Investigating $R_D$ and $R_{D^*}$ anomalies in a Left-Right model with an Inverse Seesaw

We investigate $R_D$ and $R_{D^*}$ anomalies in a low scale left-right symmetric model based on $SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ with a simplified Higgs sector consisting of only one bidoublet and one $SU(2)_R$ doublet. The Wilson coefficients relevant to the transition $b\to c\tau \nu$ are derived by integrating out the charged Higgs $H^\pm$ boson, which gives the dominant contributions. We emphasize that the charged Higgs effects, with the complex right-handed quark mixing matrix, can account for both $R_D$ and $R_{D^*}$ anomalies simultaneously, while adhering to a set of significant constraints including, for instance, ${\rm BR}(B^-_c \to \tau^- \bar{\nu}_\tau) $ and $B_{s(d)}-\bar B_{s(d)}$ mixing. In relation to this, we show that the predicted values of the $D^\ast$, $\tau$ longitudinal polarizations and $P_\tau (D)$ can be affected for the set of the parameters of the model resolving the $R_{D,D^\ast}$ anomalies.