Renormalization of U(1) gauge boson kinetic mixing

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 quantum electrodynamics with a massive “dark” photon at one-loop order. In the general covariant 𝑅𝜉 -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.