Automatic calculation of Feynman amplitudes

自动计算费曼振幅

• 批准号: 05640357
• 负责人: KATO Kiyoshi
• 金额: $ 1.09万
• 依托单位: Kogakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05640357/
• 关键词: Standard model; Expert system; Feynman amplitudes; Radiative correction; e^+e^- collision; Higgs particle; 物理でのエキスパートシステム; ファインマン振幅自動計算; Standard model; Expert system; Feynman amplitudes; Radiative correction; e^+e^- collision; Higgs particle; 物理でのエキスパートシステム; ファインマン振幅自動計算

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.

该研究项目的目的是开发一个自动化系统，以计算标准模型中的辐射校正。在1993 - 1995年的项目期间，取得了以下进展。1。开发了用于计算数值计算的库，以计算一般质量和动量的情况下的一环积分。还基于质量壳方案制备了重新归一化的计数器术语2。对于两到两个相互作用的样本，例如E^+E^ - *Hz，E^+E^ - *tt，gammagamma*tt，进行了自动计算，并且可以通过一些检查过程进行验证。3。引入了一种额外的处理来修复伽马矩阵的排序，因此对于使用γ_5的一类振幅，可能的歧义变得无害。在E^+E^ - *W^+W^ - 。4的计算中明确证明了这一点。开发了一种数值方法来计算一般质量和Momenta.5的两环标量函数。5。作为双回路自动化的一个例子，MU的异常磁矩以电渗透理论的两环顺序计算。结果的一部分已经可以证明该方法的有效性。