Momentum routing invariance in extended QED: Assuring gauge invariance beyond tree level

Abstract

We address the study of gauge invariance in the Standard Model Extension which encompasses all Lorentz-violating terms originated by spontaneous symmetry breaking at the Planck scale. In particular, we fully evaluate Ward identities involving two and three point functions and derive the conditions which assure gauge invariance of the electromagnetic sector of the Standard Model Extension at one-loop. We show that momentum routing invariance is sufficient to fix arbitrary and regularization dependent parameters intrinsic to perturbation theory in the diagrams involved. A scheme which judiciously collects finite but undetermined quantum corrections is employed, a particularly subtle issue in the presence of γ5 matrices.

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

“…Similar analyses, in many different theories and contexts, have been carried out in Refs. [78][79][80][81][82][83][84][85][86][87][88][89][90][91].…”

May the four be with you: novel IR-subtraction methods to tackle NNLO calculations

“…ST's vanish if and only if momentum routing invariance (MRI) holds in the loops of Feynman diagrams. Moreover these requirements automatically deliver gauge invariant amplitudes [90][91][92][93][94] which has been demonstrated for abelian gauge theories to arbitrary loop order [82,84] and verified for non-abelian gauge models [95][96][97]. Rephrasing it, unless MRI is verified, a symmetric integration leads to a finite definite value for the arbitrary surface term which potentially breaks (gauge) symmetry.…”

Gauge anomalies in Lorentz-violating QED

“…Moreover, the momentum routing invariance is employed in order to ensure the gauge invariance of Lorentz-violating QED. Although the authors of [32] disagree with the computation procedure employed in [31], both works show which Ward identities of Lorentz-violating QED remain valid at one-loop order.…”

“…In fact, once the anomaly parameter can be made to vanish at one-loop, a nonrenormalization theorem would be needed in order to guarantee this property up to all orders in perturbation theory. Still in this line, in [32] are analyzed the one-loop contributions coming from vacuumpolarization and three-photon vertex diagrams. Besides divergent terms, the finite contributions from the mentioned diagrams are computed through the so-called implicit regularization, in order to circumvent the problem of the ambiguity in defining a d-dimensional γ 5 -matrix algebra.…”