It is customary to assume more properties of gauge theories than is necessary to produce all of their properties. Some of those assumptions can be derived, including CP invariance.
We revisit the emergence of a Yang-Mills symmetry in theories with massless spin 1 particles from fundamental physical properties of scattering amplitudes. In the standard proofs, some symmetry and reality properties of the coupling constants in three-point amplitudes are assumed. These properties cannot be justified using only three-point amplitudes but we show that they arise as consequences of the consistent factorization of four-particle amplitudes, for particular choices of the particle basis. This applies to self-interactions of massless spin 1 particles and also to their interactions with spin 0 and 1/2 particles. CP invariance is a derived property, not an additional assumption. The situation for gravity interactions is analogous and it is dealt with in the same fashion.
Renato M. Fonseca, Clara Hernandez-Garcia, Javier M. Lizana, Manuel Perez-Victoria, "Gauge theories from scattering amplitudes with minimal assumptions" arXiv:2511.21664 (November 26, 2025).
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