AI 中文总结
本文在$\boldsymbol{\textit{N}=4}$ SYM理论框架下，采用有效场论方法，结合双、三雷吉子交换贡献，得到了MRK中八边形振幅的微扰结果，可扩展至多粒子情形。
AI 中文摘要
我们研究平面$\boldsymbol{\textit{N}=4}$超杨-米尔斯理论中曼德尔斯塔姆区域内多雷吉运动学（MRK）下的八点振幅，该振幅同时受到双雷吉子交换和三雷吉子交换的贡献。我们采用有效场论方法计算三雷吉子交换的领头阶贡献，并显式计算了相关的费曼图直至四圈精度。我们还针对该区域内双雷吉子交换的贡献提出了一种紧凑的傅里叶-梅林表示，该表示与其他曼德尔斯塔姆区域的相关成分相同，原则上可在微扰理论中计算至任意所需阶数。为验证该提议，我们证明可重现已知八边形结果的多雷吉极限，直至三圈精度。随后，我们结合双雷吉子交换和三雷吉子交换的贡献，得到了MRK中八边形的新结果：对于最大螺旋度违反（MHV）构型，精度为四圈的次领头对数精度；对于非MHV贡献，精度为三圈。我们还讨论了如何将结果扩展到更多粒子，并给出了任意腿数的三圈MHV振幅的三雷吉子交换贡献。
英文摘要
We study eight-point amplitudes in the planar $\mathcal{N}=4$ Super Yang-Mills theory in multi-Regge kinematics in the Mandelstam region that receives contributions from both two- and three-Reggeon exchange. We use an effective field theory approach to compute the leading contribution from three-Reggeon exchange, and we explicitly evaluate the relevant diagrams up to four loops. We also propose a compact Fourier-Mellin representation for the contribution from two-Reggeon exchange in this region which involves the same ingredients as in other Mandelstam regions and can in principle be evaluated to any desired order in perturbation theory. To validate our proposal, we show that we can reproduce the multi-Regge limit of the known results for octagons up to three loops. We then combine the contributions from two- and three-Reggeon exchange to obtain novel results for octagons in MRK up to next-to-leading-logarithmic accuracy at four loops for the maximally helicity violating (MHV) configuration, and up to three loops for non-MHV contributions. We also discuss how our result can be extended to more particles, and we present the contribution from three-Reggeon exchange for three-loop MHV amplitudes with an arbitrary number of legs.
Comments35 pages, 4 figures, 2 ancillary files
