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

基于 Bernstein-Tkachov 技术的电弱二环费曼图的半解析评估

• 批准号: 5416754
• 负责人: Professor Dr. Bernd A. Kniehl
• 金额: --
• 依托单位: II. Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2004
• 资助国家: 德国
• 起止时间: 2003-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5416754?language=en
• 关键词: Semi; analytical; evaluation; electroweak; two

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.

LEP、SLAC 和 FNAL 的实验达到了令人印象深刻的精度，以及下一代对撞机（例如 CERN 的 LHC 和 DESY 的 TESLA）要达到的更高的精度，需要基于标准模型中量子校正的研究对电弱可观测量进行非常精确的理论预测。这种需求尤其迫切，因为检测与当前理论范式预测的偏差很可能构成标准模型之外的新物理学存在的实验证明。在此框架中，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可观测量的输入参数； 2）电弱辐射修正理论误差的控制。上述两个目标都需要对多回路和多腿费曼图进行评估；从技术角度来看，这种计算特别复杂，因为每个图表中都涉及大量不同的质量尺度。最近，基于 Bernstein-Tkachov 定理的一种新的半数值技术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该技术并将其应用扩展到新类别的图表。最终目标是计算相关的电弱可观测量，例如规范玻色子的极质量和弱有效混合角，同时考虑全套二环电弱校正。这种精度是下一代对撞机将要达到的实验精度所需要的。