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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.