Three universal Feynman diagram cuttings explain hidden zeros, 2-splits, and smooth 3-splits in ordered tree amplitudes of Tr(φ³), YM, and NLSM.
Constructing tree amplitudes of scalar EFT from double soft theorem
7 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The well known Adler zero can fully determine tree amplitudes of non-linear sigma model (NLSM), but fails to fix tree pion amplitudes with higher-derivative interactions. To fill this gap, in this paper we propose a new method based on exploiting the double soft theorem for scalars, which can be applied to a wider range. A remarkable feature of this method is, we only assume the universality of soft behavior at the beginning, and determine the explicit form of double soft factor in the process of constructing amplitudes. To test the applicability, we use this method to construct tree NLSM amplitudes and tree amplitudes those pions in NLSM couple to bi-adjoint scalars. We also construct the simplest pion amplitudes which receive leading higher-derivative correction, with arbitrary number of external legs. All resulted amplitudes are formulated as universal expansions to appropriate basis.
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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.
Hidden zeros in tree-level amplitudes of several theories are attributed to zeros of bi-adjoint scalar amplitudes via universal expansions, with a mechanism shown to cancel potential propagator divergences in gravity.
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Understanding zeros and splittings of ordered tree amplitudes via Feynman diagrams
Three universal Feynman diagram cuttings explain hidden zeros, 2-splits, and smooth 3-splits in ordered tree amplitudes of Tr(φ³), YM, and NLSM.
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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.
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Note on hidden zeros and expansions of tree-level amplitudes
Hidden zeros in tree-level amplitudes of several theories are attributed to zeros of bi-adjoint scalar amplitudes via universal expansions, with a mechanism shown to cancel potential propagator divergences in gravity.