Three-Bosons in a Finite 4D Euclidean Volume
Three-Bosons in a Finite 4D Euclidean Volume
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有限 4D 欧几里得体积中的三玻色子
DOI：
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发表时间：
2021
期刊：
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通讯作者：
E. Ydrefors
中科院分区：
文献类型：
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作者：
T. Frederico;E. Ydrefors
回顾了无限四维 (4D) 体积中具有接触相互作用的三玻色子系统的闵可夫斯基和欧几里得齐次 Faddeev-Bethe-Salpeter (FBS) 方程的公式，并推导和讨论了有限 4D 体积中的欧几里得方程。在欧几里德 4D 盒子中，导致量化动量的周期性边界条件将连续均匀 FBS 方程转变为离散形式，其解确定运行在散射阈值之上的光谱。针对最大同位旋态的三π介子求解了一组截断的离散FBS方程，其散射长度、π介子质量和4D体积来自最近的晶格QCD计算，基态质量的近似FBS方程的结果与晶格结果定性一致。还提出了基态质量对 π-π 散射长度、π 介子质量和 4D 体积的近似依赖性。
The formulation of the Minkowskian and Euclidean homogeneous Faddeev-Bethe-Salpeter (FBS) equations for a three-boson system with a contact interaction in an infinite four-dimensional (4D) volume are reviewed, and the Euclidean one in a finite 4D volume is derived and discussed. In an Euclidean 4D box the periodic boundary conditions leading to quantized momentum turns the continuum homogeneous FBS equation into a discretized form, with solutions determining the spectrum running above the scattering threshold. A truncated set of the discretized FBS equation is solved for three-pions in the maximum isospin state, with scattering length, pion mass and 4D volume from recent lattice QCD calculations, and the results of the approximate FBS equation for the ground state mass are in qualitative agreement with the lattice result. The approximate dependence of the ground state mass on the pion-pion scattering length, pion mass and 4D volume is also suggested.