2019/08/31 by Fernando Romero-López, Stephen R. Sharpe, Tyler D. Blanton +2 · 3 citations
Mathematics · Physics and Astronomy · #Bound state #Classical mechanics #Finite volume method #Geometry #High-Energy Particle Collisions Research #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantization (signal processing) #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scalar (mathematics) #Scalar boson #Scattering #Upper and lower bounds #cond-mat.stat-mech #hep-lat #hep-ph #nucl-th #physics.atom-ph
paper · pdf · doi:10.1007/jhep10(2019)007
published as JHEP 1910 (2019) 007 · 42 pages, 16 figures, CERN-TH-2019-129, JLAB-THY-19-3011. Minor clarification and updated references
arxiv created 2019/09/09 · openalex publication_date 2019/10/01 · arxiv updated 2019/10/17 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06
A bstract 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.