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A Minimal Non-Supersymmetric $SO(10)$ Model: Gauge Coupling Unification, Proton Decay and Fermion masses

We present a minimal renormalizable non-supersymmetric SO(10) grand unified model with a symmetry breaking sector consisting of Higgs fields in the 54_H + 126_H + 10_H representations. This model admits a single intermediate scale associated with Pati-Salam symmetry along with a discrete parity. Spontaneous symmetry breaking, the unification of gauge couplings and proton lifetime estimates are studied in detail in this framework. Including threshold corrections self-consistently, obtained from a full analysis of the Higgs potential, we show that the model is compatible with the current experimental bound on proton lifetime. The model generally predicts an upper bound of few times 10^{35} yrs for proton lifetime, which is not too far from the present Super-Kamiokande limit of τ_p \gtrsim 1.29 \times 10^{34} yrs. With the help of a Pecci-Quinn symmetry and the resulting axion, the model provides a suitable dark matter candidate while also solving the strong CP problem. The intermediate scale, M_I \approx (10^{13}-10^{14}) GeV which is also the B-L scale, is of the right order for the right-handed neutrino mass which enables a successful description of light neutrino masses and oscillations. The Yukawa sector of the model consists of only two matrices in family space and leads to a predictive scenario for quark and lepton masses and mixings. The branching ratios for proton decay are calculable with the leading modes being p \rightarrow e^+ π^0 and p \rightarrow \overlineν π^+. Even though the model predicts no new physics within the reach of LHC, the next generation proton decay detectors and axion search experiments have the capability to pass verdict on this minimal scenario.