in Sec. \[sec:concrete\]. The possibility of considering (pseudo)scalar operators (i.e. only $g_{S_{L(R)}}\neq 0$) was considered in the past, but it has been recently shown that such a scenario containing is in strong tension with the $B_c$-meson lifetime constraint [@Alonso:2016oyd; @Celis:2016azn]. More specifically, the pseudoscalar interactions lift the helicity suppression of the SM rate for

     Decay mode       $a_S^M$    $a_{SV_L}^M$     $a_P^M$     $a_{PV_L}^M$    $a_T^M$     $a_{TV_L}^M$
  ----------------- ----------- -------------- ------------- -------------- ------------ --------------
      $B \to D$      $1.08(1)$    $1.54(2)$         $0$           $0$        $0.83(5)$     $1.09(3)$
   $B\to {D^\ast}$      $0$          $0$        $0.0473(5)$    $0.14(2)$     $17.3(16)$    $-5.1(4)$

  :  *Numerical values of the coefficients $a_{i}^M$ defined in Eq.  for $M\in \lbrace D,D^\ast \rbrace$ and $i \in \lbrace S, S V_L, P, P V_L, T, T V_L\rbrace$, assuming that NP only induces nonzero values of $g_{V_L}^\tau$, $g_{S_{L(R)}}^\tau$ and $g_T^\tau$, i.e. the effective couplings to light leptons is negligible [@Feruglio:2018fxo].* []{data-label="tab:RD-RDst-compact"}

$$\mathcal{B}(B_c\to \tau \bar{\nu}) = \tau_{B_c} \dfrac{m_{B_c} f_{B_c}^2 G_F^2 |V_{cb}|^2}{8 \pi} m_\tau^2 \left( 1- \dfrac{m_\tau^2}{m_{B_c}^2} \right)^2 \Bigg{|} 1 + g_{P}^\tau \dfrac{m_{B_c}^2}{m_\tau (m_b+m_c)}\Bigg{|}^2\,,$$

where $f_{B_c}=427(6)$ MeV is the $B_c$–meson decay constant [@McNeile:2012qf]. The current experimental value for $\tau_{B_c}= 0.507(9)$ ps [@Patrignani:2016xqp] allows us to set a conservative limit of $30\%$ on $\mathcal{B}(B_c\to \tau \bar{\nu})$ [@Alonso:2016oyd], which can then be translated onto the $1\,\sigma$ bound, $g_P^\tau 