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

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 (RHν) produces high energy IceCube neutrinos having type-I seesaw masses. Instead of one universal mixing and one common heavy RHν mass proposed in a recent standard model extension, we find that underlying quark–lepton symmetry resulting in naturally hierarchical RHν 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 MχS≃177 GeV. We have also discussed realization of relic density of decaying dark matter in relation to flux of IceCube neutrinos. Two separate minimal SO(10) models are further noted to predict such dark matter dynamics where a single scalar submultiplet from 126H† or 210H of intermediate mass achieves precision gauge coupling unification. Despite the presence of two large Higgs representations and the fermionic dark matter host, 45F, experimentally accessible proton lifetimes are also predicted with reduced uncertainties.