Rare\begin{document}${{\Lambda_b \rightarrow \Lambda l^+ l^- }}$\end{document} ![]()
![]()
-
Abstract:
We study the rare decays
\begin{document}$\Lambda_b \rightarrow \Lambda l^+ l^-~(l=e,\mu, \tau)$\end{document} in the Bethe-Salpeter equation approach. We find that the branching ratio is
${\rm Br}(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\times 10^{6} = 1.051 \sim 1.098$ in our model. This result agrees with the experimental data well. In the same parametric region, we find that the branching ratio is
${\rm Br}(\Lambda_b \rightarrow \Lambda e^+ e^-(\tau^+ \tau^-) )\times 10^{6} = 0.252 \sim 0.392 ~(0.286 \sim 0.489)$ .
-
Key words:
- charmonium /
- decay width /
- lattice QCD
-
Figure 1. The BS equation for
$ b(ud)_{00} $ system in the momentum space (K is the interaction kernel).
Figure 2. (color online) The BS wave functions for
$ \Lambda $ with$ E_0 = -0.19 $ GeV.
Figure 3. (color online) The BS wave functions for
$ \Lambda $ with$ E_0=-0.14 $ GeV.
Figure 4. (color online) The BS wave functions for
$ \Lambda $ with$ E_0=-0.09 $ GeV.
Figure 5. (color online) The BS wave functions for
$ \Lambda $ with$ \kappa = -0.05 $ GeV3.
Figure 6. (color online) The BS wave function for
$ \Lambda_b $ with$ E_0 = -0.19 $ GeV,$ E_0 = -0.14 $ GeV.
Figure 7. (color online) The BS wave function for
$ \Lambda_b $ with$ E_0 = -0.09 $ GeV, and$ \kappa = -0.05 $ GeV3.
Figure 8. (color online) The values of
$ R(\omega) $ for different binding energies$ E_0 $ and$ \kappa $ (the value of R decreases with increasing$ \kappa $ , and with increasing$ \kappa $ the line thickens ($ \kappa $ from$ 0.040 $ to$ 0.060 $ ) for the same color line).
Figure 9. (color online) The differential decay width of
$ \Lambda_b \rightarrow \Lambda l^+ l^- $ with the binding energy$ E_0 = -0.19 $ GeV (the decay width increases with increasing$ \kappa $ from$ 0.040 $ to$ 0.060 $ GeV3 for the same color line).
Figure 10. (color online) The differential decay width of
$ \Lambda_b \rightarrow \Lambda l^+ l^- $ with the binding energy$ E_0=-0.14 $ GeV (the decay width increases with increasing$ \kappa $ from$ 0.040 $ to$ 0.060 $ GeV3 for the same color line).
Figure 11. (color online) The differential decay width of
$ \Lambda_b \rightarrow \Lambda l^+ l^- $ with the binding energy$ E_0 = -0.09 $ GeV (the decay width increases with increasing$ \kappa $ from$ 0.040 $ to$ 0.060 $ GeV3 for the same color line).Table 1. The values of
$\alpha_{\rm seff}$ for$ \Lambda $ (the units of$ E_0 $ and$ \kappa $ are GeV and GeV3, respectively).$ E_0 $ $\alpha_{\rm seff}$ −0.19 0.616 0.611 0.661 0.606 0.601 0.596 0.592 0.588 0.584 0.580 0.577 −0.14 0.576 0.570 0.566 0.561 0.557 0.553 0.549 0.546 0.542 0.539 0.536 −0.09 0.521 0.517 0.513 0.509 0.506 0.503 0.500 0.497 0.495 0.492 0.490 $ \kappa \times 10^{3} $ 40 42 44 46 48 50 52 54 56 58 60 
下载: 导出CSV
Table 2. The values of
$\alpha_{\rm seff}$ for$ \Lambda_b $ (the units of$ E_0 $ and$ \kappa $ are GeV and GeV3, respectively).$ E_0 $ $\alpha_{\rm s}$ −0.19 0.806 0.808 0.809 0.796 0.811 0.812 0.814 0.815 0.817 0.818 0.819 −0.14 0.770 0.772 0.774 0.776 0.777 0.779 0.781 0.783 0.785 0.786 0.788 −0.09 0.729 0.732 0.735 0.737 0.713 0.740 0.742 0.744 0.747 0.749 0.751 $ \kappa \times 10^{3} $ 40 42 44 46 48 50 52 54 56 58 60
