Extended SUSY SU(5) predicting type-III seesaw testable at LHC

We propose an extension of the SUSY SU(5) which predicts LHC testable type-III seesaw. The supersymmetric SU(5) GUT model is extended by adding a 24-plet matter superfield along with a pair of $10_H$-plet and $bar{10}_H$-plet Higgs superfields. The 24-plet carries a triplet and a singlet fermion multiplet of SU(2)$_L$, which leads to type I+III seesaw. The additional $10_H$ (and $bar{10}_H$) multiplets help in achieving gauge coupling unification while keeping the triplet fermion mass in the TeV range, making them accessible at LHC. We study the phenomenology of this model in detail. Large lepton flavor violation predicted in this model puts severe constraints on the Yukawa couplings of the triplet fermion. We show that this smothers the possibility of observing the contribution of the heavy fermions in neutrinoless double beta decay experiments. The presence of the additional $10_H$ and $bar{10}_H$ in this model not only gives gauge coupling unification, it also leads to very large lepton flavor violation.

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.

Probing Seesaw in an Adjoint SUSY SU(5) Model at LHC

The SU(5) GUT model extended with fermions in the adjoint $24_F$ representation predicts triplet fermions in the 100 GeV mass range, opening up the possibility of testing seesaw at LHC. However, once the model is supersymmerized, the triplet fermion mass is constrained to be close to the GUT scale for the gauge couplings to unify. We propose an extension of the SUSY SU(5) model where type II seesaw can be tested at LHC. In this model we add a matter chiral field in the adjoint $hat{24}_F$ representation and Higgs chiral superfields in the symmetric $hat{15}_H$ and $hat{bar{15}}_H$ representations. We call this the symmetric adjoint SUSY SU(5) model. The triplet scalar and triplet fermion masses in this model are predicted to be in the 100 GeV and $10^{13}$ GeV range respectively, while the mass of the singlet fermion remains unconstrained. This gives a type I plus type II plus type III seesaw mass term for the neutrinos. The triplet scalars with masses $sim 100$ GeV range can be produced at the LHC. We briefly discuss the collider phenomenology and predictions for proton decay in this model.