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The anomalies in the measurements of $R_D$ and $R_{D^*}$ continue to providemotivation for physics beyond the Standard Model. In this work, we assume thenew physics Wilson coefficients to be complex and find their values by doing aglobal fit to the present $b\rightarrow c\tau\bar{\nu}$ data. We find that thenumber of allowed solutions depend on the choice of the upper limit on$Br(B_c\rightarrow \tau\bar{\nu})$. We find that the forward-backwardasymmetries in $B\rightarrow (D, D^*)\tau\bar{\nu}$ decays have the capabilityto distinguish between different solutions. Further we calculate the maximumvalues of CP violating triple product asymmetries in $B\to D^*\tau\bar{\nu}$decay allowed the current data. We observe that only one of the three CPasymmetries can be enhanced up to a maximum value of $\sim 2-3\%$ whereas theother asymmetries remain smaller.

Signatures of complex new physics in $b\to c\tau\bar{\nu}$ transitions