  We study radiative corrections on the photon propagator from the electroweak
sector of the minimal Lorentz- and $CPT$-violating Standard Model Extension. We
derive the most general Lorentz-violating ghost sector from BRST symmetry and
renormalization theory. We introduce a Lorentz-violating nonlinear gauge that
simplifies both the Higgs and gauge-sector extensions, which can be helpful in
radiative corrections. At one loop, these sectors contribute to the $CPT$-even
part of the photon propagator, characterized by the Riemann-type tensor
$(k_F)_{\alpha\beta\mu\nu}$. We give exact results for the contributions to the
SO(1,3) irreducible parts of $(k_F)_{\alpha \beta \mu \nu}$, namely, the
Weyl-type tensor $(\hat{k}_F)_{\alpha \beta \mu \nu}$, the Ricci-type tensor
$(k_F)_{\alpha \beta}$, and the curvature-type scalar $k_F$. In the Yukawa
sector, one-loop contributions are ultraviolet finite, but most of them are
unobservable due to finite renormalization. The only observable effect is a
contribution proportional to $(k_F)_{\alpha \beta}$ that emerges via a
dimension-6 term that is observer and gauge invariant. In the Higgs and gauge
sectors, all the irreducible parts of the corresponding Riemann-type tensors
receive divergent contributions, so they are observable. The only finite
contribution corresponds to the dimension-6 term. We think of these
contributions as radiative corrections to the renormalized tensors and assume
that both effects are of the same order of magnitude to find bounds from vacuum
birefringence and compare with the literature. Bounds on $(k_F)_{\alpha \beta}$
contributions, innocuous to birefringence, are also derived using limits on the
renormalized tensor from Laser-Interferometer-Gravitational-Wave-Observatory
data. We compare these bounds with the literature. Beta functions associated
with $(\hat{k}_F)_{\alpha \beta \mu \nu}$ and $(k_F)_{\alpha \beta}$ are
derived.
