Renormalization of U(1) Gauge Boson Kinetic Mixing

TL;DR

This paper investigates the renormalization of kinetic mixing between U(1) gauge bosons, demonstrating that despite gauge-dependent obstructions, the theory remains renormalizable and different schemes are equivalent through scale-dependent transformations.

Contribution

It provides a detailed analysis of U(1) gauge boson kinetic mixing renormalization, including gauge dependence and scheme equivalence at one-loop order.

Findings

Off-diagonal UV divergences cancel in covariant gauges.

Kinetic mixing schemes are shown to be equivalent via scale-dependent transformations.

The theory remains renormalizable despite gauge-dependent obstructions.

Abstract

Quantum field theories containing fields with the same quantum numbers allow for mixed kinetic terms in the Lagrangian, leading to off-diagonal elements in the tree-level two-point function. After removing the mixing by a field rotation, the off-diagonal UV divergences cannot be subtracted by a counterterm, still one can show that the theory is renormalizable. We study kinetic mixing of $U(1)$ gauge bosons in an extension of QED with a massive "dark" photon at one-loop order. In general covariant $R_\xi$-gauge, the gauge-fixing function naively obstructs the removal of tree-level mixing but we show that these off-diagonal gauge-dependent contributions cancel. We compare two renormalization schemes: one with and one without kinetic mixing, and relate them via a scale-dependent field transformation, showing that the schemes are equivalent.