Planck-scale induced left-right gauge theory at LHC and experimental tests

Recent measurements at LHC has inspired searches for TeV scale left-right gauge theory originating from grand unified theories. We show that inclusion of Planck-scale induced effects due to ${rm dim.}5$ operator not only does away with all the additional intermediate symmetries, but also it predicts the minimal set of light Higgs scalars tailored after neutrino masses and dilepton, or trilepton signals. The heavy-light neutrino mixings are predicted from charged fermion mass fits in $SO(10)$ and LFV constraints which lead to new predictions for dilepton or trilepton production signals. Including fine-structure constant matching and two-loop, and threshold effects predicts $M_{W_R}= g_{2R}times 10^{4.3pm 1.5 pm 0.2}$ GeV and proton lifetime $tau_p=10^{36.15pm 5.8pm 0.2}$ yrs with $W_R$ gauge boson coupling $g_{2R}=0.56-0.57$. Predictions on lepton flavour and lepton number violations are accessible to ongoing experiments. Current CMS data on di-electron excess at $sqrt s= 8$ TeV are found to be consistent with $W_R$ gauge boson mass $M_{W_R}ge 1.9-2.2$ TeV which also agrees with the values obtained from dijet resonance production data. We also discuss plausible explanations for diboson production excesses observed at LHC and make predictions expected at $sqrt s =14$ TeV

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 $J sim 2.95 times 10^{-5} - 10^{-3}$.