In this paper, we demonstrate that the factorizations for tree amplitudes in the double-cover framework, for various theories, can be generated from the gravity amplitude in the double-cover prescription. Our method employs differential operators proposed by Cheung, Shen and Wen. Using our method, the factorized formulae for amplitudes of Yang-Mills theory, special Yang-Mills-scalar theory, and bi-adjoint scalar theory, have been derived. The differential operators indicate some non-trivial relationships among factorizations for above theories, as can be understood through four angles which are factorization channels, pole-structures, gauge choices, as well as BCFW recursions.

中文翻译：

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双覆盖框架中树木振幅的因式分解：从重力到其他理论

在本文中，我们证明了双覆盖框架中树木振幅的分解，对于各种理论，可以从双覆盖处方中的重力振幅生成。我们的方法采用了 Cheung、Shen 和 Wen 提出的微分算子。利用我们的方法，推导出了杨-米尔斯理论、特殊杨-米尔斯标量理论和双伴随标量理论振幅的分解公式。微分算子表示上述理论的分解之间的一些非平凡关系，可以通过分解通道、极点结构、规范选择以及 BCFW 递归四个角度来理解。