table is valid for all three possible classes of diagrams (VFV, SFS and SFV). In some of the cases listed in Tab. \[Tab:TopoI\], only VFV or SFV exchange is possible, because in the decomposition ${\bf \bar{3}} \otimes {\bf \bar{3}} = {\bf 3}_a \oplus {\bf \bar{6}}_s$ the coupling of a scalar to two identical quarks (two ${\bf \bar{3}}$) vanishes for the ${\bf 3}_a$. These affects all the cases in T-I-3, T-I-4-ii and T-I-5-ii, see table for nomenclature.

Each of the models listed in this table leads to an effective operator with a different Lorentz structure, which needs to be projected onto the basis shown in Eqs. (\[eq:defLR\]) and (\[eps\_short\]), once the chiralities are fixed. The projection can be done by Fierz transformations and the transformations of the SM gauge group indices. This allows to identify immediately if a model gives important contributions to [$0\nu\beta\beta$ ]{}decay. More details and results of this procedure are shown in the appendix.

From this table we can identify all (T-I) contributions discussed in the literature, once the nature of the internal bosons and the chirality of the outer fermions are chosen. For example, the mass mechanism corresponds to T-I-1-i, with the bosons being vectors ($W^{\pm}$) and 