Semi-analytical evaluation of electroweak two-loop Feynman diagrams based on the Bernstein-Tkachov technique

LEP， SLAC和FNAL实验所达到的令人印象深刻的精度，以及下一代对撞机（如欧洲核子研究中心的LHC和DESY的特斯拉）所达到的更高精度，要求基于标准模型中量子修正的研究，对电弱观测进行非常精确的理论预测。这种需求尤其迫切，因为对当前理论范式预测偏差的检测很可能构成标准模型之外存在新物理学的实验证明。在这个框架中，两个不同的方面具有特殊的相关性：1)精确确定用于计算电弱观测值的输入参数；2)对电弱辐射修正理论误差的控制。这两个目标都需要对多环、多腿费曼图进行评价；从技术角度来看，这种计算特别复杂，因为每个图中都涉及大量不同的质量尺度。最近，基于Bernstein-Tkachov定理，提出了一种新的半数值技术，并将其应用于特定的Feynman图集。本研究项目的目的是进一步研究和扩展该技术在新类型图中的应用。最终目标是计算相关的电弱观测值，如规范玻色子的极质量和弱有效混合角，同时考虑全套双环电弱修正。这种精度是下一代对撞机将达到的实验精度所要求的。

The impressive precision reached by experiments at LEP, SLAC and FNAL, as well as the even greater accuracy to be attained in the next generation of colliders (such as LHC at CERN and possibly TESLA at DESY), demand very precise theoretical predictions of the electroweak observables, based on the study of quantum corrections in the Standard Model. This need is particularly acute, since the detection of deviations from the predictions of the current theoretical paradigm may well constitute an experimental proof of the existence of new physics beyond the Standard Model. In this framework, two different aspects assume a special relevance: 1) the precise determination of the input parameters for the calculation of the electroweak observables; 2) the control over the theoretical errors of the electroweak radiative corrections. Both of the above-mentioned goals require the evaluation of multi-loop and multi-leg Feynman diagrams; from the technical point of view, such calculations are particularly complex because of the presence of a large number of different mass scales that are involved in each diagram. Recently, a new semi-numerical technique, based on the Bernstein-Tkachov theorem, has been proposed and applied to specific sets of Feynman graphs. The purpose of the present research project is to further investigate and extend the applications of this technique to new classes of diagrams. The final goal is to calculate the relevant electroweak observables, such as the pole masses of the gauge bosons and the weak effective mixing angle, taking into account the full set of two-loop electroweak corrections. This kind of accuracy is required by the experimental precision that will be reached by the next generation of colliders.