estimate of $R_D$, however, lies outside $1\sigma$ of the experimental value. Similarly, with $V_L$ and $\widetilde{V}_{(L,\,R)}$ NP couplings although, the best estimates of $R_D$ and $R_{D^{\ast}}$ lie inside the $1\sigma$ experimental range, the best estimate of $R_{J/\Psi}$, however, lies outside $1\sigma$ of the experimental value.

     Coefficients      Best fit value    $R_D$    $ R_{D^{\ast}} $   $R_{J/\Psi}$   $P_{\tau}^{D^{\ast}}$   $\mathcal B(B_c \to \tau\nu)\% $   $\chi^2_{\rm min}$
  ------------------- ---------------- --------- ------------------ -------------- ----------------------- ---------------------------------- --------------------
          SM                            $0.334$       $0.255$          $0.291$            $-0.501$                       $2.3$                       $16.3$
         $V_L$            $-2.11$       $0.398$       $0.307$          $0.356$            $-0.494$                       $2.9$                       $2.1$
         $V_R$            $-0.09$       $0.276$       $0.295$          $0.345$            $-0.496$                       $2.5$                       $10.7$
         $S_L$            $-1.51$       $0.365$       $0.330$          $0.418$            $-0.140$                      $121.5$                      $5.2$
         $S_R$             $0.31$       $0.427$       $0.266$          $0.308$            $-0.431$                       $12.1$                      $9.6$
   $\widetilde{V}_L$       $0.48$       $0.398$       $0.309$          $0.367$            $-0.311$                       $2.7$                       $2.1$
   $\widetilde{V}_R$       $0.48$       $0.398$       $0.309$          $0.367$            $-0.311$                       $2.7$                       $2.1$
   $\widetilde{S}_L$       $0.73$       $0.432$       $0.262$          $0.302$            $-0.513$                       $23.2$                      $11.2$
   $\widetilde{S}_R$       $0.73$       $0.432$       $0.262$          $0.302$            $-0.513$                       $23.2$                      $11.2$
         $T_L$            $-0.08$       $0.309$       $0.302$          $0.457$            $-0.467$                       $2.0$                       $5.6$
   $\widetilde{T}_L$       $0.27$       $0.352$       $0.305$          $0.585$            $-0.412$                       $ 2.3$                      $1.7$

  : Best estimates of $R_D$, $R_{D^{\ast}}$, $R_{J/\Psi}$, $P_{\tau}^{D^{\ast}}$, and $\mathcal B(B_c \to \tau\nu)$ within the SM and within various NP scenarios.[]{data-label="tab2"}

We show in Fig. \[NP1\] the $95\%$ CL (blue band) allowed ranges in $(R_D,\,P_{\tau}^D)$, $(R_{D^{\ast}},\,P_{\tau}^{D^{\ast}})$, and $(R_{J/\Psi},\,P_{\tau}^{J/\Psi})$ for NP scenarios with 