Towards new hidden zero and 2-split of loop-level Feynman yntegrands in Tr(ϕ3) model
- 1College of Physical Science and Technology, Yangzhou University
Abstract
A bstract : We extend the hidden zeros and 2-split of tree-level Tr( ϕ ³ ) amplitudes to loop-level Feynman integrands, apart from some physically irrelevant scaleless integrals. Our method is based on a certain factorization mechanism that occurs in Feynman diagrams when summing over shuffle permutations. The loop-level hidden zeros and 2-split identified in this work differ from those in the literature. In our result, the kinematic conditions for loop-level hidden zeros and 2-split are remarkably simple. Their connection is as tight as at tree-level, with the same procedure for obtaining the 2-split condition from the zero condition. The resulting 2-split formula at loop-level represents a generalization of that at tree-level: the L -loop integrand is expressed as a sum over L + 1 terms, each of which exhibits a 2-split structure.
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BibTeX
@article{zhou2026towards,
title = {{Towards new hidden zero and 2-split of loop-level Feynman yntegrands in Tr(ϕ3) model}},
author = {Kang Zhou},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)030},
url = {https://link.springer.com/10.1007/JHEP10(2026)030},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Towards new hidden zero and 2-split of loop-level Feynman yntegrands in Tr(ϕ3) model
AU - Kang Zhou
PY - 2026
DA - 2026/10/02
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)030
UR - https://link.springer.com/10.1007/JHEP10(2026)030
AB - A bstract : We extend the hidden zeros and 2-split of tree-level Tr( ϕ ³ ) amplitudes to loop-level Feynman integrands, apart from some physically irrelevant scaleless integrals. Our method is based on a certain factorization mechanism that occurs in Feynman diagrams when summing over shuffle permutations. The loop-level hidden zeros and 2-split identified in this work differ from those in the literature. In our result, the kinematic conditions for loop-level hidden zeros and 2-split are remarkably simple. Their connection is as tight as at tree-level, with the same procedure for obtaining the 2-split condition from the zero condition. The resulting 2-split formula at loop-level represents a generalization of that at tree-level: the L -loop integrand is expressed as a sum over L + 1 terms, each of which exhibits a 2-split structure.
SN - 1029-8479
ER -