Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 (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.

19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph