AI 中文总结
本研究针对长程力理论中前向散射振幅积分导致的幺正性界限歧义问题，提出结合修正分布结构与畸变波微扰理论（DWPT）的方法，在无红外尺度下推导界限，并证明其快速收敛至精确结果，且每阶重求和无穷多费曼图。
AI 中文摘要
在长程力理论中，对散射振幅沿前向方向积分，以及由此类积分提取的幺正性约束，可能显得具有歧义性。用于约束有效场论（EFT）耦合常数的标准技术通常会产生依赖于任意红外尺度的界限。我们研究了一个非相对论模型，在该模型中标准技术产生此类歧义性界限，但该模型足够简单，使得精确界限也可以通过非微扰方法推导出来，并证明其不涉及红外尺度。然后我们展示了如何以微扰方式推导界限，且在任一阶段均不引入红外尺度。这需要两个要素：考虑长程振幅的修正分布结构，以及使用畸变波微扰理论（DWPT），该理论精确处理库仑动力学。两者结合可得到具有良好定义的分波投影且无虚假红外发散的振幅。将该模型解释为具有紫外截断$\Lambda_{\rm EFT}$的EFT，我们推导出适用于任意紫外完备化的截断依赖界限。在每一阶取$\Lambda_{\rm EFT}\to\infty$，得到的界限迅速收敛到精确界限，在展开的第四阶达到$0.002\\%$的精度。最后，我们证明DWPT展开的每一阶都将短程微扰理论的无穷多个费曼图（这些图单独求值为多重多对数函数和完全椭圆积分）重求和为一个紧凑表达式。在我们计算的阶数中，甚至不需要积分，这表明DWPT可能比标准微扰理论提供更简单的散射振幅表示。
英文摘要
Integrating scattering amplitudes over the forward direction, and consequently the unitarity constraints one extracts from such integrals, can appear ambiguous in theories with long-range forces. Standard techniques for bounding EFT couplings then typically produce bounds that depend on an arbitrary infrared scale. We study a non-relativistic model in which the standard techniques produce such an ambiguous bound, but which is simple enough that the exact bound can also be derived non-perturbatively and shown to involve no infrared scale. We then show how to derive bounds perturbatively, with no infrared scale entering at any stage. This requires two ingredients: accounting for the modified distributional structure of long-range amplitudes, and using distorted-wave perturbation theory (DWPT), which treats the Coulomb dynamics exactly. Together they give amplitudes with well-defined partial-wave projections and no spurious infrared divergences. Interpreting the model as an EFT with an ultraviolet cutoff $Λ_{\rm EFT}$, we derive cutoff-dependent bounds valid for arbitrary UV completions. Taking $Λ_{\rm EFT}\to\infty$ at each order yields bounds that rapidly converge to the exact bound, reaching $0.002\%$ accuracy at fourth order in the expansion. Finally, we demonstrate that every order of the DWPT expansion resums infinitely many Feynman diagrams of short-range perturbation theory, which individually evaluate to multiple polylogarithms and complete elliptic integrals, into a compact expression. At the orders we compute, no integration is even required, suggesting that DWPT may offer a simpler representation of scattering amplitudes than standard perturbation theory.
Comments61 pages, 2 figures, 2 tables
