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<p>In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator <i>ϵ</i>, 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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mi>ϵ</mi> <mn>2</mn> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({\epsilon}^2\right) \)</EquationSource> </InlineEquation> 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.</p>

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Two-loop six-point planar massless feynman integrals to higher ϵ orders

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月24日

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  • Yuanche Liu,
  • Antonela Matijašić,
  • Tiziano Peraro,
  • Yingxuan Xu,
  • Zihua Yang,
  • Yang Zhang

摘要

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 O ϵ 2 \( \mathcal{O}\left({\epsilon}^2\right) \) 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.