  In the context of Standard Model Extensions (SMEs), we analyse four general
classes of Super Symmetry (SuSy) and Lorentz Symmetry (LoSy) breaking, leading
to {observable} imprints at our energy scales. The photon dispersion relations
show a non-Maxwellian behaviour for the CPT (Charge-Parity-Time reversal
symmetry) odd and even sectors. The group velocities exhibit also a directional
dependence with respect to the breaking background vector (odd CPT) or tensor
(even CPT). In the former sector, the group velocity may decay following an
inverse squared frequency behaviour. Thus, we extract a massive and gauge
invariant Carroll-Field-Jackiw photon term in the Lagrangian and show that the
mass is proportional to the breaking vector. The latter is estimated by ground
measurements and leads to a photon mass upper limit of $10^{-19}$ eV or $2
\times 10^{-55}$ kg and thereby to a potentially measurable delay at low radio
frequencies.
