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 $\mathcal{BR}(\bar{B}_s\to K^+\mu^-\bar{\nu}_{\mu})$ 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 $\mathcal{BR}(\bar{B}_s\to K^+\mu^-\bar{\nu}_{\mu})$. 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 $\mathcal{BR}(\bar{B}_s\to K^+\mu^-\bar{\nu}_{\mu})$ and $\mathcal{BR}(\bar{B}\to (\rho,\omega)\ell^- \bar{\nu}_{\ell})$ in the Standard Model (SM) in small $q^2$-bins.