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The universality of the weak interactions can be tested in semileptonic $b\to c$ transitions, and in particular in the ratios $R(D^{(*)}) \equiv \Gamma(B\rightarrow D^{(*)} \tau \nu )/\Gamma(B \rightarrow D^{(*)} \ell \nu )$ (where$\ell = \mu$ or $e$). Due to the recent differences between the experimentalmeasurements of these observables by BaBar, Belle and LHCb on the one hand andthe Standard Model predicted values on the other hand, we study the predictedratios $R(D^{(*)}) = \Gamma(B \rightarrow D^{(*)} \tau +$ "missing" $)/\Gamma(B\rightarrow D^{(*)} \ell \nu )$ in scenarios with an additional sterile heavyneutrino of mass $\sim 1$ GeV. Further, we evaluate the newly defined ratio$R(0) \equiv \Gamma(B \to \tau +$ "missing" $)/\Gamma(B \to \mu \nu )$ in suchscenarios, in view of the future possibilities of measuring the quantity atBelle-II.

chinese physics c, high energy physics and nuclear physics/chinese physics c

Anomalies in (semi)-leptonic $B$ decays $B^{\pm} \to \tau^{\pm} \nu$,  $B^{\pm} \to D \tau^{\pm} \nu$ and $B^{\pm} \to D^* \tau^{\pm} \nu$, and  possible resolution with sterile neutrino