$-\frac{4}{\sqrt{3}}$           $0$                    $0$                            $0$
            $\Xi D$                                                                        $-2$               $\frac{\sqrt{2}}{3}\lambda$        $0$                    $0$                            $0$
        $\Omega_c \eta$                                                                                                   $0$                    $0$                    $0$                            $0$
           $\Xi D^*$                                                                                                                            $-2$        $-\frac{1}{\sqrt{2}}\lambda$   $\frac{1}{\sqrt{6}}\lambda$
       $\Xi_c \bar{K}^*$                                                                                                                                                $-1$                           $0$
   $\Xi^{\prime}_c\bar{K}^*$                                                                                                                                                                          $-1$

  : $D_{ij}$ coefficients of Eq.  for the meson-baryon states coupling to $J^P={1/2}^-$ in $s$-wave.

In Table \[tabDij\] we have the parameter $\lambda$ in some non diagonal matrix elements, which involve transitions from one meson without charm to one with charm, like $\bar{K} \to D$. In this case we have for the propagator of the exchanged vector $$\begin{aligned}
\frac{1}{(q^0)^2 - |{\bf q\,}|^2-m_{D^*_s}^2} \approx \frac{1}{(m_D - m_K)^2-m_{D^*_s}^2}\, ,\end{aligned}$$ and the ratio to the propagator of the light vectors is $$\begin{aligned}
\lambda \equiv \frac{-m^2_{V}}{(m_D - m_K)^2 - m^2_{D^*_s}}\approx 0.25 \, .\end{aligned}$$ We take $\lambda = 1/4$ in all these matrix elements, as it was done in Ref. [@mizutani].

The diagonal matrix elements of Table \[tabDij\] coincide with those of Ref. [@angels], but not all the non diagonal. This is not surprising. $\textrm{SU(4)}$ symmetry is used in Ref. [@angels], but only $\textrm{SU(3)}$ is effectively used in the diagonal terms, as we have argued. Then we should note that the heavy baryons that we have constructed are not eigenstates of $\textrm{SU(4)}$ since we have singled out the 