SUSY QED with Lorentz-asymmetric fermionic matter and a glance at the electron's EDM

This contribution sets out to pursue the investigation of a supersymmetric electrodynamics model with Lorentz-symmetry violation (LSV) manifested by a space-time unbalance in the propagation of the fermionic charged matter. Despite violation of Lorentz symmetry, the supersymmetry algebra is kept untouched. We then adopt a superspace approach to build up an $\mathcal{N}=1$-supersymmetric Abelian gauge theory in presence of a Lorentz-violating background supermultiplet that accommodates the space-time asymmetry parameter of the charged matter. We describe, in this scenario, how the particular Lorentz-symmetry breaking, brought about by the fermionic matter, affects its (matter) scalar partners and the photon/photino that minimally couple to charged matter. From the (modified) Dirac, Klein-Gordon and Maxwell field equations, we work out the corresponding dispersion relations to inspect and discuss the physical effects of the LSV Majorana fermion condensates that naturally emerge from the background supermultiplet. Finally, we target efforts to investigate the Gordon decomposition of the charged lepton electromagnetic current. This is carried out by iterating the (fermion and scalar) matter field equations, which points to an effective contribution to the electron's electric dipole moment (EDM). This result allows us to attain an estimate of the pseudo-vector condensate of the (LSV) Majorana background fermion.