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

LEP、SLAC和FNAL的实验达到了令人印象深刻的精确度，下一代对撞机（如CERN的LHC和DESY的TESLA）也将达到更高的精确度，这就要求在标准模型量子修正研究的基础上，对电弱可观测量进行非常精确的理论预测。这一需求特别迫切，因为对当前理论范式预测的偏差的检测很可能构成标准模型之外新物理学存在的实验证明。在这个框架中，两个不同的方面承担了特别的相关性：1）精确确定的输入参数的计算的电弱可观测量; 2）控制的理论误差的电弱辐射校正。上述两个目标都需要评估多回路和多腿费曼图;从技术角度来看，这种计算特别复杂，因为每个图中涉及大量不同的质量尺度。最近，一种新的半数值技术，基于伯恩斯坦-Tkachov定理，已被提出并应用于特定的费曼图集。本研究项目的目的是进一步研究和扩展这种技术的应用，以新的图表类。最终的目标是计算相关的电弱观测量，如规范玻色子的极质量和弱有效混合角，考虑到全套的双回路电弱修正。这种精度是下一代对撞机将要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.