Correlating new physics signals in $B \to D^{(*)} τν_τ$ with $B \to τν_τ$

Abstract: Semileptonic and purely leptonic decays of B meson to $\tau$, such as $B\to D^{(\ast)}\tau\nu_{\tau}$ and $B\to\tau\nu_\tau$ are studied. Recognizing that there already were some weak hints of possible deviations from the SM in the measurements of $\mathcal{B}(B\to\tau\nu_\tau)$ by \Babar~and Belle and the fact that detection of the $\tau$ also occurs in the measurements of $B\to D^{(\ast)}\tau\nu_{\tau}$, we stress the importance of joint studies of these processes, whenever possible. For this purpose, as an illustration, we introduce the observable, $\mathcal{R}(D^{(*)})/\mathcal{B}(B\to\tau\nu_\tau)$ where, for one thing, the unknown systematics due to $\tau$ identification are expected to largely cancel. We show that all measurements of this observable are consistent with the existing data, within somewhat largish experimental errors, with the predictions of the SM. We stress that precise experimental measurement and comparison with theory of the branching ratio for $B \to \tau \nu_\tau$ is extremely important for a reliable search of new physics. Furthermore, in view of the anticipated improved precision in experiments in the next few years, in addition to $\mathcal{R}(D^{(*)})$, host of other ratios analogous to $\mathcal{R}(D^{(*)})/\mathcal{B}(B \to \tau \nu_{\tau})$ in the SM are suggested for lattice calculations as well, so that for more stringent tests of the SM, correlations in lattice calculations can be properly taken into account to enhance precision.