微扰论中任意阶的引力康普顿振幅
Gravitational Compton Amplitude to All Orders in Perturbation Theory
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中文总结 AI 辅助
该研究在世界线有效场论框架下，求解含潮汐爱数边界条件的分波有效波方程，通过分波求和得到任意阶引力康普顿振幅，复现O(G⁴)结果并预测O(G⁷)新结果，发现O(G⁷)阶紫外发散，匹配黑洞微扰论给出施瓦西黑洞爱数相关结论。
中文摘要 AI 辅助
我们展示了如何在世界线有效场论中高效计算引力波与致密天体散射产生的振幅，其计算精度可达到牛顿常数G的任意阶。我们的方法求解了分波振幅的有效波方程，其中威尔逊系数（潮汐爱数）通过短距离处的边界条件引入。随后我们对分波求和，以椭圆多重对数函数的形式得到动量空间的康普顿振幅。我们复现了至O(G⁴)阶的最新结果，并得到了至O(G⁷)阶的新预测，其中爱数首次在O(G⁵)阶贡献。我们在O(G⁷)阶发现了经典引力振幅中的首个紫外发散，表明纯点粒子描述在广义相对论中并不自洽。通过与黑洞微扰论匹配，我们证明静态爱数在壳上为零，并预测了亚领头阶非零的施瓦西黑洞爱数。
英文摘要
We show how amplitudes from the scattering of gravitational waves off compact objects in worldline effective field theory can be efficiently computed to arbitrary order in Newton's constant $G$. Our approach solves an effective wave equation for the partial-wave amplitude in which Wilson coefficients (tidal Love numbers) enter through boundary conditions at short distances. We then perform the sum over partial waves to obtain the momentum-space Compton amplitude in terms of elliptic polylogarithms. We reproduce recent results through $\mathcal{O}(G^4)$ and obtain new predictions up to $\mathcal{O}(G^7)$, with Love numbers first contributing at $\mathcal{O}(G^5)$. We find the first ultraviolet divergence in a classical gravitational amplitude at $\mathcal{O}(G^7)$, showing that a pure point-particle description is not consistent in general relativity. Matching to black hole perturbation theory, we show that static Love numbers vanish on-shell and predict subleading non-zero Schwarzschild black hole Love numbers.
