It is well known that gravity amplitudes in four dimensions can be reconstructed by the inverse soft limit (ISL) method. According to ISL, a tree level $n$-graviton maximally-helicity-violating (MHV) amplitude is expressed in terms of deformed $(n-1)$-graviton amplitudes accompanied by soft graviton factors. On another hand, single- and double-trace tree-level Einstein-Yang-Mills (EYM) MHV amplitudes have been proven to satisfy spanning forest formulas, where each edge in a forest has the same form with a term in soft graviton factor. It is not transparent that the formulas satisfied by EYM amplitudes can be constructed with ISL. In this paper, we construct the single- and double-trace MHV amplitudes in EYM, by the ISL and show that the known formulas can be precisely reproduced. Interesting identities which are based on Schouten identity and characterized by graphs are also introduced.

中文翻译：

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通过逆软限制构建 EYM 振幅

众所周知，四个维度的重力振幅可以通过逆软极限（ISL）方法重建。根据 ISL，树级 $n$-引力子最大违背 (MHV) 振幅表示为变形的 $(n-1)$-引力子振幅伴随着软引力子因子。另一方面，单迹和双迹树级 Einstein-Yang-Mills (EYM) MHV 振幅已被证明满足生成森林公式，其中森林中的每条边都具有相同的形式和软引力因子中的一项。可以用 ISL 构造满足 EYM 振幅的公式并不透明。在本文中，我们通过 ISL 在 EYM 中构建了单道和双道 MHV 振幅，并表明可以精确地再现已知公式。