Nicholas C. Chambers | Searcharxiv

arXiv2026

An improved partial-wave projection of the one-particle exchange in relativistic three-body scattering

A critical component of relativistic three-body scattering amplitudes is the one-particle exchange (OPE) process, wherein a single particle is exchanged between incoming and outgoing two-body subsystems. We present an improved, finite-sum expression for the partial-wave OPE that is valid for three massive, spinless particles in arbitrary angular momentum configurations. A collection of analytic and numerical checks demonstrate that our finite-sum expression reproduces the known properties of the partial-wave OPE, including its threshold scaling behavior and singularity structure. Compared with previous work, this result more efficiently handles the rapid proliferation of partial waves contributing to any total angular momentum $J$, enabling the construction of robust wavesets for three-body amplitude analyses.

hep-ph↗

arXiv2025

Symmetrizing relativistic three-body partial wave amplitudes

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 $3\pi$ systems and provide numerical evidence that the symmetrization procedure is consistent with expected symmetries of Dalitz plots.

hep-ph↗