Universal interpretation of hidden zero and 2-split of tree-level amplitudes using Feynman diagrams. Part I. Tr(ϕ3), NLSM and YM

A bstract In this paper, we propose a universal diagrammatic interpretation of hidden zeros and 2-splits of tree-level amplitudes. Originally developed for Tr( ϕ 3 ) amplitudes in our previous work, this interpretation is now extended to tree-level amplitudes in Nonlinear sigma model (NLSM) and Yang-Mills (YM) theories. The interpretation is based on a certain factorization behavior of Feynman diagrams under specific kinematic constraints, which we term shuffle factorization along a specific line (SFASL). This mechanism allows us to separate Feynman diagrams along specific lines after summing over shuffle permutations. When applied to NLSM and YM amplitudes, we perform proper extensions of the SFASL used in the Tr( ϕ 3 ) case. Through the SFASL, the interpretation for the hidden zeros and 2-splits of tree amplitudes of Tr( ϕ 3 ), NLSM, and YM can be unified as: the hidden zeros are ascribed to the on-shell condition $${k}_{j}^{2}=0$$ of a massless particle, while the 2-splits are caused by separating each Feynman diagram along two lines, akin to unzipping two zippers.