Planck-scale induced left-right gauge theory at LHC and experimental tests

Recent measurements at LHC has inspired searches for TeV scale left-right gauge theory originating from grand unified theories. We show that inclusion of Planck-scale induced effects due to ${\rm dim.}5$ operator not only does away with all the additional intermediate symmetries, but also it predicts the minimal set of light Higgs scalars tailored after neutrino masses and dilepton, or trilepton signals. The heavy-light neutrino mixings are predicted from charged fermion mass fits in $SO(10)$ and LFV constraints which lead to new predictions for dilepton or trilepton production signals. Including fine-structure constant matching and two-loop, and threshold effects predicts $M_{W_R}= g_{2R}\times 10^{4.3\pm 1.5 \pm 0.2}$ GeV and proton lifetime $τ_p=10^{36.15\pm 5.8\pm 0.2}$ yrs with $W_R$ gauge boson coupling $g_{2R}=0.56-0.57$. Predictions on lepton flavour and lepton number violations are accessible to ongoing experiments. Current CMS data on di-electron excess at $\sqrt s= 8$ TeV are found to be consistent with $W_R$ gauge boson mass $M_{W_R}\ge 1.9-2.2$ TeV which also agrees with the values obtained from dijet resonance production data. We also discuss plausible explanations for diboson production excesses observed at LHC and make predictions expected at $\sqrt s =14$ TeV

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