Testing Realistic $SO(10)$ SUSY GUTs with Proton Decay and Gravitational Waves

TL;DR

This paper analyzes a realistic supersymmetric $SO(10)$ GUT model that links proton decay, gravitational waves, neutrino masses, and cosmological observations, providing testable predictions for upcoming experiments.

Contribution

It offers a detailed two-loop RG analysis of a $SO(10)$ GUT with intermediate symmetry breaking, connecting cosmic strings, gravitational waves, and particle physics phenomenology.

Findings

Cosmic strings produce a gravitational wave spectrum matching Pulsar Timing Array observations.

Model predicts proton decay rates within reach of future experiments like Hyper-K and JUNO.

Parameter space consistent with neutrino masses, baryon asymmetry, and dark matter constraints.

Abstract

We present a comprehensive analysis of a supersymmetric $SO(10)$ Grand Unified Theory, which is broken to the Standard Model via the breaking of two intermediate symmetries. The spontaneous breaking of the first intermediate symmetry, $B-L$, leads to the generation of cosmic strings and right-handed neutrino masses and further to an observable cosmological background of gravitational waves and generation of light neutrino masses via type-I seesaw mechanism. Supersymmetry breaking manifests as sparticle masses below the $B-L$ breaking but far above the electroweak scale due to proton decay limits. This naturally pushes the $B-L$ breaking scale close to the GUT scale, leading to the formation of metastable cosmic strings, which can provide a gravitational wave spectrum consistent with the recent Pulsar Timing Arrays observation. We perform a detailed analysis of this model using two-loop renormalisation group equations, including threshold corrections, to determine the symmetry-breaking scale consistent with the recent Pulsar Timing Arrays signals such as NANOGrav 15-year data and testable by the next-generation limits on proton decay from Hyper-K and JUNO. Simultaneously, we find the regions of the model parameter space that can predict the measured quark and lepton masses and mixing, baryon asymmetry of our Universe, a viable dark matter candidate and can be tested by a combination of neutrinoless double beta decay searches and limits on the sum of neutrinos masses.