Matter Parity Violating Dark Matter Decay in Minimal SO(10), Unification, Vacuum Stability and Verifiable Proton Decay

TL;DR

This paper explores how matter parity violating dark matter decay in minimal SO(10) models can explain high-energy neutrinos, predict new particles, and ensure vacuum stability and proton decay observability.

Contribution

It introduces a hierarchical right-handed neutrino mixing framework from quark-lepton symmetry, linking dark matter decay, vacuum stability, and proton decay predictions in minimal SO(10).

Findings

Predicts high-energy neutrinos from dark matter decay compatible with IceCube data.

Identifies a new matter-parity odd Higgs scalar at 178 GeV accessible at LHC.

Achieves gauge coupling unification with specific scalar submultiplets and predicts observable proton lifetimes.

Abstract

In direct breaking of non-supersymmetric SO(10) to the standard model, we investigate the possibility that dark matter (DM) decaying through its mixing with right-handed neutrino (RH$\nu$) produces high energy IceCube neutrinos having type-I seesaw masses. Instead of one universal mixing and one common heavy RH$\nu$ mass proposed in a recent standard model extension, we find that underlying quark-lepton symmetry resulting in naturally hierarchical RH$\nu$ masses predict a separate mixing with each of them. We determine these mixings from the seesaw prediction of the DM decay rates into the light neutrino flavors. We further show that these mixings originate from Planck-scale assisted spontaneously broken matter parity needed to resolve the associated cosmological domain wall problem. This leads to the prediction of a new LHC accessible matter-parity odd Higgs scalar which also completes vacuum stability in the Higgs potential for its mass $M_{\chi_S}\simeq 178$ GeV. Two separate minimal SO(10) models are further noted to predict such dark matter dynamics where a single scalar submultiplet from ${126}^{\dagger}_H$ or ${210}_H$ of intermediate mass achieves precision gauge coupling unification. Despite the presence of two large Higgs representations and the fermionic dark matter host, ${45}_F$, experimentally accessible proton lifetimes are also predicted with reduced uncertainties.