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.
Highlights
Several outstanding problems in modern-day hadronic, particle, and nuclear physics require a relativistic description of the dynamics of multihadron systems
2 shows plots for ma 1⁄4 2, 6, of jM2j as a and 16, which are the three cases we study in detail in the subsequent solutions of the integral equations
This allows one to write the integral equation as a matrix equation that could be solved numerically
Summary
Several outstanding problems in modern-day hadronic, particle, and nuclear physics require a relativistic description of the dynamics of multihadron systems. Many resonances, which challenge our understanding of the strong interaction, are observed experimentally in reactions involving final states composed of three particles or more. One example is the recently observed tetraquark candidate Xð2900Þ found in the Bþ → DþD−Kþ decay [1,2]. Three-body decays play a significant role in modern-day tests of the fundamental symmetries of the Standard Model and searches of its extensions.
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