Planar Six-Point Feynman Integrals for Four-Dimensional Gauge Theories
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910765087195136 |
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| author | Abreu, Samuel Monni, Pier Francesco Page, Ben Usovitsch, Johann |
| author_facet | Abreu, Samuel Monni, Pier Francesco Page, Ben Usovitsch, Johann |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Planar Six-Point Feynman Integrals for Four-Dimensional Gauge Theories Abreu, Samuel Monni, Pier Francesco Page, Ben Usovitsch, Johann High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Planar Six-Point Feynman Integrals for Four-Dimensional Gauge Theories |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.19884 |