Extractions of |Vub|/|Vcb| from a combined study of the exclusive b→ u(c) ℓ−ν¯ ℓ decays

We have extracted the ratio |V<inf>ub</inf>|/|V<inf>cb</inf>| from a combined study of the available inputs on B¯ → (πρω) ℓ⁻ν¯ <inf>ℓ</inf> and B¯(B¯s)→(D(∗)Ds(∗))ℓ−ν¯ℓ(ℓ=μore) decays. We have done our analysis with and without the inclusion of the available experimental results on the branching fraction BR(B¯ <inf>s</inf>→ K⁺μ⁻ν¯ <inf>μ</inf>) or the ratio of the rates Γ(B¯s→K+ℓ−ν¯ℓ)/Γ(B¯s→Ds+ℓ−ν¯ℓ) . 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<inf>ℓ</inf> exclusive decays, we have obtained |V<inf>cb</inf>| = (40.5 ± 0.6) × 10⁻³ and from all the b → uℓ ⁻ ν<inf>ℓ</inf> modes, we obtain |V<inf>ub</inf>| = (3.46 ± 0.12) × 10⁻³ which changes to |V<inf>ub</inf>| = (3.51 ± 0.13) × 10⁻³ after dropping BR(B¯ <inf>s</inf>→ K⁺μ⁻ν¯ <inf>μ</inf>) . We hence report the values of the ratio |V<inf>ub</inf>|/|V<inf>cb</inf>| = 0.085 ± 0.003 and 0.087 ± 0.003 with and without the input from B¯ <inf>s</inf>→ K⁺μ⁻ν¯ <inf>μ</inf> modes, respectively. We have also predicted the ratio Γ(B¯s→K+ℓ−ν¯ℓ)/Γ(B¯s→Ds+ℓ−ν¯ℓ) using the fit results. In addition, we provide the predictions of BR(B¯ <inf>s</inf>→ K⁺μ⁻ν¯ <inf>μ</inf>) and BR(B¯ → (ρω) ℓ⁻ν¯ <inf>ℓ</inf>) in the Standard Model (SM) in small q ²-bins.