One-loop neutrino mass in $SU(5)$

I demonstrate viability of the one-loop neutrino mass mechanism within the $SU(5)$ grand unification framework when the loop particles comprise two particular pairs of scalar leptoquarks (LQs) and the down-type quarks. The LQ multiplet components that propagate in the loop should mix for the mechanism to work. I accordingly classify all $SU(5)$ invariant operators that can yield the required mixing. If the LQs mediate proton decay at the tree-level the neutrino mass mechanism can only be viable when the LQ masses reside in a very narrow range between $10^{12}$ GeV and $5 \times 10^{13}$ GeV. I also present one realistic $SU(5)$ set-up where the LQs in the neutrino mass loop are collider accessible.