Finite naturalness and quark-lepton unification

We study the implications of finite naturalness in Pati-Salam models where SU(3)C is embedded in SU(4). For the minimal realization at low scale of quark -lepton unification, which employs the inverse seesaw for neutrino masses, we find that radiative corrections to the Higgs boson mass are at least 5m2h/m2h - O(104). The one -loop contributions to the Higgs mass are suppressed by four powers of the hypercharge gauge coupling. We find that for the vector leptoquarks the naively leading part of the twoloop corrections cancel. We assume the Dirac Yukawa couplings for neutrinos are equal to the up -type quark Yukawa couplings as predicted in the minimal theory for quark -lepton unification. Despite these findings, the two -loop corrections still dominate the finite naturalness bound. We mention a way to relax the lower bound on the vector leptoquark mass and have 5m2h/m2h - O(102).