Tension in the inclusive versus exclusive determinations of $|V_{cb}|$: a possible role of new physics

We reconsider the possibility that the tension in the $|V_{cb}|$ determinations from inclusive and exclusive $B$ decay modes is due to a new physics effect. We modify the Standard Model effective Hamiltonian for semileptonic $b to c$ transitions including a tensor operator with a lepton flavour dependent coupling $epsilon_T^ell$, and investigate separately the muon and electron modes. The interference term between SM and NP, proportional to the lepton mass, has different impact in the inclusive and exclusive $B$ modes to muon. Moreover, even when the lepton mass is small as for the electron, the NP effect is different in inclusive and exclusive $B$ channels. For both $mu$ and $e$ we find a region of $epsilon_T^{mu,,e}$ where the constraints from $B^- to D^{(*)0} ell^- {bar u}_ell$ and $B to X_c , ell , bar u_ell$ are satisfied for the same $|V_{cb}|$.