Theoretical analysis reveals the emergence of Yang-Mills gauge structures from four-particle amplitude factorization, indicating fundamental symmetries arise without initial symmetry assumptions.
A bstract We revisit the emergence of a Yang-Mills structure 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.
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Fonseca et al. (2026) studied this question.
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