Applying the relativistic quantization condition to a three-particle bound state in a periodic box

Abstract

Using our recently developed relativistic three-particle quantization condition, we study the finite-volume energy shift of a spin-zero three-particle bound state. We reproduce the result obtained using non-relativistic quantum mechanics by Meissner, Rios and Rusetsky, and generalize the result to a moving frame.

20 pages, no figures, v2: fixed issues with special characters in references, v3: minor rewording, version appearing in PRD

References in corpus (11)

• Universality in Few-body Systems with Large Scattering Length
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• A relativistic, model-independent, three-particle quantization condition
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Two Nucleons on a Lattice
• Improving the Volume Dependence of Two-Body Binding Energies Calculated with Lattice QCD
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Spectrum of three-body bound states in a finite volume
• Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates
• Perturbative results for two and three particle threshold energies in finite volume
• Hadron Structure and Spectrum from the Lattice

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