$\nu$-GMSB with Type III Seesaw and Phenomenology

Abstract

We show that when the supersymmetric SU(5) model is extended to explain small neutrino masses by the type III seesaw mechanism, the new {\bf 24}-dimensional fields needed for the purpose can act as messengers for transmitting SUSY breaking from a hidden sector to the visible sector. For the three {\bf 24} case, the constraints of grand unification and suppressed lepton flavor violation restrict the seesaw scale in this case to be in the narrow range of $10^{12}-10^{13}$ GeV. The model predicts (i) a stable LSP gravitino with mass in the range of 1-10 MeV which can be a cold dark matter of the universe; (ii) a stau NLSP which is detectable at LHC; (iii) a lower bound on the branching ratio $BR(\mu \to e \gamma)$ larger than $10^{-14}$ testable by the ongoing MEG experiment as well as characteristic particle spectrum different from other SUSY breaking scenarios. We also discuss the case with two {\bf 24} fields, which is the minimal case that can explain neutrino oscillation data.