Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
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Publication:2283349
DOI10.1007/JHEP10(2019)007zbMATH Open1427.81094arXiv1908.02411OpenAlexW2965018786WikidataQ127030258 ScholiaQ127030258MaRDI QIDQ2283349
Author name not available (Why is that?)
Publication date: 2 January 2020
Published in: (Search for Journal in Brave)
Abstract: In this work, we use an extension of the quantization condition, given in Ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two- and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimer-particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon scattering. All calculations presented here are restricted to the case of three identical scalar particles.
Full work available at URL: https://arxiv.org/abs/1908.02411
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