Radiatively induced Lorentz-violating operator of mass dimension five in QED

The first higher derivative term of the photon sector of Lorentz-violating QED, with operator of mass dimension $d=5$, is radiatively induced from the fermion sector, in which contains a derivative term with the dimensionless coefficient $g^{\lambda \mu \nu }$. The calculation is performed perturbatively in the coefficient for Lorentz violation, and due to the fact that the contributions are quadratically divergent, we adopt dimensional regularization.