Sub-dominant type-II seesaw as an origin of non-zero θ13θ13 in SO(10)SO(10) model with TeV scale Z′Z′ gauge boson

We discuss a class of left–right symmetric models where the light neutrino masses originate dominantly from type-I seesaw mechanism along with a sub-dominant type-II seesaw contribution. The dominant type-I seesaw gives rise to tri-bimaximal type neutrino mixing, whereas sub-dominant type-II seesaw acts as a small perturbation giving rise to non-zero θ13θ13 in our model which also has TeV scale right-handed neutrinos and Z′Z′ gauge boson thereby making the model verifiable at current accelerator experiments. Sub-dominant type-II and dominant type-I seesaw can be naturally accommodated by allowing spontaneous breaking of D-parity and SU(2)RSU(2)R gauge symmetry at high scale and allowing TeV scale breaking of U(1)R×U(1)B−LU(1)R×U(1)B−L into U(1)YU(1)Y. We also embed the left–right model in a non-supersymmetric SO(10)SO(10) grand unified theory (GUT) with verifiable TeV scale Z′Z′ gauge boson. Drawing it to an end, we scrutinize in detail the evaluation of one-loop renormalization group evolution for relevant gauge couplings and estimation of the proton life time which can be accessible to the foreseeable experiments. And in the aftermost part we make an estimation of branching ratio for lepton flavor violating process μ→e+γμ→e+γ as a function of type-II seesaw strength due to doubly charged component of the right-handed Higgs triplet with mass at the TeV scale, which can be accessible at ongoing experiments.