$V_L$, $\widetilde{V}_L$, and $\widetilde{T}_L$ NP couplings. We observe that, although, $V_L$ and $\widetilde{V}_L$ NP couplings can simulataneously explain the anomalies present in $R_D$ and $R_{D^{\ast}}$, these couplings, however, can not accommodate the $R_{J/\Psi}$ data within $1\sigma$. We note that with $\widetilde{T}_L$ NP coupling, the range obtained for $R_{J/\Psi}$ lies within the $1\sigma$ range of $R_{J/\Psi}$ data. However with $\widetilde{T}_L$ NP coupling, the range obtained for $R_D$ lies outside the $1\sigma$ experimental range. Again, we want to emphasise that the range in $\tau$ polarization fraction $P_{\tau}^{D^{\ast}}$ for each scenarios lies inside the $1\sigma$ allowed range reported by Belle Colaboration. However, with $\widetilde{T}_L$ and $\widetilde{V}_L$ NP couplings, the central value lies inside the $95\%$ (blue) CL allowed bands. We notice that with $V_L$ NP coupling, the central value of $P_{\tau}^{D^{\ast}}$ reported by Belle Collaboration lies much above the range obtained in this scenario. However, the uncertainty associated with $P_{\tau}^{D^{\ast}}$ is rather large. Precise determination of this parameter in the future will play a crucial role in identifying the exact nature of NP.

![The allowed ranges in $(R_D,\,P_{\tau}^D)$, $(R_{D^{\ast}},\,P_{\tau}^{D^{\ast}})$, and $(R_{J/\Psi},\,P_{\tau}^{J/\Psi})$ at $95\%$ CL are shown with blue bands. The experimental $1\sigma$ range of $R_D$, $R_{D^{\ast}}$, and $R_{J/\Psi}$ are shown with light red 