One-loop structure of the photon propagator in the standard model extension

Radiative corrections to the photon propagator from the electroweak sector are studied in the context of the minimal Lorentz- and CPT -violating standard model extension, with a focus on the Yukawa, Higgs, and gauge sectors. The most general Lorentz-violating ghost sector dictated by Becchi-Rouet-Stora-Tyutin symmetry and renormalization theory is derived. We stress the introduction of a Lorentz-violating nonlinear gauge that greatly simplifies both the Higgs-sector extension and the gauge-sector extension, which can be very helpful in radiative corrections. At one loop, these sectors contribute to the CPT -even part of the photon propagator, which is characterized by the Riemann-type tensor (kF)αβμν. Exact results for the contributions to the SO(1,3) irreducible parts of (kF)αβμν, namely, the Weyl-type tensor (^kF)αβμν, the Ricci-type tensor (kF)αβ, and the curvature-type scalar kF, are presented. In the Yukawa sector, with general flavor-violating effects, all of the one-loop contributions are ultraviolet finite, but most of them are unobservable due to finite renormalization of the field, the electric charge, (^kF)αβμν, and (kF)αβ. The only observable effect is a contribution proportional to (kF)αβ that emerges via a dimension-six term that is both observer and gauge invariant. In the Higgs and gauge sectors, all of the irreducible parts of the corresponding Riemann-type tensors receive divergent contributions, so they are observable. The only finite contribution corresponds to the previously mentioned dimension-six term. By thinking of these contributions as a radiative correction to the renormalized tensors, and assuming that both effects are of the same order of magnitude, bounds from vacuum birefringence are derived and compared with results in the literature. Bounds on contributions proportional to (kF)αβ, which are innocuous to birefringence, are also derived using limits imposed on the renormalized tensor from the Laser Interferometer Gravitational-Wave Observatory data. We compare these bounds with those already existing in the literature. The beta functions associated with the (^kF)αβμν and (kF)αβ tensors are derived.