# Triplet Leptogenesis, Type-II Seesaw Dominance, Intrinsic Dark Matter, Vacuum Stability and Proton Decay in Minimal SO(10) Breakings

## TL;DR

This paper explores a minimal SO(10) grand unified theory with type-II seesaw dominance, explaining neutrino masses, baryogenesis, dark matter, and proton decay, while predicting testable proton lifetimes and dark matter signatures.

## Contribution

It demonstrates how minimal SO(10) models can unify neutrino mass generation, baryogenesis, dark matter, and proton decay predictions with specific intermediate scales and particle content.

## Key findings

- Successful leptogenesis for normal and inverted neutrino mass orderings.
- Predicted proton lifetimes within reach of current experiments.
- Dark matter relic density consistent with direct detection constraints.

## Abstract

We implement type-II seesaw dominance for neutrino mass and baryogenesis through heavy scalar triplet leptogenesis in a class of minimal non-supersymmetric SO(10) models where matter parity as stabilising discrete symmetry as well as WIMP dark matter (DM) candidates are intrinsic predictions of the GUT symmetry. We also find modifications of relevant CP-asymmetry formulas in such minimal models. Baryon asymmetry of the universe as solutions of Boltzmann equations is further shown to be realized for both normal and inverted mass orderings in concordance with cosmological bound and best fit values of the neutrino oscillation data including $\theta_{23}$ in the second octant and large values of leptonic Dirac CP-phases. Type-II seesaw dominance is at first successfully implemented in two cases of spontaneous SO(10) breakings through SU(5) route where the presence of only one non-standard Higgs scalar of intermediate mass $\sim 10^9-10^{10}$ GeV achieves unification. Lower values of the SU(5) unification scales $\sim 10^{15}$ GeV are predicted to bring proton lifetimes to the accessible ranges of Super-Kamiokande and Hyper-Kamiokande experiments. Our prediction of WIMP DM relic density in each model is due to a $\sim$ TeV mass matter-parity odd real scalar singlet ($\subset {16}_H \subset$ SO(10)) verifiable by LUX and XENON1T experiments. This DM is also noted to resolve the vacuum stability issue of the standard scalar potential. When applied to the unification framework of M. Frigerio and T. Hambye, in addition to the minimal fermionic triplet DM solution of $2.7$ TeV mass, this procedure of type-II seesaw dominance and triplet leptogenesis is also found to make an alternative prediction of triplet fermion plus real scalar singlet DM at the TeV scale.