论文标题
任意维度的二阶后跨散射
Second-order Post-Minkowskian scattering in arbitrary dimensions
论文作者
论文摘要
我们从两到两个弹性散射幅度的两个标量颗粒之间提取远距离重力势，该质量是在第二个弹性散射幅度以任意维度的第二个弹性散射幅度。与四维情况相反，在较高的维度中，经典潜力从盒子拓扑中获得了贡献。此外，动量和经典轨迹上的位置之间的运动学关系包含一个新术语，在树级振幅中是二次的。这种新关系与散射角度的公式之间的精确相互作用可确保在散射幅度的经典部分中仍然是线性的，与此顺序相匹配，与Eikonal方法中的早期计算匹配。我们指出的是，二连核心的二核心和现实都可以看作是单位性的结果。我们最终提出了由尺寸为四到十的尺寸的散射角度的闭合表达式。
We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.
