论文标题
为三环四粒子散射构建D-log积分和计算主积分
Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
论文作者
论文摘要
我们计算了LHC上Di-Jet或Di-Photon产生的过程所需的无质量三环散射幅度的所有主积分。我们根据尺寸调节器中积分的劳伦（Laurent）扩展，最高为8 $^{\ text {th}} $功率，并以谐波polygarogariths表示的系数表示结果。作为主体积分的基础，我们选择与仅具有对数电线杆的积分 - 称为$ d $ log表单。这种选择大大通过微分方程方法来促进了随后的计算。我们详细介绍了如何通过最初由一位作者开发的改进算法获得此基础。我们提供了该算法的公开实施。我们解释了如何在单位性的背景下自然应用算法。此外，我们根据其软属性和共线属性对$ d $ log表单进行分类。
We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the dimensional regulator up to 8$^{\text{th}}$ power, with coefficients expressed in terms of harmonic polylogarithms. As a basis of master integrals we choose integrals with integrands that only have logarithmic poles - called $d$log forms. This choice greatly facilitates the subsequent computation via the method of differential equations. We detail how this basis is obtained via an improved algorithm originally developed by one of the authors. We provide a public implementation of this algorithm. We explain how the algorithm is naturally applied in the context of unitarity. In addition, we classify our $d$log forms according to their soft and collinear properties.
