chen, “Decays of the Bc Meson,” Physical Review D, Vol. 49, No. 7, 1994, pp. 3399-3411. doi:10.1103/PhysRevD.49.3399
[12] J. F. Liu and K. T. Chao, “1/mQ Corrections to Form Fac- tors and Extraction of |Vcb|,” Physical Review D, Vol. 56, No. 7, 1997, pp. 4133-4151. doi:10.1103/PhysRevD.56.4146
[13] A. Abd El-Hady, J. H. Munoz and J. P. Vary, “Semilep- tonic and Nonleptonic Bc Decays,” Physical Review D, Vol. 62, No. 1, 2000, Article ID 014019. doi:10.1103/PhysRevD.62.014019
[14] P. Colangelo and F. De Fazio, “Using Heavy Quark Spin Symmetry in Semileptonic Bc Decays,” Physical Review D, Vol. 61, No. 3, 2000, Article ID 034012. doi:10.1103/PhysRevD.61.034012
[15] M. A. Nobes and R. M. Woloshyn, “Decays of the Bc Meson in a Relativistic Quark-Meson Model,” Journal of Physics G, Vol. 26, No. 7, 2000, p. 1079. doi:10.1088/0954-3899/26/7/308
[16] E. Hernndez, J. Nieves and J. M. Verde-Velasco, “Study of Exclusive Semileptonic and Nonleptonic Decays of in a Nonrelativistic Quark Model,” Physical Review D, Vol. 74, No. 7, 2006, Article ID 074008. doi:10.1103/PhysRevD.74.074008
[17] W. Wang, et al., “Covarient Light Front Approach for Bc transition form factors,” Physical Review D, Vol. 79, No. 5, 2006, Article ID 054012.
[18] M. Lusignoli and M. Masetti, “Bc Decays,” Physics and Astronomy, Vol. 51, No. 4, 1991, pp. 549-555. doi:10.1007/BF01565579
[19] D. Du and Z. Wang, “Predictions of the Standard Model for Weak Decays,” Physical Review D, Vol. 39, No. 5, 1989, pp. 1342-1348. doi:10.1103/PhysRevD.39.1342
[20] R. Dhir, N. Sharma, and R.C. Verma, “Flavor Depen- dence of Bc Meson form Factors and Bc → PP Decays,” Journal of Physics G, Vol. 35, No. 8, 2008, Article ID 085002. doi:10.1088/0954-3899/35/8/085002
[21] S. Godfrey, “Spectroscopy of Bc Mesons in the Relativized Quark Model,” Physical Review D, Vol. 70, No. 5, 2004, Article ID 054017. doi:10.1103/PhysRevD.70.054017
[22] M. Wirbel, B. Stech and M. Bauer, “Exclusive Semileptonic Decays of Heavy Mesons,” Zeitschrift für Physik C Particles and Fields, Vol. 29, No. 4, 1985, pp. 637-642. doi:10.1007/BF01560299
[23] N. Isgur, D. Scora, B. Grinstein, and M. B. Wise, “Se- mileptonic B and D Decays in the Quark Model,” Physical Review D, Vol. 39, No. 3, 1989, pp. 799-818. doi:10.1103/PhysRevD.3 9.799
[24] B. J. Hajarika, K. K. Pathak and D. K. Choudhury, “Isgur-Wise Function in a QCD Potential Model with Coulombic Potential as Perturbation,” Modern Physics Letters A, Vol. 26, No. 21, 2011, p. 1547. doi:10.1142/S0217732311036000
[25] D. K. Choudhury, P. Das, D. D. Goswami and J. K. Sarma, “Static and Dynamic Properties of Pseudoscalar Mesons,” Pramana Journal of Physics, Vol. 44, No. 4, 1995, pp. 519-534.
[26] A. K. Ghatak and S. Lokanathan, “Quantum Mechanics,” McGraw Hill, New York, 1997.
[27] D. K. Choudhury and N. S. Bordoloi, “The Isgur-Wise Function in a QCD Inspired Quark Model,” International Journal of Modern Physics A, Vol. 15, No. 23, 2000, p. 3667. doi:10.1142/S0217751X00002743
[28] D. K. Choudhury and N. S. Bordoloi, “The Isgur-Wise Function in an Improved QCD Inspired Quark Model,” Modern Physics Letters A, Vol. 24, No. 6, 2009, p. 443. doi:10.1142/S0217732309028308
[29] I. J. R. Aitchison and J. J. Dudek, “Variationally Improved Perturbation Theory and the Potential ?α/r + βr,” European Journal of Physics, Vol. 23, No. 6, 2002, p. 605. doi:10.1088/0143-0807/23/6/302
[30] Abramowitz and Stegun, “Handbook of Mathematical Functions,” 1964, Dover Publications.
[31] H. K. Quang and X. Y. Pham, “Elementary Particles and Their Interaction,” Springer, 1998.
[32] N. Isgur and M. B. Wise, “Weak Decays of Heavy Me- sons in the Static Quark Approximation,” Physics Letters B, Vol. 232, No. 1, 1989, pp. 113-117. doi:10.1016/0370-2693(89)90566-2
[33] F. E. Close and A. Wambach, “Quark Model Form Factors for Heavy-Quark Effective Theory,” Nuclear Physics B, Vol. 412, No. 1-2, 1994, pp. 169-180. doi:10.1016/0550-3213(94)90498-7
[34] S. Deoghuria and S. Chakrabarty, “Can the Colour Hyperfine Interaction Explain 1P1 Data?” Journal of Physics G: Nuclear and Particle Physics, Vol. 15, No. 8, 1989, p. 1213.
[35] D. Ebert, R. N. Faustov and V. O. Galkin, “Weak Decay of Bc Meson,” arXiv:hep-ph/0401237, 2004.
[36] H.-M. Choi and C.-R. Ji, “Nonleptonic Two-Body Decays of the Bc Meson in the Light-Front Quark Model and the QCD Factorization Approach,” Physics Review D, Vol. 80, No. 11, 2009, Article ID 114003. doi:10.1103/PhysRevD.80.114003
[37] V. V. Kiselev, A. K. Likhoded and A. I. Onishchenko, “Semileptonic Bc-Meson Decays in Sum Rules of QCD and NRQCD,” Nuclear Physics B, Vol. 569, No. 1-3, 2000, pp. 473-504. doi:10.1016/S0550-3213(99)00505-2
[38] M. A. Sanchis-Lozano, “Weak Decays of Doubly Heavy Hadrons,” Nuclear Physics B, Vol. 440, No. 1-2, 1995, pp. 251-275. doi:10.1016/0550-3213(95)00064-Y
[39] E. Jenkins, M. Luke, A. V. Manohar and M. J. Savage, “Semileptonic Bc Decay and Heavy Quark Spin Symmetry,” Nuclear Physics B, Vol. 390 No. 2, 1993, pp. 463- 473. doi:10.1016/0550-3213(93)90464-Z
[40] M.-T. Choi and J. K. Kim, “Determination of |Vcb| from the Polarization of Vector Meson in the Semileptonic Decay of B and Bc Meson,” Nuclear Physics B, Vol. 419, No. 1-4, 1998, pp. 377-380. doi:10.1016/S0370-2693(97)01480-9
[41] K. Nakamura, et al., “Review of Particle Physics,” Journal of Physics G: Nuclear and Particle Physics, Vol. 37, No. 7A, 2010, Article ID 075021. doi:10.1088/0954-3899/37/7A/075021

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