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

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.

该研究项目的目标是开发一个用于计算标准模型中辐射校正的自动化系统。 1993-1995年项目期间，取得了以下进展： 1．开发了一个数值计算库来计算一般质量和动量情况下的单环积分。重整化的反项也基于质量壳格式提出。 2．对于一些二对二相互作用的样本，例如 e^+e^-*HZ、e^+e^-*tt、gammagamma*tt，自动计算已完成，并通过以下方法验证其准确性：很少的检查过程。3。引入了一种额外的处理来修复伽马矩阵的排序，以便对于具有 gamma_5 的一类幅度来说，可能的歧义变得无害。这在 e^+e^-*W^+W^-.4 的计算中得到了明确证明。开发了一种数值方法来计算一般质量和动量的二环标量两点和三点函数。5．作为二环自动化的一个例子，μ的反常磁矩是用弱电理论的二环阶计算的。已有部分结果证明该方法的有效性。

项目成果

加藤,潔: "ファインマン振幅の自動計算" コンピュータと教育(情報処理学会). 29-2. 9-17 (1993)

加藤清：“费曼振幅的自动计算”计算机与教育（日本信息处理协会）29-2（1993）。

K.Kato: "Hadronic jet physics." Proceedings of the workshop 'Frontier in Particle Physics' edited by K.Igi. 54-64 (1993)

K.Kato：“强子射流物理学。”

J.Fujimoto, K.Kato: "Automatic computation of radiative corrections in the standard" Radiative Corrections Status and Outlook, edited by B.F.L.Ward, World Scientific. 100-108 (1995)

J.Fujimoto、K.Kato：“标准中辐射校正的自动计算”辐射校正状态和展望，由 B.F.L.Ward 编辑，世界科学。

T. Kanako, N. Nakazawa: "Automatic calculation of 2-loop weak corrections to muon anomalous magnetic moment." Proceedings of AI'96.(1996)

T. Kanako、N. Nakazawa：“自动计算 μ 子反常磁矩的 2 环弱校正。”

K.Kato: "Automatic computation of Feynman amplitudes. (in Japanese)" Computer and Education. 29-2. 9-17 (1993)

K.Kato：“费曼振幅的自动计算。（日语）”计算机与教育。