论文标题
无质量的单壳标量盒积分 - 分支切割结构和全订单Epsilon扩展
The massless single off-shell scalar box integral -- branch cut structure and all-order epsilon expansion
论文作者
论文摘要
我们研究了具有尺寸正则化的无质量内部线的单个脱壳标量框。在维数正则化参数epsilon，其分支切割结构和运动学限制中，特别强调了更高的订单。盒子积分的共同表示会引入浅表切割，我们将其消除为Epsilon扩展中的所有订单。到目前为止，在文献中，对于此问题的一个令人满意的解决方案只能在Epsilon扩展中以有限顺序存在。但是，对于在扰动理论中NNLO的计算，需要该积分的Epsilon中的较高阶。在本文中，我们以单价值聚集体为Epsilon中的所有订单介绍了结果，并明确确定所有运动区域中框积分的实际和虚构部分。
We investigate the single off-shell scalar box integral with massless internal lines in dimensional regularization. A special emphasis is given to higher orders in the dimensional regularization parameter epsilon, its branch cut structure, and kinematic limits. Common representations of the box integral introduce superficial branch cuts, which we eliminate to all orders in the epsilon expansion. In the literature so far a satisfactory solution for this issue only exists up to finite order in the epsilon expansion. However, for calculations at NNLO in perturbation theory, higher orders in epsilon of this integral are required. In this paper, we present results to all orders in epsilon in terms of single-valued polylogarithms and explicitly determine the real and imaginary part of the box integral in all kinematic regions.
