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Understanding zeros and splittings of ordered tree amplitudes via Feynman diagrams
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In this paper, we propose new understandings for recently discovered hidden zeros and novel splittings, by utilizing Feynman diagrams. The study focus on ordered tree level amplitudes of three theories, which are ${\rm Tr}(\phi^3)$, Yang-Mills, and non-linear sigma model. We find three universal ways of cutting Feynman diagrams, which are valid for any diagram, allowing us to separate a full amplitude into two/three pieces. As will be shown, the first type of cuttings leads to hidden zeros, the second one gives rise to $2$-splits, while the third one corresponds to $3$-splits called smooth splittings. Throughout this work, we frequently use the helpful auxiliary technic of thinking the resulting pieces as in orthogonal spaces. However, final results are independent of this auxiliary picture.
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Cited by 3 Pith papers
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Universal Interpretation of Hidden Zero and $2$-Split of Tree-Level Amplitudes Using Feynman Diagrams, Part $\mathbf{I}$: ${\rm Tr}(\phi^3)$, NLSM and YM
A universal diagrammatic interpretation unifies hidden zeros (from massless on-shell conditions) and 2-splits (from double-line separation) in Tr(φ³), NLSM, and YM tree amplitudes using extended shuffle factorization ...
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Towards New Hidden Zero and $2$-Split of Loop-Level Feynman Integrands in ${\rm Tr}(\phi^3)$ Model
Loop-level hidden zeros and 2-split structures are found in Tr(φ³) Feynman integrands with simple kinematic conditions, generalizing the tree-level case to an L-loop integrand expressed as a sum over L+1 terms each wi...
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Can Locality, Unitarity, and Hidden Zeros Completely Determine Tree-Level Amplitudes?
Locality, unitarity, and hidden zeros determine tree-level YM and NLSM amplitudes by reconstructing their soft theorems.
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