Systematic Study of Super Symmertric models.

我们正在研制一个费曼振幅宽限自动计算系统。在这项研究中，我们已经扩展了这个系统的马约拉纳粒子和顶点，费米子数不守恒。GRACE系统通过一个描述MSSM费曼规则的文件，实现了从费曼图的生成到散射截面的计算和模拟事例的生成的全过程自动化，并将该系统扩展到标准模型和MSSM的单圈过程。对于标准模型，我们可以在非线性规范下进行计算，用数值方法证实所得结果的规范不变性。在MSSM中，我们有86个粒子，3803个树顶点和计数器项。我们以机器可读的形式将它们写下来，并且我们已经检查了具有6个外部粒子的所有可能过程的规范不变性，以确认输入的费曼规则的正确性。这个过程需要大量的人力和计算机资源。用手工引入如此复杂的模型并不是一件容易的事，因此有必要引入一个从任意拉格朗日量导出Feynnan规则的系统，我们已经开始开发专用的符号处理系统。由于拉格朗日函数包括各种各样的数学对象，我们正在开发它作为一种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，控制结构的功能，子程序和复合数据结构，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，我们可以用这个系统自动导出量子电动力学的费曼规则。

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.