Abstract
We 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.
Highlights
The Grand Unified Theory (GUT) [1] is one of the most attractive candidates for physics beyond the Standard Model (SM), which provides an explanation of the charge quantization
We have investigated the proton lifetime in the S O(10) GUT which is broken down by the vacuum expectation value (VEV) of H45 to the minimal LR symmetric gauge group SU (3)C × SU (2)L × SU (2)R ×U (1)Y, which is in turn broken at the intermediate LR-breaking scale MR by the SU (2)R doublet Higgs that is a part of H16
Due to the absence of the bi-doublet Higgs boson, the LRbreaking scale is determined to be at around 1010−12 GeV in order to achieve the gauge coupling unification
Summary
The Grand Unified Theory (GUT) [1] is one of the most attractive candidates for physics beyond the Standard Model (SM), which provides an explanation of the charge quantization. These contributions are too small to realize the observed masses of the heavy flavor fermions in the SM for = MGUT, for example. The three flavor model is advantageous as the masses of the extra vector-like fermions can be interrelated to the PQ symmetry breaking. As we assume that the LR-breaking scale is around 1010–1012 GeV, the masses of the active neutrinos generated by the seesaw mechanism [4,5,6,7,8] tend to be much heavier than the observed ones This is because the Dirac neutrino Yukawa coupling for the third generation is O(1) since it is unified with the top Yukawa coupling. The mixing matrices of the quarks and the neutrinos can be consistent with each other by cancellation
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