由有限体积确定矩阵元和共振宽度：危险μ项
Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms
摘要：
确定局部算子的矩阵元素和共振宽度的标准数值方法使用能级和矩阵元素的有限体积依赖性。在有效场论中，有限尺寸修正在体积中呈指数衰减，通常被忽略或用微扰展开法加以考虑。使用二维sine-Gordon场论作为“玩具模型”，它表明，一些指数有限尺寸效应可能比以前认为的要大得多，潜在地破坏了框架，如格点量子色动力学的矩阵元素的确定。这里考虑的有限尺寸修正的特定类是由散射振幅中的束缚态极点产生的μ项。在sine-Gordon模型中，这些可以被明确地评估和显示，以解释观察到的差异，以高精度。有人认为，观察到的效果是不是特别的二维设置，而是依赖于一般的场论特征，是常见的粒子物理学相关的模型。重要的是要理解这些有限尺寸的校正，因为它们为矩阵元素和谐振宽度的确定提供了潜在的危险的系统误差源。
英文摘要：
The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume are usually neglected or taken into account using perturbation expansion in effective field theory. Using two-dimensional sine-Gordon field theory as "toy model" it is shown that some exponential finite size effects could be much larger than previously thought, potentially spoiling the determination of matrix elements in frameworks such as lattice QCD. The particular class of finite size corrections considered here are mu-terms arising from bound state poles in the scattering amplitudes. In sine-Gordon model, these can be explicitly evaluated and shown to explain the observed discrepancies to high precision. It is argued that the effects observed are not special to the two-dimensional setting, but rather depend on general field theoretic features that are common with models relevant for particle physics. It is important to understand these finite size corrections as they present a potentially dangerous source of systematic errors for the determination of matrix elements and resonance widths.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
