Proton decay and new contribution to 0ν2β decay in SO(10) with low-mass Z′ boson, observable n−n¯$$ n-\overline{n} $$ oscillation, lepton flavor violation, and rare kaon decay

A bstractIn the conventional approach to observable n−n¯$$ n-\overline{n} $$ oscillation through Pati-Salam intermediate gauge symmetry in SO(10), the canonical seesaw mechanism is also constrained by the symmetry breaking scale MR ∼ MC ≤ 106 GeV which yields light neutrino masses several orders larger than the neutrino oscillation data. A method to evade this difficulty is through TeV scale gauged inverse seesaw mechanism which has been recently exploited while predicting experimentally verifiable WR±, ZR bosons with a new dominant contribution to neutrinoless double beta decay in the WL −WL channel and other observable phenomena, but with proton lifetime far beyond the accessible limits. In the present work, adopting the view that WR± may be heavy and currently inaccessible to accelerator tests, we show how a class of non-supersymmetric SO(10) models allows a TeV scale Z′ boson, experimentally testable proton decay along with observable n−n¯$$ n-\overline{n} $$ oscillation, and lepto-quark gauge boson mediated rare kaon decays without resorting to additional fine-tuning of parameters. The occurrence of Pati-Salam gauge symmetry with unbroken D-parity and two gauge couplings at the highest intermediate scale guarantees precision unification with vanishing GUT-threshold or gravitational corrections on sin2θW (MZ ) prediction in this model. Predictions for neutrinoless double beta decay in the WL − WL channel is analysed in detail including light and heavy sterile neutrino exchange contributions by means of normal and band plots and also by scattered plots while a new formula for half-life is derived. Comparison with available data from various groups by normal and scattered plots reveals how the existing experimental bounds are satisfied irrespective of the mass hierarchy in the light neutrino sector leading to the lower bound on the lightest sterile neutrino mass, M^S1≥18±2.9$$ {\widehat{M}}_{S_1}\ge 18\pm 2.9 $$ GeV. The model also predicts branching ratios for charged lepton flavor violation verifiable by ongoing search experiments. We also derive new renormalisation group equations constraining the lepto-quark gauge boson mass in the presence of SU(2)L × U(1)R × U(1)B−L × SU(3)C symmetry, specific to the occurrence of extra Z′ boson, leading to a new lower bound on the lepto-quark gauge boson mass mediating rare kaon decay, MLQ ≥ (1.54±0.06) × 106 GeV. We also discuss the symmetry breaking of non-SUSY SO(10) through the well known flipped SU(5) × Ũ(1) path and show, for the first time, how TeV scale Z′ is predicted with gauged inverse seesaw ansatz for neutrino masses and substantial lepton flavor and lepton number violations. As a significant new result along this path, we report a successful unification of the two gauge couplings of SU(5) × Ũ(1) into the single GUT coupling of SO(10).