Extractions of |V ub |/|V cb | from a combined study of the exclusive b → u c ℓ − ν ¯ ℓ $$ b\to u(c){\ell}^{-}{\overline{\nu}}_{\ell } $$ decays

Abstract

Abstract We have extracted the ratio |V ub |/|V cb | from a combined study of the available inputs on B ¯ → π ρ ω ℓ − ν ¯ ℓ $$ \overline{B}\to \left(\pi, \rho, \omega \right){\ell}^{-}{\overline{\nu}}_{\ell } $$ and B ¯ B ¯ s → D ∗ D s ∗ ℓ − ν ¯ ℓ ℓ = μ or e $$ \overline{B}\left({\overline{B}}_s\right)\to \left({D}^{\left(\ast \right)},{D}_s^{\left(\ast \right)}\right){\ell}^{-}{\overline{\nu}}_{\ell }\ \left(\ell =\mu\ \textrm{or}\ e\right) $$ decays. We have done our analysis with and without the inclusion of the available experimental results on the branching fraction BR B ¯ s → K + μ − ν ¯ μ $$ \mathcal{BR}\left({\overline{B}}_s\to {K}^{+}{\mu}^{-}{\overline{\nu}}_{\mu}\right) $$ or the ratio of the rates Γ B ¯ s → K + ℓ − ν ¯ ℓ / Γ B ¯ s → D s + ℓ − ν ¯ ℓ $$ \Gamma \left({\overline{B}}_s\to {K}^{+}{\ell}^{-}{\overline{\nu}}_{\ell}\right)/\Gamma \left({\overline{B}}_s\to {D}_s^{+}{\ell}^{-}{\overline{\nu}}_{\ell}\right) $$ . We have used all the available experimental data on the branching fractions in different q 2-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 − ν ℓ exclusive decays, we have obtained |V cb | = (40.5 ± 0.6) × 10 −3 and from all the b → uℓ − ν ℓ modes, we obtain |V ub | = (3.46 ± 0.12) × 10 −3 which changes to |V ub | = (3.51 ± 0.13) × 10 −3 after dropping BR B ¯ s → K + μ − ν ¯ μ $$ \mathcal{BR}\left({\overline{B}}_s\to {K}^{+}{\mu}^{-}{\overline{\nu}}_{\mu}\right) $$ . We hence report the values of the ratio |V ub |/|V cb | = 0.085 ± 0.003 and 0.087 ± 0.003 with and without the input from B ¯ s → K + μ − ν ¯ μ $$ {\overline{B}}_s\to {K}^{+}{\mu}^{-}{\overline{\nu}}_{\mu } $$ modes, respectively. We have also predicted the ratio Γ B ¯ s → K + ℓ − ν ¯ ℓ / Γ B ¯ s → D s + ℓ − ν ¯ ℓ $$ \Gamma \left({\overline{B}}_s\to {K}^{+}{\ell}^{-}{\overline{\nu}}_{\ell}\right)/\Gamma \left({\overline{B}}_s\to {D}_s^{+}{\ell}^{-}{\overline{\nu}}_{\ell}\right) $$ using the fit results. In addition, we provide the predictions of BR B ¯ s → K + μ − ν ¯ μ $$ \mathcal{BR}\left({\overline{B}}_s\to {K}^{+}{\mu}^{-}{\overline{\nu}}_{\mu}\right) $$ and BR B ¯ → ρ ω ℓ − ν ¯ ℓ $$ \mathcal{BR}\left(\overline{B}\to \left(\rho, \omega \right){\ell}^{-}{\overline{\nu}}_{\ell}\right) $$ in the Standard Model (SM) in small q 2-bins.

Keywords

• Bottom Quarks
• CKM Parameters
• Semi-Leptonic Decays