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

TL;DR

This paper explores how the proton decay rate in a minimal SUSY SO(10) GUT model is related to the CP-violating PMNS phase, emphasizing the importance of precise neutrino measurements for future experiments.

Contribution

It establishes a connection between proton decay suppression and the PMNS phase within the minimal SUSY SO(10) GUT framework, highlighting the role of neutrino parameters.

Findings

Proton decay suppression depends on the PMNS phase.

Precise measurements of the PMNS phase are crucial for future proton decay observations.

The model links neutrino oscillation parameters to proton decay predictions.

Abstract

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. These become especially important if the SUSY particles are found around less than a few TeV at LHC and proton decays are observed at Hyper-Kamiokande and DUNE experiments in the near future.