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.
Hidden Zeros and $2$-split via BCFW Recursion Relation
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this paper, we provide another angle to understand recent discoveries, i.e., the hidden zeros and corresponding 2-split behavior using the BCFW recursion relation. For the hidden zeros, we show that although the BCFW recursion relation is not directly applicable for computing amplitudes of the non-linear sigma model, we can indeed prove the zeros using the modified BCFW recursion relation. Our work also indicates that for the 2-split to hold, the current should be carefully defined.
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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.
Hidden zeros extend to higher-derivative tree-level gluon and graviton amplitudes, with systematic cancellation of propagator singularities shown via bi-adjoint scalar expansions.
A recursion for NLSM tree amplitudes based on hidden zeros reproduces the Adler zero, generates amplitudes from Tr(φ³) via δ-shift, expands them into bi-adjoint scalars, and claims these plus factorization uniquely determine all tree-level NLSM amplitudes.
Locality, unitarity, and hidden zeros determine tree-level YM and NLSM amplitudes by reconstructing their soft theorems.
Proof via Feynman diagrams that tree-level BAS⊕X amplitudes with X=YM,NLSM,GR obey 2-split under kinematic conditions, extended to pure X amplitudes with byproduct universal expansions of X currents into BAS currents.
Extends a 2-split factorization approach to reproduce known leading and sub-leading soft theorems for Tr(φ³) and YM single-soft and NLSM double-soft amplitudes while deriving higher-order universal forms and a kinematic relation linking YM gauge invariance to NLSM Adler zero.
citing papers explorer
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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.
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Hidden zeros for higher-derivative YM and GR amplitudes at tree-level
Hidden zeros extend to higher-derivative tree-level gluon and graviton amplitudes, with systematic cancellation of propagator singularities shown via bi-adjoint scalar expansions.
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A new recursion relation for tree-level NLSM amplitudes based on hidden zeros
A recursion for NLSM tree amplitudes based on hidden zeros reproduces the Adler zero, generates amplitudes from Tr(φ³) via δ-shift, expands them into bi-adjoint scalars, and claims these plus factorization uniquely determine all tree-level NLSM amplitudes.
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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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$2$-split from Feynman diagrams and Expansions
Proof via Feynman diagrams that tree-level BAS⊕X amplitudes with X=YM,NLSM,GR obey 2-split under kinematic conditions, extended to pure X amplitudes with byproduct universal expansions of X currents into BAS currents.
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Soft theorems of tree-level ${\rm Tr}(\phi^3)$, YM and NLSM amplitudes from $2$-splits
Extends a 2-split factorization approach to reproduce known leading and sub-leading soft theorems for Tr(φ³) and YM single-soft and NLSM double-soft amplitudes while deriving higher-order universal forms and a kinematic relation linking YM gauge invariance to NLSM Adler zero.