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$\frac{|V_{ub}|}{|V_{cb}|}$ and Quest for New Physics

Charged current semi-leptonic decays of $B$-meson are important for a precise determination of the CKM elements. The CKM elements $|V_{ub}|$ and $|V_{cb}|$ show a discrepancy between the exclusive and inclusive determinations. These determinations are however masked with hadronic and other uncertainties, and thus can't be unambiguously taken as implying new physics. In the present study, we propose a new observable: the ratio of these two CKM elements, $R_V \equiv \frac{|V_{ub}|}{|V_{cb}|}$, which is found to receive negligible corrections due to hadronic as well as QED effects. Interestingly, $R_V$ as constructed from exclusive determinations of $|V_{ub}|$ and $|V_{cb}|$ agrees quite well with that constructed from the inclusive determinations of these CKM elements. Hence, we propose that $R_V$ is a better and cleaner observable, and can serve as an excellent tool for the test of the Standard Model. We also provide an example of its probing power.