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Complete function space for planar two-loop six-particle scattering amplitudes

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arxiv 2501.01847 v2 pith:GNWUCGPK submitted 2025-01-03 hep-ph hep-th

classification hep-phhep-th
keywords integralssix-particleiteratedscatteringtwo-loopamplitudesanalyticdifferential
verification ladder T0 review T1 audit T2 compute T3 formal
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We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as Chen iterated integrals. We argue that this is sufficient information for evaluating any scattering amplitude in four dimensions up to the finite part. We support this claim by reducing, for the most complicated integral topologies, integrals with typical Yang-Mills numerators. We use the analytic solutions to the differential equations, together with dihedral symmetry, to provide the full solution space relevant for two-loop six-particle computations. This includes the relevant function alphabet, as well as the independent set of iterated integrals up to weight four. We also provide the answer for all master integrals in terms of iterated integrals that can be readily evaluated numerically. As a proof of concept, we provide a numerical implementation that evaluates the integrals in part of the Euclidean region, and validate this against numerical evaluation of the Feynman integrals. Our result removes the bottleneck of Feynman integral evaluation, paving the way to future analytic evaluations of six-particle scattering amplitudes.

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Forward citations

Cited by 5 Pith papers

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  1. QCD Scattering Amplitudes and Prescriptive Unitarity

    hep-th 2026-02 conditional novelty 7.0 of 10

    The maximally-transcendental part of planar two-loop six-gluon MHV QCD amplitudes is bootstrapped at symbol level and expressed in a 137-letter alphabet.

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  5. Singularities of massless scattering and cluster algebras

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