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  • Open Access

Symmetrizing relativistic three-body partial wave amplitudes

Andrew W. Jackura* and Nicholas C. Chambers†

Raúl A. Briceño‡

  • Department of Physics, William & Mary, Williamsburg, Virginia 23187, USA

  • *Contact author: awjackura@wm.edu
  • †Contact author: ncchambers@wm.edu
  • ‡Contact author: rbriceno@berkeley.edu
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Phys. Rev. D 113, 014019 – Published 16 January, 2026

DOI: https://doi.org/10.1103/xwht-8kft

Abstract

S matrix principles and symmetries impose constraints on three-particle scattering amplitudes, which can be formulated as a class of integral equations for their partial wave projections. However, these amplitudes are typically expressed in an asymmetric basis, where one of the initial and final state particles is singled out, and all quantum numbers are defined relative to this spectator. In this work, we show how to construct symmetric partial wave amplitudes, which have been symmetrized over all possible spectator combinations, using their asymmetric counterparts and sets of recoupling coefficients. We derive these recoupling coefficients for arbitrary angular momentum and isospin for arbitrary systems of spinless particles with SU(2) flavor symmetry. We propose a simple intensity observable suitable for visualizing the structure of three-body dynamics in Dalitz distributions. Finally, we provide some numerical examples of Dalitz distributions relevant for future lattice QCD calculations of 3π systems and provide numerical evidence that the symmetrization procedure is consistent with expected symmetries of Dalitz plots.

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Phys. Rev. D 113, 014019– Published 16 January, 2026
  • Received 25 August 2025
  • Accepted 2 December 2025
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