Numerical Approach to One-Loop Integrals
Numerical Approach to One-Loop Integrals
复制标题
单环积分的数值方法
DOI：
10.1143/ptp/87.5.1233
复制
发表时间：
1992
影响因子：
--
通讯作者：
Y. Oyanagi
中科院分区：
文献类型：
--
作者：
J. Fujimoto;Y. Shimizu;K. Katō;Y. Oyanagi
提出了计算单环标量积分的两种数值方法。在第一种方法中，通过被积函数的对称化来消除奇异性，并采用蒙特卡罗方法进行积分。在第二种方法中，将被积函数转化为标准形式后，将积分化简为规则的数值积分。这些方法为我们提供了实用的工具来计算具有理想数值精度的单回路费曼图。将其推广到带分子积分，并给出了对截面进行单回路虚校正的处理方法
Two numerical methods are proposed for the calculation of one-loop scalar integrals. In the first method, the singularity is cancelled by the symmetrization of the integrand and the integration is done by a Monte-Carlo method. In the second one, after the transform of the integrand into a standard form, the integral is reduced into a regular numerical integral. These methods provide us practical tools to evaluate one-loop Feynman diagrams with desired numerical accuracy. They are extended to the integral with numerator and the treatment of the one-loop virtual correction to the cross section is also presented