Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \rightarrow Z H$
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915970393571328 |
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| author | Li, Shu-Xiang Zhang, Ren-You Wang, Xiao-Feng Li, Pan-Feng Wei, Xiang-Jie Wang, Yi Jiang, Yi Wang, Qing-hai |
| author_facet | Li, Shu-Xiang Zhang, Ren-You Wang, Xiao-Feng Li, Pan-Feng Wei, Xiang-Jie Wang, Yi Jiang, Yi Wang, Qing-hai |
| contents | For the two-loop next-to-leading-order electroweak (NLO EW) corrections to $gg \rightarrow ZH$, the light-fermion contributions can be classified into eight distinct topologies. Using the canonical differential-equations method, we perform an analytic computation of the master integrals (MIs) associated with the four planar topologies. Canonical bases are constructed using the Magnus-expansion method, and the resulting alphabets consist of algebraic symbol letters involving nontrivial radicals. We develop a systematic framework for identifying the radical structures of the canonical MIs, enabling their organization into suitable subsystems and, whenever possible, their representation in terms of Goncharov polylogarithms (GPLs) up to $\mathcal{O}(ε^4)$. Only a few MIs at $\mathcal{O}(ε^3)$ and $\mathcal{O}(ε^4)$ are instead represented as one-fold integrals over GPLs, due to the presence of nested square roots that obstruct the simultaneous rationalization of all radicals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27314 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \rightarrow Z H$ Li, Shu-Xiang Zhang, Ren-You Wang, Xiao-Feng Li, Pan-Feng Wei, Xiang-Jie Wang, Yi Jiang, Yi Wang, Qing-hai High Energy Physics - Phenomenology For the two-loop next-to-leading-order electroweak (NLO EW) corrections to $gg \rightarrow ZH$, the light-fermion contributions can be classified into eight distinct topologies. Using the canonical differential-equations method, we perform an analytic computation of the master integrals (MIs) associated with the four planar topologies. Canonical bases are constructed using the Magnus-expansion method, and the resulting alphabets consist of algebraic symbol letters involving nontrivial radicals. We develop a systematic framework for identifying the radical structures of the canonical MIs, enabling their organization into suitable subsystems and, whenever possible, their representation in terms of Goncharov polylogarithms (GPLs) up to $\mathcal{O}(ε^4)$. Only a few MIs at $\mathcal{O}(ε^3)$ and $\mathcal{O}(ε^4)$ are instead represented as one-fold integrals over GPLs, due to the presence of nested square roots that obstruct the simultaneous rationalization of all radicals. |
| title | Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \rightarrow Z H$ |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2604.27314 |