New Physics effect on $B_c to J/psi taubar u$ in relation to the $R_{D^{(*)}}$ anomaly

We study possible new physics (NP) effects on $B_c to J/psi taubar u$, which has been recently measured at LHCb as the ratio of $R_{J/psi} = mathcal B(B_c to J/psi taubar u)/mathcal B(B_c to J/psi mubar u)$. Combining it with the long-standing $R_{D^{(*)}}$ measurements, in which the discrepancy with the prediction of the standard model is present, we find possible solutions to the anomaly by several NP types. Then, we see that adding the $R_{J/psi}$ measurement does not improve NP fit to data, but the NP scenarios still give better $chi^2$ than the SM. We also investigate indirect NP constraints from the lifetime of $B_c$ and NP predictions on the $tau$ longitudinal polarization in $bar B to D^* taubar u$.