ν-gauge mediated supersymmetry breaking with type III seesaw mechanism and phenomenology

We show that when the supersymmetric SU(5) model is extended to explain small neutrino masses by the type III seesaw mechanism, the new 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 24s 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 10¹²--10¹³ GeV. The model predicts (i) a stable lightest superpartner gravitino with mass in the range of 1--10 MeV which can be a cold dark matter of the universe; (ii) a stau next to lightest superpartner, which is detectable at the LHC; (iii) a lower bound on the branching ratio BR(μ→eγ) larger than 10^-14 testable by the ongoing Muegamma (MEG) experiment as well as a characteristic particle spectrum different from other SUSY breaking scenarios. We also discuss the case with two 24 fields, which is the minimal case that can explain neutrino oscillation data.