Post-Sphaleron baryogenesis and $n-bar{n}$ oscillation in non-SUSY SO(10) GUT with gauge coupling unification and proton decay

Post-sphaleron baryogenesis, a fresh and profound mechanism of baryogenesis accounts for the matter-antimatter asymmetry of our present universe in a framework of Pati-Salam symmetry. We attempt here to embed this mechanism in a non-SUSY SO(10) grand unified theory by reviving a novel symmetry breaking chain with Pati-Salam symmetry as an intermediate symmetry breaking step and as well to address post-sphaleron baryogenesis and neutron-antineutron oscillation in a rational manner. The Pati-Salam symmetry based on the gauge group $SU(2)_L times SU(2)_{R} times SU(4)_C$ is realized in our model at $10^{5}-10^{6}$ GeV and the mixing time for the neutron-antineutron oscillation process having $Delta B=2$ is found to be $tau_{n-bar{n}} simeq 10^{8}-10^{10},mbox{secs}$ with the model parameters which is within the reach of forthcoming experiments. Other novel features of the model includes low scale right-handed $W^{pm}_R$, $Z_R$ gauge bosons, explanation for neutrino oscillation data via gauged inverse (or extended) seesaw mechanism and most importantly TeV scale color sextet scalar particles responsible for observable $n-bar{n}$ oscillation which can be accessible to LHC. We also look after gauge coupling unification and estimation of proton life-time with and without the addition of color sextet scalars.

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.

Intermediate left-right gauge symmetry, unification of couplings and fermion masses in SUSY $SO(10)times S_4$

If left-right gauge theory occurs as an intermediate symmetry in a GUT then, apart from other advantages, it is possible to obtain the see-saw scale necessary to understand small neutrino masses with Majorana coupling of order unity. Barring threshold or non-renormalizable gravitational effects, or assumed presence of additional light scalar particles of unprescribed origin, all other attempts to achieve manifest one-loop gauge coupling unification in SUSY SO(10) with left-right intermediate symmetry have not been successful so far. Attributing this failure to lack of flavor symmetry in the GUT, we show how the spontaneous symmetry breaking of $SO(10)times S_4$ leads to such intermediate scale extending over a wide range, $M_R simeq 5times 10^{9}$ GeV to $10^{15}$ GeV. All the charged fermion masses are fitted at the see-saw scale, $M_Nsimeq M_R simeq 4 times 10^{13}$ GeV which is obtained with Majorana coupling $f_0 simeq 1$. Using a constrained parametrization in which CP-violation originates only from quark sector, besides other predictions made in the neutrino sector, the reactor mixing angle is found to be $theta_{13} simeq 3^{circ} - 5^{circ}$ which is in the range accessible to ongoing and planned experiments. The leptonic Dirac phase turns out to be $delta sim 2.9- 3.1$ radians with Jarlskog invariant $J sim 2.95 times 10^{-5} - 10^{-3}$.