Inverse seesaw mechanism in nonsupersymmetricSO(10), proton lifetime, nonunitarity effects, and a low-massZ′boson

Abstract

Recently realization of TeV scale inverse seesaw mechanism in supersymmetric $SO(10)$ framework has led to a number of experimentally verifiable predictions including low-mass ${W}_{R}^{\ifmmode\pm\else\textpm\fi{}}$ and ${Z}^{\ensuremath{'}}$ gauge bosons and nonunitarity effects. Using nonsupersymmetric $SO(10)$ grand unified theory, we show how a TeV scale inverse seesaw mechanism for neutrino masses is implemented with a low-mass ${Z}^{\ensuremath{'}}$ boson accessible to Large Hadron Collider. We derive renormalization group equations for fermion masses and mixings in the presence of the intermediate symmetries of the model and extract the Dirac neutrino mass matrix at the TeV scale from successful grand unified theory-scale parametrization of fermion masses. We estimate leptonic nonunitarity effects measurable at neutrino factories and lepton flavor violating decays expected to be probed in the near future. While our prediction on the nonunitarity matrix element ${\ensuremath{\eta}}_{\ensuremath{\mu}\ensuremath{\tau}}$ for degenerate right-handed neutrinos is similar to the supersymmetric $SO(10)$ case, we find new predictions with significantly enhanced value of its phase ${\ensuremath{\delta}}_{\ensuremath{\mu}\ensuremath{\tau}}\ensuremath{\simeq}{10}^{\ensuremath{-}4}--{10}^{\ensuremath{-}2}$ when partial degeneracy among these neutrino masses is adequately taken into account by a constraint relation that emerges naturally in this approach. Other predictions on branching ratios and $CP$-violating parameters are discussed. An important distinguishing characteristic as another test of the minimal model is that the threshold corrected two-loop prediction of the proton lifetime with maximum value $({\ensuremath{\tau}}_{p}{)}_{\mathrm{max}}\ensuremath{\simeq}{10}^{35}\text{ }\text{ }\mathrm{yrs}$. is accessible to ongoing search experiments for the decay $p\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\pi}}^{0}$ in the near future. Simple model extensions with longer proton lifetime predictions are also discussed.