represents the central value of $P_{\tau}^{D^{\ast}}$ reported by BELLE.[]{data-label="NP1"}](rjpsi_ptjpsi_vlt_1sig_95cl.png "fig:"){width="5.8cm" height="5.5cm"}

Now let us consider that NP contributions are coming from two different operators characterized by two NP WC. We consider total $45$ such NP scenarios. In Table. \[tab3\], we show the best estimates of $R_D$, $R_{D^{\ast}}$, $R_{J/\Psi}$, $P_{\tau}^{D^{\ast}}$ and $\mathcal B(B_c \to \tau\nu)$ for each of these scenarios. We find that there are various NP scenarios that can simultaneously explain $R_D$, $R_{D^{\ast}}$, and $R_{J/\Psi}$ anomalies. We notice that with $(V_R,\,\widetilde{T}_L)$ NP couplings we obtain the best fit with the data with $\chi^2_{\rm min} = 0.43\times 10^{-2}$ followed by $(\widetilde{V}_R,\,\widetilde{T}_L$), $(S_R,\,\widetilde{T}_L)$, and $(\widetilde{V}_L,\,\widetilde{T}_L)$ NP couplings with $\chi^2_{\rm min} =0.013,\,0.026,\,{\rm and}\, 0.11$, respectively. However, with $(S_R,\,\widetilde{T}_L)$ NP couplings, the best estimates of $\mathcal B(B_c \to \tau\nu)=80.6\%$ is much above the upper bound of $\mathcal B(B_c \to \tau\nu) \le 30\%$ estimated in the SM. Hence although, we get a much better fit with this NP structure, $(S_R,\,\widetilde{T}_L)$ NP couplings can not accommodate the $B_c \to \tau\nu$ data.

                    Coefficients                      Best fit value      $R_D$    $ R_{D^{\ast}} $   $R_{J/\Psi}$   $P_{\tau}^{D^{\ast}}$   $\mathcal B(B_c \to \tau\nu)\% $    $\chi^2_{\rm min}$
  ------------------------------------------------- ------------------- --------- ------------------ -------------- ----------------------- ---------------------------------- ----------------------
                    $(V_L,\,V_R)$                    $(-2.14,\,-0.04)$   $0.406$       $0.308$          $0.357$            $-0.500$                       $2.7$                        $2.1$
                    $(V_L,\,S_L)$                    $(-1.94,\,1.62)$    