We study possible new physics (NP) effects on Bc → J/ψτν, which has been recently measured at LHCb as the ratio of R J/ψ = B(Bc → J/ψτν)/B(Bc → J/ψµν). Combining it with the longstanding 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/ψ measurement does not improve NP fit to data, but the NP scenarios still give better χ 2 than the SM. We also investigate indirect NP constraints from the lifetime of Bc and NP predictions on the τ longitudinal polarization inB → D * τν.[UdeM-GPP-TH-17-259]* Electronic address: watanabe@lps.umontreal.ca 1 The S 1 type operator (c L b R )(τ R ν L ) never accommodates the experimental values of R D and R D * at the same time. Henceforth, we skip the S 1 scenario in this paper from the beginning. 2 At the scale where LQ models are defined, the corresponding relations are C S 2 = ±4C T . These relations are realized for the scalar leptoquark bosons (R 2 and S 1 ) that transform as (3, 2, 7/6) and (3, 1, 1/3) under SU (3)c × SU (2) L × U (1) Y , respectively.