Abstract
Finite volume multiple-particle interaction is studied in a two-dimensional complex $\phi^4$ lattice model. The existence of analytical solutions to the $\phi^4$ model in two-dimensional space and time makes it a perfect model for the numerical study of finite volume effects of multi-particle interaction. The spectra from multiple particles are extracted from the Monte Carlo simulation on various lattices in several moving frames. The $S$-matrix of multi-particle scattering in $\phi^4$ theory is completely determined by two fundamental parameters: single particle mass and the coupling strength of two-to-two particle interaction. These two parameters are fixed by studying single-particle and two-particle spectra. Due to the absence of the diffraction effect in the $\phi^{4}$ model, three-particle quantization conditions are given in a simple analytical form. The three-particle spectra from simulation show remarkable agreement with the prediction of exact solutions.
Highlights
One of the outstanding but challenging goals in nuclear/ hadron physics is to understand the dynamics of particle interaction
Given the values of particle mass, m, and coupling strength, V0, that we learned from discussion in previous sections, three-particle spectra do not provide any new insight into the fundamental parameters of φ4 theory due to the absence of a three-body force
The lattice simulation of multiparticle interaction is studied by using a complex φ4 lattice model
Summary
One of the outstanding but challenging goals in nuclear/ hadron physics is to understand the dynamics of particle interaction. A three-particle lattice simulation was recently performed based on a complex φ4 toy model [71]; the data analysis was carried out by adopting the effective theory framework. We aim to perform a simulation on multiple-particle interaction using the φ4 model and study the finite volume effect on multipleparticle spectra in a better-controlled environment and a more systematic way. For this purpose, multiple numbers of multiparticle operators are used in our simulation, and variational analysis [72,73,74] is implemented to extract excited state energy levels.
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