We perform a comprehensive study of on-shell recursion relations for Born amplitudes in spontaneously broken gauge theories and identify the minimal shifts required to construct amplitudes with a given particle content and spin quantum numbers. We show that two-line or three-line shifts are sufficient to construct all amplitudes with five or more particles, apart from amplitudes involving longitudinal vector bosons or scalars, which may require at most five-line shifts. As an application, we revisit selection rules for multi-boson amplitudes using on-shell recursion and little-group transformations.

中文翻译：

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自发破缺规范理论中玻恩振幅的壳上可构造性

我们对自发破缺规范理论中波恩振幅的壳上递归关系进行了全面研究，并确定了构建具有给定粒子含量和自旋量子数的振幅所需的最小位移。我们表明，除了涉及纵向矢量玻色子或标量的振幅外，两线或三线位移足以构建具有五个或更多粒子的所有振幅，这可能需要最多五线位移。作为一个应用，我们使用壳上递归和小群变换重新审视多玻色子振幅的选择规则。