  The objective of this article is to discuss the coupling of fermionic fields
with mass dimension one to the O'Raifeartaigh model to study supersymmetry
breaking for fermionic fields with mass dimension one.
  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.
  These results show that the presented model for fermionic fields with mass
dimension one is a viable candidate for supersymmetric dark matter that could
be accessible to experiments in the near future.
