Systematic Study of Super Symmertric models.

超对称模型的系统研究。

基本信息

批准号：
10640285
负责人：
KANEKO Toshiaki
金额：
$ 0.64万
依托单位：
Meiji Gakuin University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640285/
关键词：
automatic calculation Feynman amplitudes Super symmetry MSSM Feynman rules Non-linear gauge Computer algebra Lagrangian GRACE SUSY 自動計算数式処理摂動論

项目摘要

We have been developing an automatic calculating system of Feynman amplitudes grace. In this Study, we have extended this system for Majorana particles and vertices in which Fermion numbers do not conserve. With a file describing Feynman rules of MSSM, grace system automatizes the whole proeess from the generation of Feynman graphs to the calculation of scattering cross sections and the generation of simulated events.We have also extended the system for 1 loop processes in both standard model and MSSM. For standard model, calculation in non-linear gauge is available, with which one can numerically confirm the gauge invariance of the obtained results.In MSSM, we have 86 particles, 3803 tree vertices and counter terms. We wrote them down in a machine readable form and we have checked gauge invariance for all possible processes with 6 external particles in order to confirm the correctness of the input Feynman rules. This procedure requires a large amount of man power and computer resources. It is not easy task to introduce such a complicated models by hand and is necessary to introduce a system which derive Feymnan rules from arbitral Lagrangian.We have started to develop special purpose symbolic manipulating system. Since a Lagrangian includes wide varieties of mathematical objects, we are developing it as an interpreter of a newly designed computer programming language. It includes as usual computer programming language, functions of control structures, sub-program and composite data structures such as lists, arrays and records. It also manipulates rational numbers of arbitrary precision, mathematical symbols and symbolic mathematical operations. At this moment, we can derive Feynman rules automatically for QED with this system.

我们一直在开发费曼振幅恩典的自动计算系统。在这项研究中，我们将这个系统扩展到费米子数不守恒的马约拉纳粒子和顶点。 Grace系统通过描述MSSM的费曼规则的文件，自动化了从费曼图的生成到散射截面的计算和模拟事件的生成的整个过程。我们还在标准模型和模型中扩展了系统的1个循环过程。 MSSM。对于标准模型，可以进行非线性规范计算，可以在数值上确认所得结果的规范不变性。在MSSM中，我们有86个粒子、3803个树顶点和反项。我们以机器可读的形式将它们写下来，并用 6 个外部粒子检查了所有可能过程的规范不变性，以确认输入费曼规则的正确性。该过程需要大量的人力和计算机资源。手工引入如此复杂的模型并不是一件容易的事，有必要引入一个从仲裁拉格朗日推导出费姆南规则的系统。我们已经开始开发专用符号处理系统。由于拉格朗日函数包含各种各样的数学对象，因此我们正在将其开发为新设计的计算机编程语言的解释器。它包括通常的计算机编程语言、控制结构函数、子程序和复合数据结构，例如列表、数组和记录。它还可以处理任意精度的有理数、数学符号和符号数学运算。此时，我们可以利用该系统自动推导出QED的费曼规则。