Proton decay and new contribution to neutrino-less double beta decay in SO(10) with low-mass Z-prime boson, observable n-nbar oscillation, lepton flavor violation, and rare kaon decay

Conventionally for observable $n-{bar n}$ oscillation through Pati-Salam intermediate gauge symmetry in $SO(10)$, the canonical seesaw mechanism is also constrained by $M_R sim M_C le 10^6$ GeV which yields light neutrino masses much larger than the neutrino oscillation data. Recently, this difficulty has been evaded via inverse seesaw mechanism, but with proton lifetime far beyond the experimentally accessible limits. In the present work, adopting the view that we may have only a TeV scale $Z^{prime}$ gauge boson, we show how a class of non-SUSY $SO(10)$ models allow experimentally verifiable proton lifetime and the new contributions to neutrinoless double beta decay in the $W_L-W_L$ channel, lepton flavor violating branching ratios, observable $n-{bar n}$ oscillation, and lepto-quark gauge boson mediated rare kaon decays. The occurrence of Pati-Salam gauge symmetry with unbroken D-parity and two gauge couplings at the highest intermediate scale guarantees precision unification in such models. This symmetry also ensures vanishing GUT threshold uncertainy on $sin^2theta_W$ or on the highest intermediate scale. Although the proton lifetime prediction is brought closer to the ongoing search limits with GUT threshold effects in the minimal model, no such effects are needed in a non-minimal model. We derive a new analytic expression for the $0 ubetabeta$ decay half-life and show how the existing experimental limits impose the lower bound on the lightest of the three heavy sterile neutrino masses, $M_{S_1}ge 14pm 4$ GeV. We also derive a new lower bound on the lepto-quark gauge boson mass mediating rare kaon decay, $M_{rm lepto} ge (1.53{pm 0.06})times 10^6$ GeV. The $n-{bar n}$ mixing times are predicted in the range$tau_{n-{bar n}}simeq 10^8-10^{13}$ sec.

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

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 ($0 ubetabeta$) 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 $mbox{Br} left(K_{rm L} rightarrow mu, bar{e}right) simeq left(10^{-9}- 10^{-11} right)$.

Neutrinoless double beta decay and pseudo-Dirac neutrino mass predictions through inverse seesaw mechanism

In the inverse seesaw extension of the standard model, supersymmetric or non-supersymmetric, while the light left-handed neutrinos are Majorana, the heavy right-handed neutrinos are pseudo-Dirac fermions. We show how one of these latter category of particles can contribute quite significantly to neutrinoless double beta decay. The neutrino virtuality momentum is found to play a crucial role in the non-standard contributions leading to the prediction of the pseudo-Dirac fermion mass in the range of $120, {MeV}-500, {MeV}$. When the Dirac neutrino mass matrix in the inverse seesaw formula is similar to the up-quark mass matrix, characteristic of high scale quark-lepton symmetric origin, the predicted branching ratios for lepton flavor violating decays are also found to be closer to the accessible range of ongoing experiments.