Leptoquark mechanism of neutrino masses within the grand unification framework

We demonstrate viability of the one-loop neutrino mass mechanism within the framework of grand unification when the loop particles comprise scalar leptoquarks (LQs) and quarks of the matching electric charge. This mechanism can be implemented in both supersymmetric and non-supersymmetric models and requires the presence of at least one LQ pair. The appropriate pairs for the neutrino mass generation via the up-type and down-type quark loops are $S_3$-$R_2$ and $S_{1,\,3}$-$\tilde{R}_2$, respectively. We consider two phenomenologically distinct regimes for the LQ masses in our analysis. First regime calls for very heavy LQs in the loop. It can be naturally realised with the $S_{1,\,3}$-$\tilde{R}_2$ scenarios when the LQ masses are roughly between $10^{12}$ GeV and $5 \times 10^{13}$ GeV. These lower and upper bounds originate from experimental limits on partial proton decay lifetimes and perturbativity constraints, respectively. Second regime corresponds to the collider accessible LQs in the neutrino mass loop. That option is viable for the $S_3$-$\tilde{R}_2$ scenario in the models of unification that we discuss. If one furthermore assumes the presence of the type II see-saw mechanism there is an additional contribution from the $S_3$-$R_2$ scenario that needs to be taken into account beside the type II see-saw contribution itself. We provide a complete list of renormalizable operators that yield necessary mixing of all aforementioned LQ pairs using the language of $SU(5)$. We furthermore discuss several possible embeddings of this mechanism in $SU(5)$ and $SO(10)$ gauge groups.