The three-loop form factor in $ \mathcal{N} = {4} $ super Yang-Mills
The three-loop form factor in $ \mathcal{N} = {4} $ super Yang-Mills
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$ mathcal{N} = {4} $ super Yang-Mills 中的三环路形状系数
DOI：
10.1007/jhep03(2012)101
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发表时间：
2011
影响因子：
5.4
通讯作者：
T. Huber
中科院分区：
文献类型：
--
作者：
T. Gehrmann;J. Henn;T. Huber
本文研究了三圈阶超Yang-Mills理论中的Sudakov形状因子。后者表示在平面和非平面回路积分。我们表明，它是可能的，以选择一个表示，其中每个循环积分具有统一的超越性。我们验证分析预期的指数的红外发散与正确的价值观的三圈尖点和共线异常尺寸的尺寸正规化。我们发现$N = {4} $ super Yang-Mills的形状因子可以与QCD中夸克和胶子形状因子的超前超越性部分联系起来。我们还研究了D > 4维中形状因子的紫外特性，并发现了意想不到的取消，从而改善了紫外行为。
A bstractIn this paper we study the Sudakov form factor in $ \mathcal{N} = {4} $ super Yang-Mills theory to the three-loop order. The latter is expressed in terms of planar and non-planar loop integrals. We show that it is possible to choose a representation in which each loop integral has uniform transcendentality. We verify analytically the expected exponentiation of the infrared divergences with the correct values of the three-loop cusp and collinear anomalous dimensions in dimensional regularisation. We find that the form factor in $ \mathcal{N} = {4} $ super Yang-Mills can be related to the leading transcendentality part of the quark and gluon form factors in QCD. We also study the ultraviolet properties of the form factor in D > 4 dimensions, and find unexpected cancellations, resulting in an improved ultraviolet behaviour.