论文标题
一致性检查两体有限体积矩阵元素：ii。扰动系统
Consistency checks for two-body finite-volume matrix elements: II. Perturbative systems
论文作者
论文摘要
使用参考文献中提出的一般形式主义。 [1,2]，我们研究了$ \ mathbf {2}+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ m athbf {2} $矩阵元素的有限体积效应，该效应与扰动相互作用相同的两个固定量表状态。在有限的立方卷中，我们通过$ \ Mathcal O（1/l^5）$得出了矩阵元素的$ 1/L $扩展，并发现它由两个通用电流依赖性参数，标量电荷和阈值两粒子形式。我们通过对一般形式主义的数值研究以及通过独立的扰动计算来确认结果。我们进一步证明了与Feynman-Hellmann定理的一致性，该定理可用于将$ 1/L $扩展的地面能量和基质元素的扩展相关联。后者可以简单了解为什么对矩阵元素的领先卷更正与能量中的缩放量相同，$ 1/l^3 $与早期的工作相矛盾，后者发现$ 1/l^2 $对矩阵元素的贡献。我们在这里表明，在扰动计算中中间阶段出现了这样的术语，但在最终结果中取消。
Using the general formalism presented in Refs. [1,2], we study the finite-volume effects for the $\mathbf{2}+\mathcal{J}\to\mathbf{2}$ matrix element of an external current coupled to a two-particle state of identical scalars with perturbative interactions. Working in a finite cubic volume with periodicity $L$, we derive a $1/L$ expansion of the matrix element through $\mathcal O(1/L^5)$ and find that it is governed by two universal current-dependent parameters, the scalar charge and the threshold two-particle form factor. We confirm the result through a numerical study of the general formalism and additionally through an independent perturbative calculation. We further demonstrate a consistency with the Feynman-Hellmann theorem, which can be used to relate the $1/L$ expansions of the ground-state energy and matrix element. The latter gives a simple insight into why the leading volume corrections to the matrix element have the same scaling as those in the energy, $1/L^3$, in contradiction to earlier work, which found a $1/L^2$ contribution to the matrix element. We show here that such a term arises at intermediate stages in the perturbative calculation, but cancels in the final result.
