论文标题
一种用于计算量子电动力学中轻顿磁矩的柔性消除方法
A Flexible Divergence Elimination Method for Calculating Lepton Magnetic Moments in Quantum Electrodynamics
论文作者
论文摘要
Lepton异常磁矩（AMM）的精确计算需要评估量子电动力学（QED）Feynman图，最多可达五个独立的环路。相应积分中紫外线（UV），红外（IR）和混合差异的复杂结构使得在合理的计算机时间范围内很难计算这些高阶贡献。 我们演示了一种方法，该方法可以在Feynman参数空间（集成之前）中消除所有分歧点，并具有可用于提高数值集成精度的灵活性。这种灵活性对于计算带有电子环对MUON AMM的Feynman图的贡献尤其是实际。提供了3循环和4循环数值测试结果。 减法程序基于一个森林公式，其线性算子应用于紫外线发散子图的Feynman振幅。它类似于BPHZ；区别在于使用的线性运算符和将它们组合在一起。在图表上求和之后，它等同于壳重新归一化：不需要残余重归于。
A precise calculation of the lepton anomalous magnetic moments (AMM) requires an evaluation of the quantum electrodynamics (QED) Feynman diagrams up to five independent loops. The complicated structure of ultraviolet (UV), infrared (IR) and mixed divergences in the corresponding integrals makes it difficult to calculate these high-order contributions in reasonable computer time frame. We demonstrate a method that eliminates all divergences point by point in Feynman parametric space (before integration) and possesses a flexibility that can be used for improving the precision of the numerical integration. This flexibility is especially actual for calculating the contributions of the Feynman diagrams with electron loops to the muon AMM. 3-loop and 4-loop numerical test results are provided. The subtraction procedure is based on a forest formula with linear operators applied to the Feynman amplitudes of UV divergent subdiagrams. It is similar to BPHZ; the difference is in the linear operators used and in the way of combining them. It is equivalent to the on-shell renormalization after summation over diagrams: no residual renormalization is required.
