引力拉曼散射：一般相对论中潮汐效应的系统工具包
Gravitational Raman Scattering: a Systematic Toolkit for Tidal Effects in General Relativity
AI总结：
本文提出了一种系统计算引力拉曼散射的框架，用于研究一般相对论中的潮汐效应，通过有效场论和散射幅技术推导了不同自旋场的Love数，并揭示了动态Love数的对数运行特性。
摘要：
我们提出了一种框架，用于系统计算引力拉曼散射的散射幅，即质量less场在紧凑相对论物体上的非弹性散射。我们专注于小频率（后闵可夫斯基，PM）区域，这在研究潮汐效应时是相关的，可以映射到并合阶段的引力波可观测变量上。我们证明这种设置非常适合系统研究潮汐效应，且不受坐标、规范和场重新定义的歧义影响。我们结合世界线有效场论、背景场方法和先进的散射幅技术，推导出在第三PM阶上，旋0、1、2场在通用紧凑物体上的相位移。我们证明了物体的反冲的包含对于此计算的一致性至关重要。聚焦于黑洞的特定情况，我们通过匹配我们的EFT幅和广义相对论中的计算，提取出旋0场的主导静态和动态Love数，以及旋1场的静态Love数。我们证明，在完全本征上，主导静态Love数恒为零，而动态Love数不为零且呈对数运行。后者解决了之前偏本征匹配计算的歧义。我们还扩展了结果到七维，其中旋2Love数在2PM下经历重整化群运行，我们明确计算了它。此外，我们提取了五维中旋0和旋1场的主导静态Love数，它们也呈运行。
英文摘要：
We present a framework for systematic computations of scattering amplitudes for gravitational Raman scattering, -- the inelastic scattering of massless fields off compact relativistic objects. We focus on the small-frequency (post-Minkowskian, PM) regime relevant for the study of tidal effects, which can be mapped onto gravitational wave observables during the inspiraling phase of a merger. We demonstrate that this setup is ideal for systematic studies of tidal effects, in a way that is free from coordinate, gauge, and field redefinition ambiguities. We use a combination of worldline effective field theory, the background field method, and advanced scattering amplitude techniques to derive phase shifts for scattering of spin-$0,1,2$ fields off generic compact objects at third PM order. We demonstrate that the inclusion of the recoil of the object is crucial for consistency of this calculation. Focusing on a particular case of black holes, we extract the leading static and dynamical Love numbers of the spin-0 field and the static Love number of the spin-1 field in four dimensions by matching our EFT amplitudes and calculations in General Relativity. We show, fully on-shell, that the leading static Love numbers vanish identically, while the dynamical Love numbers are not zero and run logarithmically. The latter resolves the ambiguities of previous off-shell matching calculations. We also extend our results to seven dimensions, where spin-2 Love numbers undergo a renormalization group running at 2PM, which we compute explicitly. In addition, we extract the leading static Love numbers of spin-0 and spin-1 fields in five dimensions, which also run.
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