Abstract
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.
Highlights
We show that three-body threshold amplitude can be extracted from energy shifts of scattering states [29]
We have demonstrated that the 2-body low-energy constants (LECs) can be encoded in phase shift for both particle-dimer scattering equation and 3-body quantization condition [18]
We have reviewed the effective field theory describing 3body system
Summary
A rapid progress is developed aiming to analyze of the lattice data in the three-particle sector [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29] (for the recent review, see Ref. [30]). This is the request of lattice simulation which has touched the three-body kinematics region. Among these approaches, our works [17, 18, 20, 29] has showed its transparent and powerful to the problem via the non-relativistic effective theory and the particle-dimer picture in a finite volume We apply the quantization condition to analyze the 3-body bound states and scattering states in Sec. 4 and 5.
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