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Title Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
Authors Raul Briceno,Maxwell Hansen,Stephen Sharpe,Tyler Blanton,Fernando Romero-Lo┬┤pez
JLAB number JLAB-THY-19-3011
LANL number arXiv:1908.02411
Other number DOE/OR/23177-4759
Document Type(s) (Journal Article) 
Supported by U.S. Naval Research: No
Supported by Jefferson Lab LDRD Funding: No
Funding Source: Nuclear Physics (NP)

Compiled for arXiv
Publication 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. In this work, we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K matrix 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.
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