We construct tree-level amplitude for massive particles using on-shell recursion relations based on two classes of momentum shifts: an all-line transverse shift that deforms momentum by its transverse polarization vector, and a massive Britto-Cachazo-Feng-Witten-type shift. We illustrate that these shifts allow us to correctly calculate four-point and five-point amplitudes in massive QED, without an ambiguity associated with the contact terms that may arise from a simple “gluing” of lower-point on-shell amplitudes. We discuss various aspects and applicability of the two shifts, including the large-𝑧 behavior and complexity scaling. We show that there exists a “good” all-line transverse shift for all possible little group configurations of the external particles, which can be extended to a broader class of theories with massive particles such as massive QCD and theories with massive spin-1 particles. The massive Britto-Cachazo-Feng-Witten-type shift enjoys more simplicity, but a “good” shift does not exist for all the spin states due to the specific choice of spin axis.

中文翻译：

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动量偏移和壳上可构造的大振幅


我们使用基于两类动量偏移的壳上递归关系为大质量粒子构建树级振幅：通过其横向极化矢量使动量变形的全线横向偏移，以及巨大的 Britto-Cachazo-Feng-Witten 型偏移。我们说明这些偏移使我们能够正确计算大规模 QED 中的四点和五点振幅，而不会因低点壳层振幅的简单“粘合”而可能产生的与接触项相关的歧义。我们将讨论这两个转变的各个方面和适用性，包括 large-z 行为和复杂性扩展。我们表明，对于外部粒子的所有可能的小群构型，都存在一个“良好的”全线横向偏移，这可以扩展到更广泛的大质量粒子理论，例如大质量 QCD 和大质量自旋 1 粒子的理论。大规模的 Britto-Cachazo-Feng-Witten 类型偏移更加简单，但由于自旋轴的特定选择，并非所有自旋态都存在“好的”偏移。