Neutrino masses, dominant neutrinoless double beta decay, and observable lepton flavor violation in left-right models and SO(10) grand unification with low mass ${\mathbf{W}}_{\mathbf{R}},{\mathbf{Z}}_{\mathbf{R}}$ bosons

Abstract

While the detection of $W_R$-boson at the Large Hadron Collider is likely to resolve the mystery of parity violation in weak interaction, observation of neutrinoless double beta decay ($0\nu \beta \beta$) is expected to determine whether neutrinos are Majorana fermions. In this work we consider a class of LR models with TeV scale $W_R,Z_R$ bosons but having parity restoration at high scales where they originate from well known Pati-Salam symmetry or $SO(10)$ grand unified theory minimally extended to accommodate inverse seesaw frame work for neutrino masses. Most dominant new contribution to neutrinoless double beta decay is noted to occur via $W_L^{-}{W}_L^{-}$ mediation involving lighter sterile neutrino exchanges. The next dominant contribution is found to be through $W_L^{-}{W}_R^{-}$ mediation involving both light and heavy right-handed neutrino or sterile neutrino exchanges. The quark-lepton symmetric origin of the computed value of the Dirac neutrino mass matrix is also found to play a crucial role in determining these and other results on lepton flavor violating branching ratios for $\tau \to e+\gamma$, $\tau \to \mu +\gamma$, and $\mu \to e+\gamma$ accessible to ongoing search experiments. The underlying non-unitarity matrix is found to manifest in substantial CP-violating effects even when the leptonic Dirac phase ${\delta }_{\mathrm{CP}}\simeq 0,\pi ,2\pi$. Finally we explore a possible origin of the model in non-supersymmetric SO(10) grand unified theory where, in addition to low mass $W_R^{\pm }$ and $Z_R$ bosons accessible to Large Hadron Collider, the model is found to predict observable neutron-antineutron oscillation and lepto-quark gauge boson mediated rare kaon decay with $\mbox{Br} \left(K_{\rm L} \rightarrow μ\, \bar{e}\right) \simeq \left(10^{-9}- 10^{-11} \right)$.

46 pages latex, 13 figures, 11 Tables, JHEP version accepted for publication

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