Towards New Hidden Zero and $2$-Split of Loop-Level Feynman Integrands in ${\rm Tr}(ϕ^3)$ Model
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908966457442304 |
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| author | Zhou, Kang |
| author_facet | Zhou, Kang |
| contents | We extend the hidden zeros and $2$-split of tree-level ${\rm Tr}(ϕ^3)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13810 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards New Hidden Zero and $2$-Split of Loop-Level Feynman Integrands in ${\rm Tr}(ϕ^3)$ Model Zhou, Kang High Energy Physics - Theory We extend the hidden zeros and $2$-split of tree-level ${\rm Tr}(ϕ^3)$ 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. |
| title | Towards New Hidden Zero and $2$-Split of Loop-Level Feynman Integrands in ${\rm Tr}(ϕ^3)$ Model |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.13810 |