Finite naturalness and quark-lepton unification

Abstract

We study the implications of finite naturalness in Pati-Salam models where SU(3)꜀ 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 δmℎ²/mℎ² ~ 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 two-loop 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 δmℎ²/mℎ² ~ O(10²).

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