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

Abstract: Pion scattering amplitudes were recently found to vanish on specific kinematic loci, and to factorise 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 generalises the near-zero factorisation 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.