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Conventionally for observable $n-{\bar n}$ oscillation through Pati-Salamintermediate gauge symmetry in $SO(10)$, the canonical seesaw mechanism is alsoconstrained by $M_R \sim M_C \le 10^6$ GeV which yields light neutrino massesmuch larger than the neutrino oscillation data. Recently, this difficulty hasbeen evaded via inverse seesaw mechanism, but with proton lifetime far beyondthe experimentally accessible limits. In the present work, adopting the viewthat we may have only a TeV scale $Z^{\prime}$ gauge boson, we show how a classof non-SUSY $SO(10)$ models allow experimentally verifiable proton lifetime andthe 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. Theoccurrence of Pati-Salam gauge symmetry with unbroken D-parity and two gaugecouplings at the highest intermediate scale guarantees precision unification insuch models. This symmetry also ensures vanishing GUT threshold uncertainy on$\sin^2\theta_W$ or on the highest intermediate scale. Although the protonlifetime prediction is brought closer to the ongoing search limits with GUTthreshold effects in the minimal model, no such effects are needed in anon-minimal model. We derive a new analytic expression for the $0\nu\beta\beta$decay half-life and show how the existing experimental limits impose the lowerbound on the lightest of the three heavy sterile neutrino masses, $M_{S_1}\ge14\pm 4$ GeV. We also derive a new lower bound on the lepto-quark gauge bosonmass 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$\tau_{n-{\barn}}\simeq 10^8-10^{13}$ sec.

the journal of high energy physics/the journal of high energy physics

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