论文标题
非等级标量的相对论三粒子量化条件
Relativistic three-particle quantization condition for nondegenerate scalars
论文作者
论文摘要
到目前为止，已经开发了相对或变性颗粒的相对论三粒子无限散射幅度与有限体积光谱的形式主义。我们对具有任意质量的三个非平衡标量颗粒的情况提供了概括。这种形式主义中的关键数量是量化条件，将频谱与中间K矩阵联系起来。我们得出了该量化条件的三个版本，每个版本都是相同颗粒的相应结果的自然概括。在每种情况下，我们还确定将中间K矩阵与三粒子散射幅度（$ \ Mathcal M_3 $）相关的积分方程。最实用的版本涉及单个Lorentz-Invariant Intermediate K Matrix，$ \ widetilde {\ Mathcal K} _ {\ rm df，3} $。其他版本涉及k矩阵的矩阵，其元素由选择的元素和最终粒子为观众而区别。我们的方法应允许对所有其他三粒子系统的相对论方法直接概括。
The formalism relating the relativistic three-particle infinite-volume scattering amplitude to the finite-volume spectrum has been developed thus far only for identical or degenerate particles. We provide the generalization to the case of three nondegenerate scalar particles with arbitrary masses. A key quantity in this formalism is the quantization condition, which relates the spectrum to an intermediate K matrix. We derive three versions of this quantization condition, each a natural generalization of the corresponding results for identical particles. In each case we also determine the integral equations relating the intermediate K matrix to the three-particle scattering amplitude, $\mathcal M_3$. The version that is likely to be most practical involves a single Lorentz-invariant intermediate K matrix, $\widetilde{\mathcal K}_{\rm df,3}$. The other versions involve a matrix of K matrices, with elements distinguished by the choice of which initial and final particles are the spectators. Our approach should allow a straightforward generalization of the relativistic approach to all other three-particle systems of interest.
