Solving relativistic three-body integral equations in the presence of bound states
| Autor: | Sebastian M. Dawid, Habib E Islam, A. Jackura, Raúl A. Briceño, Connor McCarty |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Nuclear Theory High Energy Physics - Lattice (hep-lat) Lattice field theory Scalar (mathematics) Strong interaction FOS: Physical sciences Lattice QCD Integral equation Nuclear Theory (nucl-th) Scattering amplitude High Energy Physics - Phenomenology High Energy Physics - Phenomenology (hep-ph) Amplitude High Energy Physics - Lattice Bound state Applied mathematics |
| Zdroj: | Physical Review |
| Popis: | 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. 20 pages, 9 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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