CP Conservation in the Strong Interactions

Wen Yuan Ai, Björn Garbrecht, Carlos Tamarit

Research output: Contribution to journalArticlepeer-review


We discuss matters related to the point that topological quantization in the strong interaction is a consequence of an infinite spacetime volume. Because of the ensuing order of limits, i.e., infinite volume prior to summing over topological sectors, (Formula presented.) is conserved. Here, we show that this reasoning is consistent with the construction of the path integral from steepest-descent contours. We reply to some objections that aim to support the case for (Formula presented.) violation in strong interactions that are based on the role of the (Formula presented.) -odd theta-parameter in three-form effective theories, the correct sampling of all configurations in the dilute instanton gas approximation and the volume dependence of the partition function. We also show that the chiral effective field theory derived from taking the volume to infinity first is in no contradiction with analyses based on partially conserved axial currents.

Original languageEnglish
Article number189
Issue number5
StatePublished - May 2024


  • CP violation
  • neutron electric dipole moment
  • quantum chromodynamics


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