Renormalizable SO (10) grand unified theory with suppressed dimension-5 proton decays

Abstract

Abstract We study a renormalizable supersymmetric (SUSY) $SO(10)$ grand unified theory model where the Yukawa couplings of single ${\bf 10}$, single ${\bf \overline{126}}$, and single ${\bf 120}$ fields ($Y_{10}$, $Y_{126}$, and $Y_{120}$) account for the quark and lepton Yukawa couplings and the neutrino mass. We pursue the possibility that $Y_{10}$, $Y_{126}$, and $Y_{120}$ reproduce the correct quark and lepton masses, Cabibbo–Kobayashi–Maskawa and Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrices and neutrino mass differences, and at the same time suppress dimension-5 proton decays (proton decays via colored Higgsino exchange) through their texture, so that the soft SUSY-breaking scale can be reduced as much as possible without conflicting the current experimental bound on proton decays. We perform a numerical search for such a texture, and investigate implications of that texture on unknown neutrino parameters, the Dirac CP phase of the PMNS matrix, the lightest neutrino mass, and the $(1,1)$-component of the neutrino mass matrix in the charged lepton basis. Here we concentrate on the case when the active neutrino mass is generated mostly by the Type-2 seesaw mechanism, in which case we can obtain predictions for the neutrino parameters from the condition that dimension-5 proton decays be suppressed as much as possible.