A first look at the function space for planar two-loop six-particle Feynman integrals
arXiv:2112.10605 · doi:10.1007/JHEP03(2022)056
Abstract
Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle processes. In this paper, we initiate the study of the function space for planar two-loop six-particle processes. We study all genuine six-particle Feynman integrals, and derive the differential equations they satisfy on maximal cuts. Performing a leading singularity analysis in momentum space, and in Baikov representation, we find an integral basis that puts the differential equations into canonical form. The corresponding differential equation in the eight independent kinematic variables is derived with the finite-field reconstruction method and the symbol letters are identified. We identify the dual conformally invariant hexagon alphabet known from maximally supersymmetric Yang-Mills theory as a subset of our alphabet. This paper constitutes an important step in the analytic calculation of planar two-loop six-particle Feynman integrals.
arXiv commentminor corrections, updated reference list
References in corpus (73)
- Higgs boson production at hadron colliders in NNLO QCD
- Multiloop integrals in dimensional regularization made simple
- Differential Equations for Two-Loop Four-Point Functions
- Differential Equations for Feynman Graph Amplitudes
- Classical Polylogarithms for Amplitudes and Wilson Loops
- Dimensionally Regulated Pentagon Integrals
- LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
- Local Integrals for Planar Scattering Amplitudes
- FIRE6: Feynman Integral REduction with Modular Arithmetic
- Lectures on differential equations for Feynman integrals
- Dual Superconformal Invariance, Momentum Twistors and Grassmannians
- A novel approach to integration by parts reduction
- Bootstrapping the three-loop hexagon
- Scattering amplitudes over finite fields and multivariate functional reconstruction
- FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
- Motivic Amplitudes and Cluster Coordinates
- Reducing differential equations for multiloop master integrals
- Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
- Feynman Integrals and Intersection Theory
- Hexagon functions and the three-loop remainder function
- Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
- Vector Space of Feynman Integrals and Multivariate Intersection Numbers
- Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
- A Two-Loop Five-Gluon Helicity Amplitude in QCD
- Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
- To , or not to : Recent developments and comparisons of regularization schemes
- Collider Physics at the Precision Frontier
- The two-loop five-point amplitude in super-Yang-Mills theory
- Cuts of Feynman Integrals in Baikov representation
- All master integrals for three-jet production at NNLO
- Iterative structure of finite loop integrals
- epsilon: A tool to find a canonical basis of master integrals
- Pentagon Functions for Scattering of Five Massless Particles
- Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
- Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
- On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
- Sharpening The Leading Singularity
- A first next-to-next-to-leading order study of three-jet production at the LHC
- Triphoton production at hadron colliders in NNLO QCD
- Decomposition of Feynman Integrals by Multivariate Intersection Numbers
- The Two-Loop Master Integrals for
- Transforming differential equations of multi-loop Feynman integrals into canonical form
- Libra: a package for transformation of differential systems for multiloop integrals
- Analytic result for a two-loop five-particle amplitude
- New differential equations for on-shell loop integrals
- Two-Loop Integrals for Planar Five-Point One-Mass Processes
- Bootstrapping pentagon functions
- Pentagon Functions for One-Mass Planar Scattering Amplitudes
- Analytic result for the nonplanar hexa-box integrals
- Cluster algebras for Feynman integrals
- Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
- Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
- Differential equations from unitarity cuts: nonplanar hexa-box integrals
- Two-loop helicity amplitudes for diphoton plus jet production in full color
- Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
- Baikov-Lee Representations Of Cut Feynman Integrals
- Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg
- Physics at the FCC-hh, a 100 TeV pp collider
- Constructing Canonical Feynman Integrals with Intersection Theory
- Beyond the Standard Model Physics at the HL-LHC and HE-LHC
- Next-to-leading order QCD corrections to diphoton-plus-jet production through gluon fusion at the LHC
- Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders
- Two-loop leading-color helicity amplitudes for three-photon production at the LHC
- Local integrands for two-loop all-plus Yang-Mills amplitudes
- Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC
- Bootstrapping two-loop Feynman integrals for planar N=4 sYM
- Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
- Multivariate Residues and Maximal Unitarity
- Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- What can we learn about QCD and collider physics from N=4 super Yang-Mills?
- Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
- QCD calculations for the LHC: status and prospects
- Explicit solutions of the n--loop vacuum integral recurrence relations
Cited by in corpus (7)
- Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
- A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
- Full-colour double-virtual amplitudes for associated production of a Higgs boson with a bottom-quark pair at the LHC
- One-loop hexagon integral to higher orders in the dimensional regulator
- Illustrations of Integrand-Basis Building at Two Loops
- On the finite basis topologies for multi-loop high-multiplicity Feynman integrals
- A new method for finding more symmetry relations of Feynman integrals