下载: 导出CSV
Table 3. The values of the branching ratios for
$ \Lambda_b\rightarrow \Lambda l^+ l^- $ , and comparison with other models.$ -E_0 $( $ \times 10^2 $ GeV)
$ \kappa $( $ \times 10^3 $ GeV3)present work 1450±5 present work 14±550 HQET [55] QCD sum rules [32] Exp. [54] $ Br( \Lambda_b\rightarrow \Lambda e^+ e^- ) \times 10^{6} $ 0.464−1.144 0.611−0.867 2.23−3.34 4.6±1.6 − $ Br( \Lambda_b\rightarrow \Lambda \mu^+ \mu^- )\times 10^{6} $ 0.602−1.482 0.856−1.039 2.08−3.19 4.0±1.2 1.08±0.28 $ Br( \Lambda_b\rightarrow \Lambda \tau^+ \tau^- )\times 10^{6} $ 0.177−0.437 0.233−0.331 0.179−0.276 0.8±0.3 −
下载: 导出CSV
-
[1] T.Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett., 107: 201802 (2011) doi: 10.1103/PhysRevLett.107.201802 [2] R. Aaij et al. (LHCB Collaboration), Phys. Lett. B, 725: 25 (2013) doi: 10.1016/j.physletb.2013.06.060 [3] R. Aaij et al., LHCB collaboration, JHEP, 06: 115 (2017); 09: 145 (2018) [4] R. Aaij et al. (LHCB Collaboration), Phys. Rev. Lett., 123: 031801 (2019) doi: 10.1103/PhysRevLett.123.031801 [5] R. Aaij et al. (LHCB Collaboration), LHCB collaboration. JHEP, 09: 146 (2018) [6] T. Mannel and S. Recksiegel, J. Phys. G: Nucl. Part. Phys., 24: 979 (1998) doi: 10.1088/0954-3899/24/5/006 [7] R. Mohanta et al., Prog. Theor. Phys., 102: 645 (1999) doi: 10.1143/PTP.102.645 [8] Y. M. Wang, M. J. Aslam, and C. D. Lü, Eur. Phys. J. C, 59: 847 (2009) doi: 10.1140/epjc/s10052-008-0835-8 [9] T. Gutsche et al., Phys. Rev. D, 87: 074031 (2013) doi: 10.1103/PhysRevD.87.074031 [10] R. N. Faustov and V. O. Galkin, Phys. Rev. D, 96: 053006 (2017) doi: 10.1103/PhysRevD.96.053006 [11] R. F. Alnahdi, T. Barakat, and H. A. Alhendi, Prog. Theor. Exp. Phys.,073B04 (2017) [12] C. S. Huang and H. G. Yan, Phys. Rev. D, 59: 114022 (1999) doi: 10.1103/PhysRevD.59.114022 [13] X. H. Guo and T. Huang, Phys. Rev. D, 53: 4946 (1996) doi: 10.1103/PhysRevD.53.4946 [14] C. S. Huang and C. Q. Geng, Phys. Rev. D, 63: 114024 (2001) doi: 10.1103/PhysRevD.63.114024 [15] T. M. Aliev, A. Özpineci, and M. Savcı, Nucl. Phys. B, 649: 168 (2003) doi: 10.1016/S0550-3213(02)00964-1 [16] T. M. Aliev, A. Özpineci, M. Savcı et al., Phys. Lett. B, 542: 229 (2002) doi: 10.1016/S0370-2693(02)02381-X [17] T. M. Aliev, A. Özpineci, M. Savcı et al., Phys. Rev. D, 67: 035007 (2003) doi: 10.1103/PhysRevD.67.035007 [18] T. M. Aliev, V. Bashiry, and M. Savcı, Eur. Phys. J. C, 38: 283 (2004) doi: 10.1140/epjc/s2004-02045-6 [19] T. M. Aliev, V. Bashiry, and M. Savcı, Nucl. Phys. B, 709: 115 (2005) doi: 10.1016/j.nuclphysb.2004.12.012 [20] T. M. Aliev and M. Savcı, Eur. Phys. J. C, 48: 117 (2006) doi: 10.1140/epjc/s2006-02593-7 [21] T. M. Aliev, M. savcı, and B. B. Şircanlı, Eur. Phys. J. C, 52: 375 (2007) doi: 10.1140/epjc/s10052-007-0356-x [22] T. M. Aliev and M. Savcı, JHEP, 05: 001 (2006) [23] A. K. Giri and R. Mohanta, Eur. Phys. J. C, 45: 151 (2006) doi: 10.1140/epjc/s2005-02407-6 [24] K. Azizi and N. Katırcı, JHEP, 01: 087 (2011) [25] T. M. Aliev, K. Azizi, and M. Savcı, Phys. Rev. D, 81: 056006 (2010) doi: 10.1103/PhysRevD.81.056006 [26] L. F. Gan, Y. L. Liu, W. B. Chen et al., Commu. Theor. Phys., 58: 872 (2012) doi: 10.1088/0253-6102/58/6/14 [27] T. M. Aliev and M. Savcı, Phys. Lett. B, 718: 566 (2012) doi: 10.1016/j.physletb.2012.11.013 [28] T. M. Aliev and M. Savcı, Nucl. Phys. B, 863: 398 (2012) doi: 10.1016/j.nuclphysb.2012.05.027 [29] W. Detmold and S. Meinel, Phys. Rev. D, 93: 074501 (2016) doi: 10.1103/PhysRevD.93.074501 [30] D. Das, Eur. Phys. J. C, 78: 230 (2018) doi: 10.1140/epjc/s10052-018-5731-2 [31] CLEO Collaboration, Phys. Rev. Lett., 75: 624 (1995) doi: 10.1103/PhysRevLett.75.624 [32] C. H. Chen and C. Q. Geng, Phys. Lett. B, 516: 327 (2001) doi: 10.1016/S0370-2693(01)00937-6 [33] Liang-Liang Liu, Chao Wang, and Xin-Heng Guo, Chin. Phys. C, 42: 103106 (2018) doi: 10.1088/1674-1137/42/10/103106 [34] Liang-Liang Liu, Chao Wang, Ying Liu et al., Phys. Rev. D, 95: 054001 (2017) doi: 10.1103/PhysRevD.95.054001 [35] Liang-Liang Liu, Chao Wang, Xian-Wei Kang et al., Eur. Phys. J. C, 80: 193 (2020) doi: 10.1140/epjc/s10052-020-7667-6 [36] X.-H. Guo and T. Muta, Phys. Rev. D, 54: 4629 (1996) [37] L. Zhang and X.-H. Guo, Phys. Rev. D, 87: 076013 (2013) doi: 10.1103/PhysRevD.87.076013 [38] Y. Liu, X.-H. Guo, and C. Wang, Phys. Rev. D, 91: 016006 (2015) doi: 10.1103/PhysRevD.91.016006 [39] X.-H. Guo and H.-K. Wu, Phys. Lett. B, 654: 97 (2007) doi: 10.1016/j.physletb.2007.05.007 [40] M.-H. Weng, X.-H. Guo, and A.W. Thomas, Phys. Rev. D, 83: 056006 (2011) doi: 10.1103/PhysRevD.83.056006 [41] Xin-Heng Guo, Ke-Wei Wei, and Xing-hua Wu, Phys. Rev. D, 77: 036003 (2008) doi: 10.1103/PhysRevD.77.036003 [42] G.P. Lepage and S.J. Brodsky, Phys. Rev. D, 22: 2157 (1980) doi: 10.1103/PhysRevD.22.2157 [43] X.-H. Guo and X.-H. Wu, Phys. Rev. D, 76: 056004 (2007) doi: 10.1103/PhysRevD.76.056004 [44] M. B. Hecht, C. D. Roberts, M. Oettel et al., Phys. Rev. C, 65: 055204 (2002) doi: 10.1103/PhysRevC.65.055204 [45] G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Rev. Mod. Phys., 68: 1125 (1996) doi: 10.1103/RevModPhys.68.1125 [46] W. Detmold, C. J. David Lin, S. Meinel et al., Phys. Rev. D, 87: 074502 (2013) doi: 10.1103/PhysRevD.87.074502 [47] C. K. Chua, X. G. He, and W. S. Hou, Phys. Rev. D, 60: 014003 (1999) doi: 10.1103/PhysRevD.60.014003 [48] CLEO Collaboration, Phys. Rev. Lett., 94: 191801 (2005) doi: 10.1103/PhysRevLett.94.191801 [49] C. F. Perdristat, V. Punjabi, and M. Vanderhaeghen, Prog. Part. Nucl. Phys., 59: 694 (2007) doi: 10.1016/j.ppnp.2007.05.001 [50] S. J. Brofsky and G. R. Farrar, Phys. Rev. D, 11: 1309 (1975) [51] K. Azizi, S. Kartal, A. T. Olgun et al., JHEP, 10: 118 (2012) [52] M. J. Aslam, C. D. Lü, and Y. M. Wang, Phys. Rev. D, 79: 074007 (2009) doi: 10.1103/PhysRevD.79.074007 [53] W. J. Li, Y. B. Dai, and C. S. Huang, Eur. Phys. J. C, 40: 565 (2005) doi: 10.1140/epjc/s2005-02132-2 [54] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D, 98: 030001 (2018) [55] C. H. Chen and C.Q. Geng, Phys. Rev. D, 64: 074001 (2001) doi: 10.1103/PhysRevD.64.074001 [56] M. Oettel, G. Hellstern, R. Alkorfer et al., Phys. Rev. C, 58: 2459 (1998) doi: 10.1103/PhysRevC.58.2459 [57] M. Oettel, M. A. Pichowsky, and L.von. Smekal, Eur. Phys. J. A, 8: 251 (2000) doi: 10.1007/s10053-000-8808-y [58] M. Oettel, R. Alkorfer, and L.von. Smekal, Eur. Phys. J. A, 8: 553 (2000) doi: 10.1007/s100500070078 -
点击查看大图
计量
- 文章访问数: 24
- HTML全文浏览量: 14
- PDF下载量: 0
- 被引次数: 0
京公网安备 11010502036328号 京ICP备17033152号