Nine-propagator master integrals for massless three-loop form factors
Nine-propagator master integrals for massless three-loop form factors
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无质量三环形状因数的九传播器主积分
DOI：
10.1016/j.physletb.2009.06.038
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发表时间：
2009
影响因子：
4.4
通讯作者：
Heinrich G
中科院分区：
文献类型：
--
作者：
Heinrich G
我们完成了主积分的计算无质量的三圈形状因子通过计算以前未知的三个图与九个传播维正则化。每个积分产生一个六重梅林-巴恩斯表示，我们用它来计算在牛顿的洛朗展开系数。使用黎曼函数的重量高达6，我们给充分的分析结果的一个积分;第二，分析结果，但所有的有限项;第三，分析结果，但所有的最后两个系数在洛朗展开。其余的系数数值给出了足够高的精度为现象学的应用。
We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold Mellin–Barnes representation which we use to compute the coefficients of the Laurent expansion in ϵ. Using Riemann ζ functions of up to weight six, we give fully analytic results for one integral; for a second, analytic results for all but the finite term; for the third, analytic results for all but the last two coefficients in the Laurent expansion. The remaining coefficients are given numerically to sufficiently high accuracy for phenomenological applications.