发表机构
PRISMA ++ Cluster of Excellence & Mainz Institute for Theoretical Physics, FB 08 - Physics, Mathematics and Computer Science, Johannes Gutenberg-Universität Mainz; Theoretical Particle Physics Laboratory (LPTP), Institute of Physics, EPFL（美因茨约翰内斯·古腾堡大学 PRISMA++ 卓越集群与理论物理研究所; 洛桑联邦理工学院 EPFL 物理学院理论粒子物理实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过双通道模型证明弱跃迁可导致非微扰辐射俘获，并围绕有限动量曲面构建EFT，恢复幺正性并提供系统展开。
AI 中文摘要
非相对论系统中的辐射俘获即使在其底层跃迁相互作用较弱时也可能变得非微扰。我们通过一个具有系统功率计数的简单量子力学双通道模型展示了这一机制，其中散射态与束缚态之间的强混合在有限动量$k_0$附近的窄区域内发展，导致幺正性的微扰破坏。在该区域中，增强的贡献可因子化，将动力学简化为通过强局域耦合相互作用的自由散射态。在因子化标度的RG演化下，该局域相互作用趋近于一个幺正不动点，类似于具有异常大散射长度的系统。这激发了一个围绕有限动量曲面$|\mathbf{k}|=k_0$组织的EFT，描述了具有线性色散关系的幺正性费米子。由EFT产生的重求和恢复了幺正性，并为弹性散射和辐射俘获提供了系统展开。
英文摘要
Radiative capture in a non-relativistic system can become non-perturbative even when the underlying transition interaction is weak. We demonstrate this mechanism in a simple quantum-mechanical two-channel model with a systematic power counting, where strong mixing between scattering and bound states develops in a narrow region around a finite momentum $k_0$, leading to a perturbative violation of unitarity. In this regime, the enhanced contributions factorize, reducing the dynamics to a free scattering state interacting through a strong local coupling. Under RG evolution in the factorization scale, this local interaction approaches a unitary fixed point, analogous to that of systems with an anomalously large scattering length. This motivates an EFT organized around the finite-momentum surface $|\mathbf{k}|=k_0$, describing fermions at unitarity with a linear dispersion relation. The resummation resulting from the EFT restores unitarity and provides a systematic expansion for both elastic scattering and radiative capture.
Comments56 pages, 5 figures
