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Renormalization and invariants for two U(1)s

Sacha Davidson1,* and Martin Gorbahn2,†

  • *Contact author: s.davidson@ip2i.in2p3.fr
  • †Contact author: martin.gorbahn@liverpool.ac.uk
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Phys. Rev. D 114, 055020 – Published 11 September, 2026

DOI: https://doi.org/10.1103/cjy8-36vv

Abstract

We revisit the renormalization of models with two U(1) gauge symmetries, in a formulation with noncanonical gauge kinetic terms which is covariant under field reparametrizations among the two gauge bosons. This approach is convenient to study the appearance of kinetic mixing in scale evolution because a coupling matrix is attributed to the gauge kinetic terms. We obtain simple MS¯ renormalization group equations up to two-loop, which can be solved to give effective millicharges at low energy which depend on the running couplings and heavy mass scales of the model. This formulation allows one to construct “invariants” out of running Lagrangian parameters, which are invariant under generic gauge field reparametrizations, including rescalings, and which can be related directly to observables such as the millicharge.

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Phys. Rev. D 114, 055020– Published 11 September, 2026
  • Received 3 June 2026
  • Accepted 3 August 2026
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