heavy quarks and used symmetrized wave functions for the light quarks. This induces a spin-flavor dependence different from the one of pure $\textrm{SU(4)}$ symmetry.

With respect to Ref. [@romanets], we have some diagonal matrix elements equal but not all of them, and there are also differences in the non diagonal terms. These matrix elements are also different from those of Ref. [@angels].

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

  : $D_{ij}$ coefficients of Eq.  for the meson-baryon states coupling to $J^P={3/2}^-$.

\[tabDij2\]

To calculate the matrix elements for the states that couple to $J^P={3/2}^-$ of Table \[tab2\] we proceed in the same way as in Appendix \[app\]. We must take into account that the $VVV_{ex}$ are like those of $PPV_{ex}$ under the approximation of neglecting $({\bf p}/m_V)^2$, where ${\bf p}$ is the momentum of the external vector. In addition one has for the factor $\vec{{\bf \epsilon}} \cdot  \vec{{\bf \epsilon\,}}^{\prime}$ for the vector polarization, which 