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Neutrino mass from higher than d=5 effective operators in SUSY, and its test at the LHC

We discuss neutrino masses from higher than d=5 effective operators in a supersymmetric framework, where we explicitly demonstrate which operators could be the leading contribution to neutrino mass in the MSSM and NMSSM. As an example, we focus on the d=7 operator L L H_u H_u H_d H_u, for which we systematically derive all tree-level decompositions. We argue that many of these lead to a linear or inverse see-saw scenario with two extra neutral fermions, where the lepton number violating term is naturally suppressed by a heavy mass scale when the extra mediators are integrated out. We choose one example, for which we discuss possible implementations of the neutrino flavor structure. In addition, we show that the heavy mediators, in this case SU(2) doublet fermions, may indeed be observable at the LHC, since they can be produced by Drell-Yan processes and lead to displaced vertices when they decay. However, the direct observation of lepton number violating processes is on the edge at LHC.