Frixione Stefano, Webber Bryan R
INFN, Sezione di Genova, Via Dodecaneso 33, I-16146 Genoa, Italy.
PH Department, TH Division, CERN, CH-1211 Geneva 23, Switzerland.
J High Energy Phys. 2021;2021(11):45. doi: 10.1007/JHEP11(2021)045. Epub 2021 Nov 8.
We discuss how colour flows can be used to simplify the computation of matrix elements, and in the context of parton shower Monte Carlos with accuracy beyond leading-colour. We show that, by systematically employing them, the results for tree-level matrix elements and their soft limits can be given in a closed form that does not require any colour algebra. The colour flows that we define are a natural generalization of those exploited by existing Monte Carlos; we construct their representations in terms of different but conceptually equivalent quantities, namely colour loops and dipole graphs, and examine how these objects may help to extend the accuracy of Monte Carlos through the inclusion of subleading-colour effects. We show how the results that we obtain can be used, with trivial modifications, in the context of QCD+QED simulations, since we are able to put the gluon and photon soft-radiation patterns on the same footing. We also comment on some peculiar properties of gluon-only colour flows, and their relationships with established results in the mathematics of permutations.
我们讨论了如何利用色流来简化矩阵元的计算，以及在部分子淋浴蒙特卡罗方法的背景下，如何达到超越领头色精度的情况。我们表明，通过系统地运用色流，树图级矩阵元及其软极限的结果可以以封闭形式给出，而无需任何色代数运算。我们定义的色流是现有蒙特卡罗方法所利用色流的自然推广；我们根据不同但概念上等效的量，即色圈和偶极图，构建它们的表示形式，并研究这些对象如何通过纳入次领头色效应来帮助扩展蒙特卡罗方法的精度。我们展示了我们所获得的结果如何在进行微不足道的修改后，应用于QCD+QED模拟的背景中，因为我们能够将胶子和光子的软辐射模式置于相同的基础上。我们还评论了仅胶子色流的一些特殊性质，以及它们与排列数学中既定结果的关系。
