An improved partial-wave projection of the one-particle exchange in relativistic three-body scattering
Abstract
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.
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BibTeX
@misc{chambers2026improved,
title = {{An improved partial-wave projection of the one-particle exchange in relativistic three-body scattering}},
author = {Nicholas C. Chambers and Andrew W. Jackura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10306},
eprint = {2609.10306},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10306},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An improved partial-wave projection of the one-particle exchange in relativistic three-body scattering
AU - Nicholas C. Chambers
AU - Andrew W. Jackura
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10306
UR - https://arxiv.org/abs/2609.10306
AB - 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.
ER -