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.

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。

项目成果

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。

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。”

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）。

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

J.Fujimoto，K.Kato：“标准模型中辐射校正的自动计算。”

加藤潔 他: "ファインマン振幅の自動計算" 日本物理学会誌. (発表予定).

Kiyoshi Kato 等：“费曼振幅的自动计算”，日本物理学会杂志（待出版）。