ϵ-finite basis of master integrals for the integration-by-parts method
ϵ-finite basis of master integrals for the integration-by-parts method
复制标题
分部积分法主积分的 ϵ-有限基
DOI：
10.1016/j.nuclphysb.2006.02.030
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
M. Tentyukov
中科院分区：
文献类型：
--
作者：
K. Chetyrkin;M. Faisst;C. Sturm;M. Tentyukov
结果表明，对于每一个在维度正则化范围内的问题，利用分部积分法可以构造一组主积分，使得每个相应的系数函数在维数极限为4时是有限的。我们认为这种基的使用简化和稳定了主积分的数值计算。作为一个例子，我们明确地为所有类qed的四环大蝌蚪集合构造ϵ-finite基。利用基于pad<s:1>近似的半数值方法，对主积分集的发散部分进行解析求值，对有限部分进行数值求值。计算结果证实了Schröder和Vuorinen最近的结果。在不使用任何数值输入的情况下，通过拟合高精度数值结果得到的所有贡献都得到了直接解析计算的证实。
It is shown that for every problem within dimensional regularization, using the integration-by-parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of dimension equal to four. We argue that the use of such a basis simplifies and stabilizes the numerical evaluation of the master integrals. As an example we explicitly construct the ϵ-finite basis for the set of all QED-like four-loop massive tadpoles. Using a semi-numerical approach based on Padé approximations we evaluate analytically the divergent and numerically the finite part of this set of master integrals. The calculations confirm the recent results of Schröder and Vuorinen. All the contributions found there by fitting the high precision numerical results have been confirmed by direct analytical calculation without using any numerical input.
DOI：
10.1016/j.nuclphysb.2005.01.012
发表时间：
2004-11
期刊：
Nuclear Physics
影响因子：
--
作者：
M. Czakon
通讯作者：
M. Czakon