Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data

Most strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered X, Y, and Z resonances. In order to study such resonances from first principles using lattice QCD, one must understand finite-volume effects for three particles in the cubic box used in calculations. We review efforts to develop a three-particle quantization condition that relates finite-volume energies to infinite-volume scattering amplitudes. We describe in detail the three approaches that have been followed, and present new results on the relationship between the corresponding results. We show examples of the numerical implementation of all three approaches and point out the important issues that remain to be resolved.

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Extracting observables from lattice data in the three-particle sector

EPJ Web of Conferences ◽

10.1051/epjconf/201817511006 ◽

2018 ◽

Vol 175 ◽

pp. 11006

Author(s):

Akaki Rusetsky ◽

Hans-Werner Hammer ◽

Jin-Yi Pang

Keyword(s):

Finite Volume ◽

Energy Shift ◽

Bound State ◽

Effective Field ◽

Quantization Condition ◽

Unitary Limit ◽

Lattice Data ◽

Volume Energy ◽

Three Body

The three-particle quantization condition is derived, using the particle-dimer picture in the non-relativistic effective field theory. The procedure for the extraction of various observables in the three-particle sector (the particle-dimer scattering amplitudes, breakup amplitudes, etc.) from the finite-volume lattice spectrum is discussed in detail. As an illustration of the general formalism, the expression for the finite-volume energy shift of the three-body bound-state in the unitary limit is re-derived. The role of the threebody force, which is essential for the renormalization, is highlighted, and the extension of the result beyond the unitary limit is studied. Comparison with other approaches, known in the literature, is carried out.

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Three-particle system in a finite volume: formalism, quantization condition, spectrum and energy shift

EPJ Web of Conferences ◽

10.1051/epjconf/202024102005 ◽

2020 ◽

Vol 241 ◽

pp. 02005

Author(s):

Jin-Yi Pang

Keyword(s):

Finite Volume ◽

Bound States ◽

Particle System ◽

Energy Shift ◽

Effective Field ◽

Quantization Condition ◽

High Current ◽

Scattering States ◽

Three Body ◽

Hadronic Process

Lattice QCD calculations provide an ab initio access to hadronic process. These calculations are usu ally performed in a small cubic volume with periodic boundary conditions. The infinite volume extrapolations for three-body systems are indispensable to understand many systems of high current interest. We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Our work shows a powerful and transparent method to read off three-body physical observables from lattice simulations. In this paper, we review the formalism, quantization condition, spectrum analysis and energy shifts calculation both for 3-body bound states and scattering states.

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