Diagrammatic Derivation of Hidden Zeros and Exact Factorization of Pion Scattering Amplitudes

Pion scattering amplitudes were recently found to vanish on specific kinematic loci, and to factorize close to these loci into a product of two lower-point amplitudes of an extended theory. We propose a diagrammatic representation of pion amplitudes that makes their vanishing on the loci manifest diagram by diagram. Moreover, we provide evidence that there is a closed-form expression for the amplitudes that generalizes the near-zero factorization in an exact manner, not only close to the loci but for all kinematic configurations. Our approach crucially relies on a novel formulation of the effective field theory of pions, in which tree-level scattering amplitudes are extracted from classical field equations for a set of covariantly conserved currents and emergent composite gauge fields.