Two-loop Six-point Planar Massless Feynman Integrals to Higher $ε$ Orders
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915907924656128 |
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| author | Liu, Yuanche Matijašić, Antonela Peraro, Tiziano Xu, Yingxuan Yang, Zihua Zhang, Yang |
| author_facet | Liu, Yuanche Matijašić, Antonela Peraro, Tiziano Xu, Yingxuan Yang, Zihua Zhang, Yang |
| contents | In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $ε$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up to weight four for the purpose of two-loop gauge theory amplitudes. Using modern rational reconstruction methods, we identify the complete alphabet with $269$ letters relevant to all weights, derive the analytic canonical differential equation and obtain the symbols up to weight six. As a proof of concept, using a new method with Chebyshev pseudospectral transport, we show that the corresponding pure basis can be efficiently evaluated up to weight six, i.e., to $ \mathcal{O}(ε^2)$ in a physical scattering region. The results of this work can be applied to future three-loop amplitudes and provide new data for the formal study of symbols and cluster algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16831 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-loop Six-point Planar Massless Feynman Integrals to Higher $ε$ Orders Liu, Yuanche Matijašić, Antonela Peraro, Tiziano Xu, Yingxuan Yang, Zihua Zhang, Yang High Energy Physics - Phenomenology High Energy Physics - Theory In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $ε$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up to weight four for the purpose of two-loop gauge theory amplitudes. Using modern rational reconstruction methods, we identify the complete alphabet with $269$ letters relevant to all weights, derive the analytic canonical differential equation and obtain the symbols up to weight six. As a proof of concept, using a new method with Chebyshev pseudospectral transport, we show that the corresponding pure basis can be efficiently evaluated up to weight six, i.e., to $ \mathcal{O}(ε^2)$ in a physical scattering region. The results of this work can be applied to future three-loop amplitudes and provide new data for the formal study of symbols and cluster algebras. |
| title | Two-loop Six-point Planar Massless Feynman Integrals to Higher $ε$ Orders |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.16831 |