The very recent experimental information obtained from Belle experiment, along with the one accumulated by the BABAR and LHCb experiments have shown the existence of anomalies in the ratios R(D) and R(D * ) associated with the charged current transition b → cτντ . Although the Belle measurements are in agreement with the SM predictions, the new experimental world averages still exhibit a tension. In addition, the D * longitudinal polarization FL(D * ) related with the channel B → D * τντ observed by the Belle and the ratio R(J/ψ) measured by the LHCb also show discrepancies with their corresponding SM estimations. In this work, we present a modelindependent study based on the most general effective Lagrangian that yields to a tree-level effective contribution to the transition b → cτντ induced by a general W gauge boson. Instead of considering any specific new physics (NP) realization, we performed an analysis by considering all the different chiral charges to the charm-bottom and τ -ντ interaction terms with a charged W boson that explain the anomalies. We present a phenomenological study of parameter space allowed by the new experimental b → cτντ data and with the mono-tau signature pp → τ h X + MET at the LHC. For comparison, we include some of the W boson NP realizations that have already been studied in the literature.