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Rare\begin{document}${{\Lambda_b \rightarrow \Lambda l^+ l^- }}$\end{document}decay in the Bethe-Salpeter equation approach

Liang-Liang Liu Xian-Wei Kang Zhen-Yang Wang Xin-Heng Guo

Liang-Liang Liu, Xian-Wei Kang, Zhen-Yang Wang, Xin-Heng Guo. Rare\begin{document}${{\Lambda_b \rightarrow \Lambda l^+ l^- }}$\end{document}decay in the Bethe-Salpeter equation approach[J]. Rhhz Test. doi: 10.1088/1674-1137/44/8/083107
Citation: Liang-Liang Liu, Xian-Wei Kang, Zhen-Yang Wang, Xin-Heng Guo. Rare\begin{document}${{\Lambda_b \rightarrow \Lambda l^+ l^- }}$\end{document}decay in the Bethe-Salpeter equation approach

[J]. Rhhz Test. doi: 10.1088/1674-1137/44/8/083107

doi: 10.1088/1674-1137/44/8/083107

Rare\begin{document}${{\Lambda_b \rightarrow \Lambda l^+ l^- }}$\end{document}decay in the Bethe-Salpeter equation approach

Funds: Supported by National Natural Science Foundation of China (11775024, 11575023, 11905117, 11847052, 11805012, 11947001)
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  • 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
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  • 收稿日期:  2020-03-25
  • 网络出版日期:  2020-07-14

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