Extractions of $|V_{ub}|/|V_{cb}|$ from a combined study of the exclusive $b\to u(c)\ell {\nu }_{\ell }$ decays

Abstract

We have extracted the ratio $|V_{ub}|/|V_{cb}|$ from a combined study of the available inputs on $\bar{B}\to (\pi ,\rho ,\omega ){\ell }^{-}{\bar{\nu }}_{\ell }$ and $\bar{B}({\bar{B}}_s)\to (D^{(\ast )},D_s^{(\ast )}){\ell }^{-}{\bar{\nu }}_{\ell }$ ($\ell =\mu$ or $e$) decays. We have done our analysis with and without the inclusion of the available experimental results on the branching fraction $\mathcal{B}\mathcal{R}({\bar{B}}_s\to K^{+}{\mu }^{-}{\bar{\nu }}_{\mu })$ or the ratio of the rates $\Gamma ({\bar{B}}_s\to K^{+}{\ell }^{-}{\bar{\nu }}_{\ell })/\Gamma ({\bar{B}}_s\to D_s^{+}{\ell }^{-}{\bar{\nu }}_{\ell })$. 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 $b\to c{\ell }^{-}{\bar{\nu }}_{\ell }$ exclusive decays, we have obtained $|V_{cb}|=(40.5\pm 0.6)\times 10^{-3}$ and from all the $b\to u{\ell }^{-}{\bar{\nu }}_{\ell }$ modes, we obtain $|V_{ub}|=(3.46\pm 0.12)\times 10^{-3}$ which changes to $|V_{ub}|=(3.51\pm 0.13)\times 10^{-3}$ after dropping $\mathcal{B}\mathcal{R}({\bar{B}}_s\to K^{+}{\mu }^{-}{\bar{\nu }}_{\mu })$. We hence report the values of the ratio $|V_{ub}|/|V_{cb}|=0.085\pm 0.003$ and $0.087\pm 0.003$ with and without the input from ${\bar{B}}_s\to K^{+}{\mu }^{-}{\bar{\nu }}_{\mu }$ modes, respectively. We have also predicted the ratio $\Gamma ({\bar{B}}_s\to K^{+}{\ell }^{-}{\bar{\nu }}_{\ell })/\Gamma ({\bar{B}}_s\to D_s^{+}{\ell }^{-}{\bar{\nu }}_{\ell })$ using the fit results. In addition, we provide the predictions of $\mathcal{B}\mathcal{R}({\bar{B}}_s\to K^{+}{\mu }^{-}{\bar{\nu }}_{\mu })$ and $\mathcal{B}\mathcal{R}(\bar{B}\to (\rho ,\omega ){\ell }^{-}{\bar{\nu }}_{\ell })$ in the Standard Model (SM) in small $q^2$-bins.

Comments: Results updated with the latest experimental inputs, version accepted for publication in JHEP