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  • Open Access

Renormalization of U(1) gauge boson kinetic mixing

Felix Forner1,* and Felix Tellander2,3,†

  • *Contact author: felix.forner@tum.de
  • †Contact author: felix@tellander.se
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Phys. Rev. D 113, 056015 – Published 18 March, 2026

DOI: https://doi.org/10.1103/tqw9-zm9x

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.

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Phys. Rev. D 113, 056015– Published 18 March, 2026
  • Received 10 January 2026
  • Accepted 27 February 2026
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