%0 Journal Article
%T Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
%A Romero-Lopez, F.
%A Sharpe, S. R.
%A Blanton, T. D.
%A Briceno, R. A.
%A Hansen, M. T.
%J Journal of High Energy Physics
%D 2019
%V 10
%N 10
%I Springer
%@ 1029-8479
%G English
%F Romero-Lopez_etal2019
%O WOS:000497979000001
%O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=4207), last updated on Fri, 06 Dec 2019 10:59:13 +0000
%X 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.
%K Lattice QCD
%K Scattering Amplitudes
%R 10.1007/JHEP10(2019)007
%U https://arxiv.org/abs/1908.02411
%U https://doi.org/10.1007/JHEP10(2019)007
%P 007-43pp