Abstract
We have extracted the ratio |Vub|/|Vcb| from a combined study of the available inputs on \( \overline{B}\to \left(\pi, \rho, \omega \right){\ell}^{-}{\overline{\nu}}_{\ell } \) and \( \overline{B}\left({\overline{B}}_s\right)\to \left({D}^{\left(\ast \right)},{D}_s^{\left(\ast \right)}\right){\ell}^{-}{\overline{\nu}}_{\ell }\ \left(\ell =\mu\ \textrm{or}\ e\right) \) decays. We have done our analysis with and without the inclusion of the available experimental results on the branching fraction \( \mathcal{BR}\left({\overline{B}}_s\to {K}^{+}{\mu}^{-}{\overline{\nu}}_{\mu}\right) \) or the ratio of the rates \( \Gamma \left({\overline{B}}_s\to {K}^{+}{\ell}^{-}{\overline{\nu}}_{\ell}\right)/\Gamma \left({\overline{B}}_s\to {D}_s^{+}{\ell}^{-}{\overline{\nu}}_{\ell}\right) \). We have used all the available experimental data on the branching fractions in different q2-bins, the available theory inputs on the form factors from lattice and the light cone sum rule (LCSR) approach; analysed the data in different possible scenarios and presented the results. From a combined analysis of all the b → cℓ−νℓ exclusive decays, we have obtained |Vcb| = (40.5 ± 0.6) × 10−3 and from all the b → uℓ−νℓ modes, we obtain |Vub| = (3.46 ± 0.12) × 10−3 which changes to |Vub| = (3.51 ± 0.13) × 10−3 after dropping \( \mathcal{BR}\left({\overline{B}}_s\to {K}^{+}{\mu}^{-}{\overline{\nu}}_{\mu}\right) \). We hence report the values of the ratio |Vub|/|Vcb| = 0.085 ± 0.003 and 0.087 ± 0.003 with and without the input from \( {\overline{B}}_s\to {K}^{+}{\mu}^{-}{\overline{\nu}}_{\mu } \) modes, respectively. We have also predicted the ratio \( \Gamma \left({\overline{B}}_s\to {K}^{+}{\ell}^{-}{\overline{\nu}}_{\ell}\right)/\Gamma \left({\overline{B}}_s\to {D}_s^{+}{\ell}^{-}{\overline{\nu}}_{\ell}\right) \) using the fit results. In addition, we provide the predictions of \( \mathcal{BR}\left({\overline{B}}_s\to {K}^{+}{\mu}^{-}{\overline{\nu}}_{\mu}\right) \) and \( \mathcal{BR}\left(\overline{B}\to \left(\rho, \omega \right){\ell}^{-}{\overline{\nu}}_{\ell}\right) \) in the Standard Model (SM) in small q2-bins.
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Acknowledgments
We would like to thank Marcello Rotondo and Mirco Dorigo for some useful communication. Also, we would like to thank Paolo Gambino for pointing out an error in our first version of the draft. This work of SN is supported by the Science and Engineering Research Board, Govt. of India, under the grant CRG/2018/001260. Also, AB received financial support from the Spanish Ministry of Science and Innovation (Grant No. PID2020-112965GBI00/AEI/10.13039/501100011033).
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Biswas, A., Nandi, S. & Ray, I. Extractions of |Vub|/|Vcb| from a combined study of the exclusive \( b\to u(c){\ell}^{-}{\overline{\nu}}_{\ell } \) decays. J. High Energ. Phys. 2023, 24 (2023). https://doi.org/10.1007/JHEP07(2023)024
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DOI: https://doi.org/10.1007/JHEP07(2023)024