Running Couplings in CP Violating Abelian Theories
Abstract
We calculate the one- and two-loop running couplings for a massless photon coupled to dyons, including CP violating couplings. The electric and magnetic source vertices in the most general theory form a real coupling matrix C, while a current-current interaction depends on CT C and the quantized determinant det C. These determine, respectively, the continuously running Coulombic interactions and the fixed antisymmetric Dirac--Schwinger--Zwanziger charge quantization condition which also determines pairwise helicity. The running preserves det C, showing that the electric and magnetic couplings run inversely while every pairwise helicity remains constant. We comment on how the running of the CP-odd coupling θ relates to physical CP violation, which also depends on the spectrum, mass phases, and threshold corrections. We also show that an invertible field redefinition moves the CP-odd coupling between the current source terms and the photon kinetic terms; these are two descriptions of the same local interaction. Finally, we show that the result agrees with the Argyres--Douglas β function ansatz.
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BibTeX
@misc{newey2026running,
title = {{Running Couplings in CP Violating Abelian Theories}},
author = {Joshua Newey and John Terning and Christopher B. Verhaaren},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07016},
eprint = {2611.07016},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07016},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Running Couplings in CP Violating Abelian Theories
AU - Joshua Newey
AU - John Terning
AU - Christopher B. Verhaaren
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07016
UR - https://arxiv.org/abs/2611.07016
AB - We calculate the one- and two-loop running couplings for a massless photon coupled to dyons, including CP violating couplings. The electric and magnetic source vertices in the most general theory form a real coupling matrix C, while a current-current interaction depends on C^T C and the quantized determinant det C. These determine, respectively, the continuously running Coulombic interactions and the fixed antisymmetric Dirac--Schwinger--Zwanziger charge quantization condition which also determines pairwise helicity. The running preserves det C, showing that the electric and magnetic couplings run inversely while every pairwise helicity remains constant. We comment on how the running of the CP-odd coupling θ relates to physical CP violation, which also depends on the spectrum, mass phases, and threshold corrections. We also show that an invertible field redefinition moves the CP-odd coupling between the current source terms and the photon kinetic terms; these are two descriptions of the same local interaction. Finally, we show that the result agrees with the Argyres--Douglas β function ansatz.
ER -