Exact Splitting of Amplitudes and One-Loop Integrands: A Classical Origin of Zeros
Abstract
We introduce a recursion based on hidden zeros that reconstructs complete tree level scattering amplitudes and one-loop integrands at generic kinematics. The recursion takes a universal exact-splitting form: both tree amplitudes and one-loop surface integrands are expressed as sums of products of complete tree functions, with the chosen zero conditions manifest in every term. We establish this structure for cubic scalar theory, the nonlinear sigma model, and inverse string Kawai--Lewellen--Tye (KLT) functions. We derive the tree splitting formula from the equations of motion, showing that hidden zeros arise when the product of two currents solves the equations of motion, while corrections away from the zero reconstruct the full amplitude. We further show that inverse KLT is the unique extension of Tr(ϕ3) with higher-point non-derivative interactions that preserves hidden zeros.
Related
- Ligand-mediated Origin of Altermagnetic Spin-Splitting
- Exact Fock Amplitudes of the Cubic-Phase Gate on Arbitrary Pure Gaussian States
- Exact color sums for multi-gluon amplitudes: direct, multiplet and symmetric-group Fourier methods
- Exact Ionization Amplitudes for a Delta-Function Well in an Arbitrary-Strength DC Electric Field
- Spin splitting without symmetry: a nearly compensated ferrimagnet and the origin of altermagnetism
BibTeX
@misc{li2026exact,
title = {{Exact Splitting of Amplitudes and One-Loop Integrands: A Classical Origin of Zeros}},
author = {Yang Li and Laurentiu Rodina and Zhi-Zhen Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06810},
eprint = {2611.06810},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06810},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact Splitting of Amplitudes and One-Loop Integrands: A Classical Origin of Zeros
AU - Yang Li
AU - Laurentiu Rodina
AU - Zhi-Zhen Wang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06810
UR - https://arxiv.org/abs/2611.06810
AB - We introduce a recursion based on hidden zeros that reconstructs complete tree level scattering amplitudes and one-loop integrands at generic kinematics. The recursion takes a universal exact-splitting form: both tree amplitudes and one-loop surface integrands are expressed as sums of products of complete tree functions, with the chosen zero conditions manifest in every term. We establish this structure for cubic scalar theory, the nonlinear sigma model, and inverse string Kawai--Lewellen--Tye (KLT) functions. We derive the tree splitting formula from the equations of motion, showing that hidden zeros arise when the product of two currents solves the equations of motion, while corrections away from the zero reconstruct the full amplitude. We further show that inverse KLT is the unique extension of Tr(ϕ^3) with higher-point non-derivative interactions that preserves hidden zeros.
ER -