Speaker
Description
The precise estimate of the ratio $|V_{ub}|/|V_{cb}|$ is of utmost importance since it plays an essential role in the determination of the sides of the Unitarity Triangle and is an important ingredient in understanding the CKM picture of the
Standard Model. It can be measured directly or indirectly from the extraction of $|V_{ub}|$ and $|V_{cb}|$ from the respective exclusive and inclusive $b \to u l \nu_l$ and $b \to c l \nu_l$ decays. We have worked on the $b \to u \ell\nu$ modes, for eg. $B\to (\pi,\rho,\omega)\ell\nu_{\ell}$ and $B_s\to K \mu\nu_{\mu}$ for a combined extraction of $|V_{ub}|^{exc}$ and the exclusive $b \to c \ell \nu$ channels for eg. $B(B_s) \to D^{(*)} (D_s^{(*)}) l \nu$ for combined extraction of $|V_{cb}|^{exc}$. There has been a recent measurement of the ratio $BR(B_s \to K \mu \nu)/BR(B_s \to D_s \mu \nu)$ from LHCb which is proportional to $|V_{ub}|^2/|V_{cb}|^2$. Thus, from a simultaneous analysis of $b$ $\rightarrow$ $ul\nu$ and $b$ $\rightarrow$ $cl\nu$ modes in different fit scenarios with or without the inputs on the ratios of the branching fractions in the two bins, we obtain the ratio $|V_{ub}|/|V_{cb}|$. We have also extracted the correlation between $|V_{ub}|$ and $|V_{cb}|$ for different cases and provided the predictions of $\mathcal{BR}(B_s\to K\mu\nu_{\mu})$ and $\mathcal{BR}(B\to (\rho,\omega)\ell\nu_{\ell})$ in the Standard Model in small $q^2$-bins. We find a value for $|V_{ub}|/|V_{cb}|$ which is consistent with the determination from the ratio of partial rates of baryonic decays $\text{BR}(\Lambda_b \to p \mu \nu)/\text{BR}(\Lambda_b \to \Lambda_c \mu \nu)$ from LHCb.
