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

Understand

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.