AI 中文总结
该研究针对LHC及未来对撞机高精度计算需求，在OpenLoops框架下提出双圈张量积分约化的递归算法，实现相关数值工具并完成算法验证，为开发次领头阶散射振幅计算自动化工具提供核心支持。
AI 中文摘要
为充分发挥大型强子对撞机（LHC）及未来对撞机的全部潜力，大量可观测量的高精度计算至关重要。因此，用于微扰散射振幅次领头阶（NNLO）计算的自动化工具是高度理想的目标。迄今为止，我们已在OpenLoops框架中开发了此类工具的若干核心组件。在我们的方法中，将散射振幅的计算拆分为三个部分：圈动量张量积分、对应的过程相关张量系数，以及被积函数的(D-4)维部分与积分发散项的相互作用。在本文献中，我们提出一种新的递归算法，用于将任意双圈张量积分约化为标量积分，该算法已被实现为高效数值工具。我们还实现了后续约化至主积分的首个版本，可对该算法进行完整验证。我们给出首个成功的验证计算，并讨论其对外部计算的主积分精度的依赖性。
英文摘要
In order to exploit the full potential of the LHC and future colliders, high-precision calculations of a very wide range of observables are crucial. Automated tools for next-to-next-to-leading order calculations of perturbative scattering amplitudes are therefore a highly desirable goal. So far, we have developed several major ingredients of such a tool in the OpenLoops framework. In our approach we split the calculation of scattering amplitudes into three components: loop momentum tensor integrals, the corresponding process-dependent tensor coefficients, and the interplay of $(D-4)$-dimensional parts of the integrand with divergences of the integrals. In these proceedings, we present a new recursive algorithm to reduce arbitrary two-loop tensor integrals to scalar integrals, which has been implemented into an efficient numerical tool. We also implemented a first version of the subsequent reduction to master integrals, which allows for a full validation of the algorithm. We present a first successful validation computation and discuss its dependence on the precision of the externally computed master integrals.
Comments10 pages, 2 figures, 1 table; contribution to the proceedings of the Loops and Legs in Quantum Field Theory conference (LL2026), April 12-17, 2026, Bayreuth, Germany
