从散射振幅看两圈阶的光线偏折
Light bending at two-loop order from scattering amplitudes
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中文总结 AI 辅助
本文用散射振幅方法在第三后闵可夫斯基阶计算光子受黑洞的保守偏折，通过五点树图振幅与割积分得到两圈对数项，进而导出三阶偏折角，与史瓦西测地线弱偏折展开一致。
中文摘要 AI 辅助
我们利用散射振幅方法，在第三后闵可夫斯基阶计算了光子被大质量无自旋源（如黑洞）的保守偏折。我们工作在重源和长程极限下，并采用几何光学近似。所需的光子-引力子五点树图振幅通过壳上递推构造，并在五重割上缝合到三个标量-引力子顶点。多项式除法将割信息组织成十六项贡献，包括具有较少传播子的留数。我们执行源能量积分，并在剩余的空间积分中保留近壳光子区域。在静态区域中，所有交换动量均为软动量，我们将光子极点处方与从保守核中减去三次树图迭代联系起来。十六项贡献之和确定了经典的两圈对数项。其横向傅里叶变换给出相互作用径向作用量，并产生三阶偏折角。结果与史瓦西零测地线的弱偏折展开一致，并展示了非线性经典光线偏折如何编码在平直时空周围的圈振幅中。
英文摘要
We calculate the conservative deflection of a photon by a massive spinless source, such as a black hole, at third post-Minkowskian order using scattering amplitudes. We work in the heavy-source and long-range limits and adopt the geometric-optics approximation. The required five-point photon-graviton tree amplitude is constructed by on-shell recursion and sewn to three scalar-graviton vertices across a five-fold cut. Polynomial division organizes the cut information into sixteen contributions, including the residues with fewer propagators. We perform the source energy integrations and retain the near-on-shell photon regions in the remaining spatial integrals. Within the static region in which all exchanged momenta are soft, we relate a photon pole prescription to the subtraction of the cubic tree iteration from the conservative kernel. The sum of the sixteen contributions determines the classical logarithmic term at two loops. Its transverse Fourier transform gives the interaction radial action and yields the third-order deflection angle. The result agrees with the weak-deflection expansion of Schwarzschild null geodesics and demonstrates how nonlinear classical light bending is encoded in loop amplitudes around flat spacetime.
发表机构
- Sun Yat-sen University (Zhuhai Campus)（中山大学（珠海校区））
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