B decays with $\tau$-leptons in non-universal left-right models

Recent measurements of semileptonic $B$-meson decays into $\tau$-leptons are somewhat higher than expected in the standard model. Although the deviations are less than 3$\sigma$, they suggest the possibility of new physics affecting primarily the $\tau$-lepton. In this paper we examine these results within the context of non-universal left-right models. We find that strong constraints from $b\to s \gamma$ on $W-W^\prime$ mixing lead to a prediction of approximately equal enhancements for the $B\to D \tau \nu$ and the $B\to D^\star \tau \nu$ modes. The model predicts approximately the same enhancement for the inclusive semileptonic rate $\bar{B} \to X_c \tau\nu$ as well as for the leptonic decay $B_c^-\to \tau^- \nu$. An enhancement in the leptonic decay $B^-\to \tau^-\nu$ is also possible but is not uniquely correlated with the other modes. For this explanation to be viable, the mass of the non-universal $W^\prime$ would be below 1 TeV, within LHC reach.