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 along specific lines.
Can Locality, Unitarity, and Hidden Zeros Completely Determine Tree-Level Amplitudes?
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abstract
In this note, we address the question of whether locality, unitarity, and newly discovered hidden zeros can completely determine tree-level amplitudes, from the perspective of soft limit. We reconstruct the single-soft theorems of tree YM amplitudes and the double-soft theorems of tree NLSM amplitudes from locality, unitarity, and hidden zeros. A series of studies have shown that the full YM and NLSM amplitudes can be constructed from these soft theorems; therefore, we conclude that locality, unitarity, and hidden zeros completely determine the tree-level YM and NLSM amplitudes.
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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 with 2-split structure.
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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 along specific lines.
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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 with 2-split structure.