Proton decay and axion dark matter in $SO$(10) grand unification via minimal left–right symmetry

International audienceWe study the proton lifetime in the SO(10) Grand Unified Theory (GUT), which has the left–right (LR) symmetric gauge theory below the GUT scale. In particular, we focus on the minimal model without the bi-doublet Higgs field in the LR symmetric model, which predicts the LR-breaking scale at around $10^{10-12}$ GeV. The Wilson coefficients of the proton decay operators turn out to be considerably larger than those in the minimal SU(5) GUT model especially when the Standard Model Yukawa interactions are generated by integrating out extra vector-like multiplets. As a result, we find that the proton lifetime can be within the reach of the Hyper-Kamiokande experiment even when the GUT gauge-boson mass is in the $10^{16}$–$10^{17}$ GeV range. We also show that the mass of the extra vector-like multiplets can be generated by the Peccei–Quinn symmetry breaking in a consistent way with the axion dark matter scenario