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

Fuente: arXiv
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Autori principali: Liu, Yuanche, Matijašić, Antonela, Peraro, Tiziano, Xu, Yingxuan, Yang, Zihua, Zhang, Yang
Natura: Preprint
Pubblicazione: 2026
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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