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arXiv 2406.03540hep-phhep-th
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Wilson 线形状因子的递推关系

Recursion for Wilson-line Form Factors

Timothy Cohen, Marc Riembau

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28 pages + appendix
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AI总结：

本文利用单线复动量平移推导递推关系，以低点形状因子与在壳振幅为输入高效计算树图阶螺旋度形状因子，并给出 QCD 中 $1\ o 2$ 和 $1\ o 3$ 劈裂函数的新紧凑表达式。

摘要：

Wilson 线修饰算符的矩阵元在规范理论中软模与共线模的因子化中起着核心作用。当用旋量螺旋度变量表示时，这些所谓的形状因子允许从最大螺旋度破坏组态出发进行分类，这与规范理论振幅的情形非常类似。我们证明，单线复动量平移可用来推导递推关系，从而在树图阶高效计算这些螺旋度形状因子：低点形状因子与在壳振幅的组合充当输入构件。我们得到了 QCD 中 $1\ o 2$ 和 $1\ o 3$ 劈裂函数的新颖紧凑表达式，这也用于验证我们的方法。

英文摘要：

Matrix elements of Wilson-line dressed operators play a central role in the factorization of soft and collinear modes in gauge theories. When expressed using spinor helicity variables, these so-called form factors admit a classification starting from a Maximally Helicity Violating configuration, in close analogy with gauge theory amplitudes. We show that a single-line complex momentum shift can be used to derive recursion relations that efficiently compute these helicity form factors at tree-level: a combination of lower point form factors and on-shell amplitudes serve as the input building blocks. We obtain novel compact expressions for the $1\to 2$ and $1\to 3$ splitting functions in QCD, which also serves to validate our methods.

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