Soft theorems of tree-level ${\rm Tr}(ϕ^3)$, YM and NLSM amplitudes from $2$-splits

Fuente: arXiv
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Main Author: Zhou, Kang
Format: Preprint
Published: 2025
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author Zhou, Kang
author_facet Zhou, Kang
contents In this paper, we extend the method proposed in \cite{Arkani-Hamed:2024fyd} for deriving soft theorems of amplitudes, which relies exclusively on factorization properties including conventional factorizations on physical poles, as well as newly discovered $2$-splits on special loci in kinematic space. Using the extended approach, we fully reproduce the leading and sub-leading single-soft theorems for tree-level ${\rm Tr}(ϕ^3)$ and Yang-Mills (YM) amplitudes, along with the leading and sub-leading double-soft theorems for tree-level amplitudes of non-linear sigma model (NLSM). Furthermore, we establish universal representations of higher-order single-soft theorems for tree-level ${\rm Tr}(ϕ^3)$ and YM amplitudes in reduced lower-dimensional kinematic spaces. All obtained soft factors maintain consistency with momentum conservation; that is, while each explicit expression of the resulting soft behavior may changes under re-parameterization via momentum conservation, the physical content remains equivalent. Additionally, we find two interesting by-products: First, the single-soft theorems of YM amplitudes and the double-soft theorems of NLSM, at leading and sub-leading orders, are related by a simple kinematic replacement. This replacement also transmutes gauge invariance to Adler zero. Second, we obtain universal sub-leading soft theorems for the resulting pure YM and NLSM currents in the corresponding $2$-splits.
format Preprint
id arxiv_https___arxiv_org_abs_2506_00747
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Soft theorems of tree-level ${\rm Tr}(ϕ^3)$, YM and NLSM amplitudes from $2$-splits
Zhou, Kang
High Energy Physics - Theory
In this paper, we extend the method proposed in \cite{Arkani-Hamed:2024fyd} for deriving soft theorems of amplitudes, which relies exclusively on factorization properties including conventional factorizations on physical poles, as well as newly discovered $2$-splits on special loci in kinematic space. Using the extended approach, we fully reproduce the leading and sub-leading single-soft theorems for tree-level ${\rm Tr}(ϕ^3)$ and Yang-Mills (YM) amplitudes, along with the leading and sub-leading double-soft theorems for tree-level amplitudes of non-linear sigma model (NLSM). Furthermore, we establish universal representations of higher-order single-soft theorems for tree-level ${\rm Tr}(ϕ^3)$ and YM amplitudes in reduced lower-dimensional kinematic spaces. All obtained soft factors maintain consistency with momentum conservation; that is, while each explicit expression of the resulting soft behavior may changes under re-parameterization via momentum conservation, the physical content remains equivalent. Additionally, we find two interesting by-products: First, the single-soft theorems of YM amplitudes and the double-soft theorems of NLSM, at leading and sub-leading orders, are related by a simple kinematic replacement. This replacement also transmutes gauge invariance to Adler zero. Second, we obtain universal sub-leading soft theorems for the resulting pure YM and NLSM currents in the corresponding $2$-splits.
title Soft theorems of tree-level ${\rm Tr}(ϕ^3)$, YM and NLSM amplitudes from $2$-splits
topic High Energy Physics - Theory
url https://arxiv.org/abs/2506.00747