Master integrals for fermionic contributions to massless three-loop form factors
Master integrals for fermionic contributions to massless three-loop form factors
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费米子对无质量三环形状因数贡献的主积分
DOI：
10.1016/j.physletb.2008.03.028
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发表时间：
2008
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
在这封信中，我们继续计算无质量三圈形状因子的主积分，给出与NF 2、NF/N和NF/N成比例的费米子贡献相关的那些积分的解析结果。在维数正则化中，我们用一个封闭的形式来表示其中一个积分，它对所有阶都是精确的，包含单位辐角的Γ-函数和超几何函数。在所有其他情况下，我们得到多个梅林-巴恩斯表示，从其中的系数的洛朗展开在λ中提取的分析形式。为了得到三圈夸克和胶子形状因子的有限部分，必须包含黎曼函数中所有通过超越性6的系数。
In this Letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those integrals which are relevant for the fermionic contributions proportional to NF2, NF⋅N, and NF/N. Working in dimensional regularisation, we express one of the integrals in a closed form which is exact to all orders in ϵ, containing Γ-functions and hypergeometric functions of unit argument. In all other cases we derive multiple Mellin–Barnes representations from which the coefficients of the Laurent expansion in ϵ are extracted in an analytical form. To obtain the finite part of the three-loop quark and gluon form factors, all coefficients through transcendentality six in the Riemann ζ-function have to be included.