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We develop a rigorous, semi-analytical method for maximizing any $b\toc\tau\nu$ observable in the full 20-real-dimensional parameter space of thedimension 6 effective Hamiltonian, given some fixed values of $R_{D^{(*)}}$. Weapply our method to find the maximum allowed values of $F^L_{D^*}$ and$R_{J/\psi}$, two observables which have both come out higher than their SMpredictions in recent measurements by the Belle and LHCb collaborations. Whilethe measurements still have large error bars, they add to the existing$R_{D^{(*)}}$ anomaly, and it is worthwhile to consider NP explanations. It hasbeen shown that none of the existing, minimal models in the literature canexplain the observed values of $F^L_{D^*}$ and $R_{J/\psi}$. Using our method,we will generalize beyond the minimal models and show that there is nocombination of dimension 6 Wilson operators that can come within $1\sigma$ ofthe observed $R_{J/\psi}$ value. By contrast, we will show that the observedvalue of $F^L_{D^*}$ can be achieved, but only with sizable contributions fromtensor and mixed-chirality vector Wilson coefficients.

Maximizing the Impact of New Physics in $b\rightarrow c \tau \nu$ Anomalies