Neutrino Mass from a d=7 Effective Operator in a SUSY-GUT Framework

Models, where neutrino mass originates from physics at the TeV scale and which are potentially testable at the LHC, need additional suppression mechanisms to describe the smallness of neutrino masses. We consider models in which neutrino mass is generated from the d=7 operator $L L H_u H_u H_d H_u$ in the context of SUSY-GUTs containing an SU(5) subgroup, here the d=5 Weinberg operator can be forbidden by a discrete symmetry. That is, we identify the embeddings in GUT multiplets and their consequences for phenomenology and renormalization group evolution. We use a specific example to exemplify the challenges. In this case, additional heavy d-quarks are predicted, which are constrained by cosmology, in particular, by big bang nucleosynthesis and direct searches for heavy nuclei. We show that in the NMSSM extension of the model, the discrete symmetry needs to be broken, which can be the origin of deviations from tri-bimaximal mixings. Finally we demonstrate that our example is the only tree level decomposition which is consistent with perturbativity up to the GUT scale and neutrino mass generation by a leading d=7 contribution.