particles to the SM particle content, which are (a) a diquark, which is either a vector $V_{{\rm DQ}}^{4/3}$ or a scalar $S_{\rm DQ}^{4/3}$, (b) an exotic coloured (${\bf 3}$) vector-like fermion $\Psi^{5/3}$ with electric charge ${5/3}$, and (c) a leptoquark, which is again either a vector $V_{{\rm LQ}}^{2/3}$ or a scalar $S_{\rm LQ}^{2/3}$. We will concentrate on the case where both the diquark and the leptoquark are scalars. The vector case is qualitatively similar from the point of view of LHC phenomenology.[^14] The [$0\nu\beta\beta$ ]{}decay is generated through the diagram shown in Fig. \[Fig:0nbbExample\].

(250,130) (10,10)(60,60) (10,120)(60,60) (60,60)(100,60)[5]{} (100,60)(150,60) (150,60)(190,60)[5]{} (190,60)(240,120) (190,60)(240,10) (100,60)(100,120) (150,60)(150,120) (5,10)\[r\][$\overline{u_{R}}$]{} (5,120)\[r\][$\overline{u_{R}}$]{} (100,125)\[b\][$d_{L}$]{} (150,125)\[b\][$\overline{e_{R}}$]{} (245,10)\[l\][$d_{R}$]{} (245,120)\[l\][$\overline{e_{L}}$]{} (80,55)\[t\][$S_{\rm DQ}^{4/3}$]{} (125,55)\[t\][$\Psi^{5/3}$]{} (170,55)\[t\][$S^{2/3}_{\rm LQ}$]{}

So far, the chiralities of the outer fermions are not determined. When taking into account the fact that the effective operator should be a component of a SM gauge invariant operator, the number of the choices is limited. There are three possibilities of the SM gauge invariant operators that can contain the T-I-4-ii-a operator,[^15] which are $(\overline{Q} \overline{Q}) (d_{R}) (\overline{L}) (\overline{L} d_{R})$, $(\overline{u_{R}} \overline{u_{R}}) (Q) (\overline{e_{R}})
(\overline{L} d_{R})$, and $(\overline{u_{R}} \overline{u_{R}}) (d_{R}) (\overline{L})
(\overline{e_{R}} Q)$. We note in passing that they correspond to the effective 