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arXiv · 2603.16831

Two-loop Six-point Planar Massless Feynman Integrals to Higher $\epsilon$ Orders

Yuanche Liu·Antonela Matijašić·Tiziano Peraro·Yingxuan Xu·Zihua Yang·Yang Zhang
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Abstract

In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, 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}(\epsilon^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.

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Yuanche Liu, Antonela Matijašić, Tiziano Peraro, Yingxuan Xu, Zihua Yang, Yang Zhang. 2026-03-17. Two-loop Six-point Planar Massless Feynman Integrals to Higher $\epsilon$ Orders. https://arxiv.org/abs/2603.16831

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