Implementing the three-particle quantization condition for π⁺π⁺K⁺ and related systems

Journal Article · 13 February 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep02(2022)098 · OSTI ID:1906206

Blanton, Tyler D. ^[1]; Romero-López, Fernando  ^[2]; Sharpe, Stephen R. ^[3]

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1. Univ. of Maryland, College Park, MD (United States); University of Washington
2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); CSIC-Universitat de València, Paterna (Spain)
3. Univ. of Washington, Seattle, WA (United States)

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K_df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L⁵); and we calculate the leading-order predictions in chiral perturbation theory for K_df,3 in the π⁺π⁺K⁺ and π⁺K⁺K⁺ systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π⁺π⁺K⁺ levels using the two- and three-particle interactions predicted by chiral perturbation theory.

• Research Organization: Massachusetts Institute of Technology (MIT), Cambridge, MA (United States); Univ. of Washington, Seattle, WA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: FG02-93ER40762; SC0011090; SC0011637; SC0021006; SC0021143
• OSTI ID: 1906206
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2022; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English