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Solving relativistic three-body integral equations in the presence of bound states

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arxiv 2010.09820 v1 pith:PUMZ2PLU submitted 2020-10-19 hep-lat hep-phnucl-th

Andrew W. Jackura , Raúl A. Briceño , Sebastian M. Dawid , Md Habib E Islam , Connor McCarty This is my paper · ORCID
classification hep-lathep-phnucl-th
keywords equationsintegralsolvingthree-bodyboundcontinuummatrixmethod
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abstract

We present a systematically improvable method for numerically solving relativistic three-body integral equations for the partial-wave projected amplitudes. The method consists of a discretization procedure in momentum space, which approximates the continuum problem with a matrix equation. It is solved for different matrix sizes, and in the end, an extrapolation is employed to restore the continuum limit. Our technique is tested by solving a three-body problem of scalar particles with an $S$ wave two-body bound state. We discuss two methods of incorporating the pole contribution in the integral equations, both of them leading to agreement with previous results obtained using finite-volume spectra of the same theory. We provide an analytic and numerical estimate of the systematic errors. Although we focus on kinematics below the three-particle threshold, we provide numerical evidence that the methods presented allow for determination of amplitude above this threshold as well.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Coupled-channel approach to isotensor $\pi\pi\pi$ scattering from lattice QCD

    hep-lat 2026-01 conditional novelty 6.0 of 10

    The I=2 three-pion spectrum from lattice QCD is described by a repulsive rho-pi S-wave interaction, consistent with a leading-order effective Lagrangian.

  2. Symmetrizing relativistic three-body partial wave amplitudes

    hep-ph 2025-07 unverdicted novelty 6.0 of 10

    The authors derive spectator-symmetric three-body partial wave amplitudes using new recoupling coefficients for arbitrary angular momentum and isospin, and demonstrate them with 3π Dalitz distributions.

  3. Analytic decomposition of two-body electroweak processes with left-hand cuts

    hep-lat 2026-07 accept novelty 5.0 of 10

    An on-shell decomposition of 2+J o2 electroweak amplitudes isolates OPE poles, logs, and triangle singularities, leaving only smooth short-distance functions.

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