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

Yang Li (李阳)1,*, Tianzhi Wang (王天志)1,†, Tomáš Brauner2,‡, and Diederik Roest1,§

  • *Contact author: y.l.li@rug.nl
  • †Contact author: tian.wang@rug.nl
  • ‡Contact author: tomas.brauner@uis.no
  • §Contact author: d.roest@rug.nl
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Phys. Rev. Lett. 135, 181601 – Published 29 October, 2025

DOI: https://doi.org/10.1103/1krs-lfqv

Abstract

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.

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References (34)

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Phys. Rev. Lett. 135, 181601– Published 29 October, 2025
  • Received 28 March 2025
  • Revised 8 July 2025
  • Accepted 22 August 2025
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