Relation between proton decay and PMNS phase in the minimal SUSY $SO(10)$ GUT

Understand

Proton decay is one of the most important predictions of the grand unified theory (GUT).

• In the supersymmetric (SUSY) GUT, proton decays via the dimension-five operators need to be suppressed.
• In the $SO(10)$ model where ${\bf 10}+\overline{\bf 126}$ Higgs fields couple to fermions, neutrino oscillation parameters including the CP-violating Pontecorvo-Maki-Nakagawa-Sakata (PMNS) phase can be related to the Yukawa couplings to generate the dimension-five operators in the unified framework.
• We show how the suppressed proton decay depends on the PMNS phase, and stress the importance of the precise measurements of the PMNS phase as well as the neutrino 23-mixing angle.