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arXiv · 2409.15577

Partial-wave projection of relativistic three-body amplitudes

Raúl A. Briceño·Caroline S. R. Costa·Andrew W. Jackura
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Abstract

We derive the integral equations for partial-wave projected three-body scattering amplitudes, starting from the integral equations for three-body amplitudes developed for lattice QCD analyses. The results, which hold for generic three-body systems of spinless particles, build upon the recently derived partial-wave projected one-particle exchange, a primary component of the relativistic framework proven to satisfy S matrix unitarity. We derive simplified expressions for factorizable short-distance interactions, $\mathcal{K}_{3}$, in two equivalent formalisms - one symmetric under particle interchange and one asymmetric. For the asymmetric case, we offer parameterizations useful for amplitude analysis. Finally, we examine toy models for $3\pi$ systems at unphysically heavy pion masses with total isospins 0,1, and 2.

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Raúl A. Briceño, Caroline S. R. Costa, Andrew W. Jackura. 2024-09-23. Partial-wave projection of relativistic three-body amplitudes. https://arxiv.org/abs/2409.15577

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