Neutrino masses, dominant neutrinoless double beta decay, and observable lepton flavor violation in left-right models and SO(10) grand unification with low mass $\bf W_R, Z_R$ bosons

TL;DR

This paper explores low-scale left-right models within SO(10) grand unification, analyzing their implications for neutrinoless double beta decay, lepton flavor violation, CP violation, and rare processes, with potential signals accessible at current experiments.

Contribution

It introduces a class of TeV-scale left-right models with high-scale parity restoration from SO(10), detailing their predictions for neutrinoless double beta decay and lepton flavor violation.

Findings

Dominant neutrinoless double beta decay mediated by $W_L W_L$ involving sterile neutrinos.

Significant lepton flavor violation effects with observable branching ratios.

Predictions of neutron-antineutron oscillation and rare kaon decays within reach of experiments.

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 $\tau \rightarrow e + \gamma$, $\tau \rightarrow \mu + \gamma$, and $\mu \rightarrow e + \gamma$ 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 $\delta_{\rm CP} \simeq 0, \pi, 2 \pi$. 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 $\mbox{Br} \left(K_{\rm L} \rightarrow \mu\, \bar{e}\right) \simeq \left(10^{-9}- 10^{-11} \right)$.