A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec

The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable amount of time. For many multi-loop integrals, the fraction of time required to perform the numerical integration is significant and it is therefore beneficial to have efficient and well-implemented numerical integration methods. With this goal in mind, we present a new stand-alone integrator based on the use of (quasi-Monte Carlo) rank-1 shifted lattice rules. For integrals with high variance we also implement a variance reduction algorithm based on fitting a smooth function to the inverse cumulative distribution function of the integrand dimension-by-dimension. Additionally, the new integrator is interfaced to pySecDec to allow the straightforward evaluation of multi-loop integrals and dimensionally regulated parameter integrals. In order to make use of recent advances in parallel computing hardware, our integrator can be used both on CPUs and CUDA compatible GPUs where available.

多圈积分与散射振幅的纯数值评估，可作为解析方法的可行替代方案，尤其在存在多个质量标度的场景下——前提是能够在可接受的时间开销内达成足够的精度。对于多数多圈积分而言，数值积分所需的耗时占比往往较高，因此采用高效且实现完备的数值积分方法将颇具裨益。基于此目标，我们提出了一款全新的独立积分器，其核心基于准蒙特卡洛（quasi-Monte Carlo）秩1移位格点规则。针对高方差积分场景，我们还实现了一款方差缩减算法，该算法通过逐维度对被积函数的逆累积分布函数进行平滑函数拟合。此外，该新型积分器已与pySecDec实现对接，可直接完成多圈积分与维度正则化参数积分的评估。为充分利用并行计算硬件的最新技术进展，本积分器支持在中央处理器（CPU）以及兼容CUDA的图形处理器（GPU，若可用）上运行。