A Lagrangian for mass dimension one fermionic dark matter

The mass dimension one fermionic field associated with Elko satisfies the Klein–Gordon but not the Dirac equation. However, its propagator is not a Green's function of the Klein–Gordon operator. We propose an infinitesimal deformation to the propagator such that it admits an operator in which the deformed propagator is a Green's function. The field is still of mass dimension one, but the resulting Lagrangian is modified in accordance with the operator.