Abstract
We discuss the coupling of fermionic fields with mass dimension one to the O'Raifeartaigh model to study supersymmetry breaking for these fermions. We find that the coupled model has two distinct solutions. The first solution represents a local minimum of the superpotential which spontaneously breaks supersymmetry in perfect analogy to the O'Raifeartaigh model. The second solution is more intriguing as it corresponds to a global minimum of the superpotential. In this case, the coupling to the fermionic sector restores supersymmetry. However, this is achieved at the cost of breaking Lorentz invariance. Finally, the mass matrices for the multiplets of the coupled model are presented. It turns out that it contains two bosonic triplets and one fermionic doublet which are mass multiplets. In addition, it contains a massless fermionic doublet as well as one fermionic triplet which is not a mass multiplet but rather an interaction multiplet that contains component fields of different mass dimension. The results also imply that the presented model for fermionic fields with mass dimension one is an interesting candidate for supersymmetric dark matter (DM).
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