#### Document Type

Article

#### Publication Date

10-2019

#### DOI

10.1007/JHEP10(2019)007

#### Publication Title

Journal of High Energy Physics

#### Issue

10

#### Pages

007 (43 pg.)

#### 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.

#### Original Publication Citation

Romero-Lopez, F., Sharpe, S. R., Blanton, T. D., Briceno, R. A., & Hansen, M. T. (2019). Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states. *Journal of High Energy Physics*(10), 007. doi:10.1007/jhep10(2019)007

#### ORCID

0000-0003-1109-1473 (Briceño)

#### Repository Citation

Romero-López, Fernando; Sharpe, Stephen R.; Blanton, Tyler D.; Briceño, Raúl A.; and Hansen, Maxwell T., "Numerical Exploration of Three Relativistic Particles in a Finite Volume Including Two-Particle Resonances and Bound States" (2019). *Physics Faculty Publications*. 402.

https://digitalcommons.odu.edu/physics_fac_pubs/402

## Comments

Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

© The Authors. Article funded by SCOAP

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