We compute the two-loop helicity amplitudes for the scattering of five gluons, including all contributions beyond the leading-color approximation. The analytic expressions are represented as linear combinations of transcendental functions with rational coefficients, which we reconstruct from finite-field samples obtained with the numerical unitarity method. Guided by the requirement of removing unphysical singularities, we find a remarkably compact generating set of rational coefficients, which we display entirely in the manuscript. We implement our results in a public code, which provides efficient and reliable numerical evaluations for phenomenological applications.

中文翻译：

---

五部分子散射的双虚拟 NNLO QCD 校正。一、胶子通道

我们计算五个胶子散射的双环螺旋度振幅，包括主色近似之外的所有贡献。解析表达式表示为超越函数与有理系数的线性组合，我们根据数值幺正性方法获得的有限场样本对其进行重建。在消除非物理奇点的要求的指导下，我们发现了一个非常紧凑的有理系数生成集，我们将其完全显示在手稿中。我们在公共代码中实现我们的结果，为现象学应用提供高效可靠的数值评估。