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Planar Six-Point Feynman Integrals for Four-Dimensional Gauge Theories

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arxiv 2412.19884 v1 pith:ESHEV57W submitted 2024-12-27 hep-ph hep-th

Samuel Abreu , Pier Francesco Monni , Ben Page , Johann Usovitsch This is my paper · ORCID
classification hep-phhep-th
keywords gaugeintegralsscatteringtheoriescomputeconstraintsfeynmanfour-dimensional
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We compute all planar two-loop six-point Feynman integrals entering scattering observables in massless gauge theories such as QCD. A central result of this paper is the formulation of the differential-equations method under the algebraic constraints stemming from four-dimensional kinematics, which in this case leaves only 8 independent scales. We show that these constraints imply that one must compute topologies with only up to 8 propagators, instead of the expected 9. This leads to the decoupling of entire classes of integrals that do not contribute to scattering amplitudes in four dimensional gauge theories. We construct a pure basis and derive their canonical differential equations, of which we discuss the numerical solution. This work marks an important step towards the calculation of massless $2\to 4$ scattering processes at two loops.

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Cited by 6 Pith papers

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  1. QCD Scattering Amplitudes and Prescriptive Unitarity

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    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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    hep-ph 2026-07 conditional novelty 6.0 of 10

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    hep-th 2026-03 conditional novelty 6.0 of 10

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