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<p>In this paper, we investigate the 2-split behavior of tree-level amplitudes of bi-adjoint scalar (BAS), Yang-Mills (YM), non-linear sigma model (NLSM), and general relativity (GR) theories under certain kinematic conditions. Our approach begins with a proof, based on the Feynman diagram method, of the 2-split property for tree-level BAS<sub>⊕</sub>X amplitudes with X = YM<i>,</i> NLSM<i>,</i> GR. The proof relies crucially on a particular pattern in the Feynman rules of various vertices. Building on this, we use the expansion of X amplitudes into BAS<sub>⊕</sub>X amplitudes to establish the 2-split behavior. As a byproduct, we derive universal expansions of the resulting pure X currents into BAS currents, which closely parallel the corresponding on-shell amplitude expansions.</p>

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2-split from Feynman diagrams and expansions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月19日

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  • Bo Feng,
  • Liang Zhang,
  • Kang Zhou

摘要

In this paper, we investigate the 2-split behavior of tree-level amplitudes of bi-adjoint scalar (BAS), Yang-Mills (YM), non-linear sigma model (NLSM), and general relativity (GR) theories under certain kinematic conditions. Our approach begins with a proof, based on the Feynman diagram method, of the 2-split property for tree-level BAS⊕X amplitudes with X = YM, NLSM, GR. The proof relies crucially on a particular pattern in the Feynman rules of various vertices. Building on this, we use the expansion of X amplitudes into BAS⊕X amplitudes to establish the 2-split behavior. As a byproduct, we derive universal expansions of the resulting pure X currents into BAS currents, which closely parallel the corresponding on-shell amplitude expansions.