Work

Symmetrizing relativistic three-body partial wave amplitudes

Year: 2025

Type: article

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

Source: Physical review. D/Physical review. D.

DOI: 10.1103/xwht-8kft

Authors: Andrew W. Jackura, Nicholas C. Chambers, Raúl A. Briceño

Institutions: William & Mary, Lawrence Berkeley National Laboratory, University of California, Berkeley

Language: English

Topic: Quantum Chromodynamics and Particle Interactions

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: U.S. Department of Energy, Virginia Space Grant Consortium, Office of Science, Nuclear Physics

Awards: G1286236842, G1553439044, G3282003731