精确检验标准模型要求人们在尽可能高的精度上给出有关物理量的理论预言，并为实验上直接发现标准模型之外的新物理提供理论指导。采用维数正规化技术和相应的重整化方案，目前人们可以准确地得到单圈阶近似下有关物理量的辐射修正。由于缺乏计算多重Feynman参数积分的数学手段，即使只限在标准模型框架内目前人们也还不能准确地预言双圈乃至更高阶近似下所有相关物理量的辐射修正。本项目中，我们计划利用Mellin变换，将多重Feynman参数积分转化为依赖于多个复变量线性叠加的Barnes形式的多重路径积分。根据被积函数的解析性以及积分路径的拓扑性质，我们将多维复空间中的路径积分转换为相应函数在以相应路径作为骨架的超曲面上的面积分，进而应用多变量复变函数论中的留数定理得到多重Feynman参数积分的解析表达式。

The precise test of the standard model indicates that we should derive the theoretical evaluations on the physics parameters as far as possible high precision, then provides the direction to search the new physics beyond the standard model experimentally. Adopting the dimensional regularization and concrete renormalization scheme, we can obtain the radiative corrections to physics parameters at 1-loop level so far. Lacking the techniques to calculate the multiple integral of Feynman parameters, one cannot get the radiative corrections to physics parameters exactly at 2-loop or more higher order yet. Applying the Mellin transformation, we change the multiple integrals on Feynman parameters into iterated Barnes integrals. According the analytical property of integrand and the topological property of integration path, we transform iterated complex line integrals into corresponding integrals on hypersurface which skeleton is the integration path in multidimensional complex space, then derive the analytical expressions of the multiple integrals on Feynman parameters through the Residue theorem of multidimensional complex analysis.