发表机构
Lund University; University of Bern（隆德大学; 伯尔尼大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文比较直接收缩、多重态基和对称群FFT三种颜色求和方法，FFT在六至十一个胶子时最快，显著降低计算时间。
AI 中文摘要
我们比较了三种计算树级全胶子平方矩阵元颜色求和的方法：在迹分解和伴随分解中使用直接收缩的评估、正交归一多重态基，以及基于对称群不可约表示的快速傅里叶变换（FFT）用于迹分解和伴随分解。多重态方法将颜色求和简化为绝对平方之和，并利用由SU(3)表示标记的振幅递推。FFT利用颜色重叠的相对置换依赖性，用更小的独立收缩替代直接双重求和，使用标准的颜色有序部分振幅。这在胶子标签层面引入了对称群，因此最大限度地利用了置换对称性。我们比较了四到十一个胶子的CPU时间和内存使用。在十一个胶子时，直接伴随收缩在初始化后估计用1.7×10^3秒评估一个固定螺旋度颜色求和矩阵元，而多重态递推为19.8秒，FFT伴随方法为0.814秒。伴随FFT在六到十一个胶子范围内最快，尽管其阶乘标度相比多重态递推的指数标度。
英文摘要
We compare three approaches for computing color-summed tree-level all-gluon squared matrix elements: evaluation using direct contraction in the trace and adjoint decompositions, orthonormal multiplet bases, and fast Fourier transforms (FFT) based on the irreducible representations of the symmetric group for the trace and adjoint decompositions. The multiplet method reduces the color sum to a sum of absolute squares and utilizes an amplitude recursion labeled by SU(3) representations. The FFT exploits the relative-permutation dependence of color overlaps to replace the direct double sum with smaller independent contractions, using standard color-ordered partial amplitudes. This invokes the symmetric group at the level of gluon labels, and therefore makes maximal use of the permutation symmetry. We compare CPU time and memory use for four through eleven gluons. At eleven gluons, the direct adjoint contraction evaluates a fixed-helicity color-summed matrix element in an estimated 1.7 10${}^3$ s after initialization, compared with 19.8 s for the multiplet recursion and 0.814 s for the FFT adjoint method. The adjoint FFT is fastest from six through eleven gluons, despite its factorial scaling compared with the exponential scaling of the multiplet recursion.
Comments6 pages, 1 figure
