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

TL;DR

This paper introduces a diagrammatic method for pion scattering amplitudes that makes their vanishing on specific kinematic loci explicit and suggests a closed-form expression valid for all configurations, based on a novel EFT formulation.

Contribution

It presents a new diagrammatic representation of pion amplitudes and proposes an exact, general expression for these amplitudes beyond near-zero factorisation.

Findings

Amplitudes vanish on specific kinematic loci.

Amplitudes factorise into lower-point amplitudes near these loci.

A potential closed-form expression for all kinematic configurations.

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.