Automatic calculation of Feynman amplitudes

本研究计画的目标是发展一个自动化的系统来计算标准模式中的辐射修正。在1993-1995年的项目期内，取得了以下进展。开发了一个数值计算库，用于计算一般质量和动量情况下的单圈积分。重整化的反项也是基于质量壳方案准备的。对于一些二对二相互作用的例子，例如，e^+e^-*HZ，e^+e^-*tt，γ *tt，进行了自动计算，并通过几次校验过程验证了其准确性.一个额外的处理，以固定的伽玛矩阵的顺序，使可能的模糊性变得无害的一类振幅与gamma_5。这在计算e^+e^-*W^+W^-.4时得到了明确的证明。发展了计算一般质量和动量的双圈标量二点和三点函数的数值方法.作为双回线自动化的一个例子，用弱电理论的双回线顺序计算了μ的反常磁矩。已有部分结果证明了该方法的有效性。

The goal of this research project is to develop an automated system for the calculation of radiative corrections in the standard model. In the term of project, 1993-1995, the following progress is achieved.1. A library for the numerical computation is developed to calculate one-loop integrals for the case of general masses and momenta. The counter terms for the renormalization are also prepared based on the on-mass-shell scheme.2. For a few sample of two-to-two interactions, e.g., e^+e^-*HZ, e^+e^-*tt, gammagamma*tt, the automatic computation is done and it is verified to be exact through a few checking processes.3. An extra treatment to fix the ordering of gamma matrices is introduced, so that the possible ambiguity becomes harmless for a class of amplitudes with gamma_5. This is explicitly demonstrated in the calculation of e^+e^-*W^+W^-.4. A numerical method is developed to calculate the two-loop scalar two- and three-point functions for the general masses and momenta.5. As an example of automation in two-loop, the anomalous magnetic moment of mu is calculated in two-loop order of electro-weak theory. A part of result is already available to prove the validity of the method.