Neutrino Mass, Coupling Unification, Verifiable Proton Decay, Vacuum Stability and WIMP Dark Matter in SU(5)

Abstract

Nonsupersymmetric minimal SU(5) with Higgs representations ${24}_H$ and $5_H$ and standard fermions in ${\bar 5}_F\oplus {10}_F$ is well known for its failure in unification of gauge couplings and lack of predicting neutrino masses. Like standard model, it is also affected by the instability of the Higgs scalar potential. We note that extending the Higgs sector by ${75}_H$ and ${15}_H$ not only leads to the popular type-II seesaw ansatz for neutrino masses with a lower bound on the triplet mass $M_Δ > 2\times 10^9$ GeV, but also achieves precision unification of gauge couplings without proliferation of non-standard light Higgs scalars or fermions near the TeV scale. Consistent with recent LUX-2016 lower bound, the model easily accommodates a singlet scalar WIMP dark matter near the TeV scale which resolves the vacuum stability issue even after inclusion of heavy triplet threshold effect. We estimate proton lifetime predictions for $p\to e^+π^0$ including uncertainties due to input parameters and threshold effects due to superheavy Higgs scalars and superheavy $X^{\pm 4/3},Y^{\pm 1/3}$ gauge bosons. The predicted lifetime is noted to be verifiable at Super Kamiokande and Hyper Kamiokande experiments.