Numerical higher-order calculations

这项更新建议的目标是进一步发展精确粒子物理中高阶计算的数值方法。与其他方法相比，数值方法对末态粒子的数量具有很好的标度特性，因此非常适合于涉及大量末态粒子的精确计算。这个方案的具体目标是：(I)发展一种方法，在所有运动构型的环动量积分中产生小的蒙特卡罗积分误差；(Ii)将形式推广到NNOL。点(I)是目前的瓶颈，对于NLO和NNOL的数值方法必须有满意的解决方案。通过本方案的研究计划，我们有信心获得满意的解决方案。

The goal of this renewal proposal is the further development of the numerical approach to higher-order calculations in precision particle physics. Compared to other approaches the numerical approach offers a very good scaling behaviour with the number of final-state particles and is therefore well suited for precision calculations involving a large number of final-state particles. Masses are easily incorporated within the numerical approach.The concrete goals of this proposal are (i) the development of a method, which leads to small Monte Carlo integration errors for the integration over the loop momentum in all kinematical configurations and(ii) the extension of the formalism to NNLO.Point (i) is the current bottleneck and a satisfactory solution will be mandatory for the numerical approach at NLO and NNLO.With the research programme of this proposal we are confident to achieve a satisfactory solution.