Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states

Journal Article · 03 October 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP10(2019)007 · OSTI ID:1574401

Romero-López, Fernando  ^[1]; Sharpe, Stephen R. ^[2]; Blanton, Tyler D. ^[2]; Briceño, Raúl A. ^[3]; Hansen, Maxwell T. ^[4]

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1. CSIC-Univ. de Valéncia, Paterna (Spain)
2. Univ. of Washington, Seattle, WA (United States). Dept. of Physics
3. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States). Dept. of Physics
4. European Organization for Nuclear Research (CERN), Geneva (Switzerland)

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.

• Research Organization: Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Univ. of Washington, Seattle, WA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); European Union (EU); Australian Research Council (ARC); Kyoto University (Japan)
• Grant/Contract Number: AC05-06OR23177; SC0011637; SC0019229
• OSTI ID: 1574401
• Report Number(s): JLAB-THY--19-3011; DOE/OR/--23177-4759; arXiv:1908.02411
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2019; ISSN 1029-8479
• Publisher: Springer BerlinCopyright Statement
• Country of Publication: United States
• Language: English