Two-Loop Five-Point Two-Mass Planar Integrals and Double Lagrangian Insertions in a Wilson Loop

Abstract

We consider the complete set of planar two-loop five-point Feynman integrals with two off-shell external legs. These integrals are relevant, for instance, for the calculation of the second-order QCD corrections to the production of two heavy vector bosons in association with a jet or a photon at a hadron collider. We construct pure bases for these integrals and reconstruct their analytic differential equations in canonical form through numerical sampling over finite fields. The newly identified symbol alphabet, one of the most complex to date, provides valuable data for bootstrap methods. We then apply our results to initiate the study of double Lagrangian insertions in a four-cusp Wilson loop in planar maximally supersymmetric Yang-Mills theory, computing it through two loops. We observe that it is finite, conformally invariant in four dimensions, and of uniform transcendentality. Furthermore, we provide numerical evidence for its positivity within the amplituhedron region through two loops.

arXiv comment33 pages, 6 figures, 2 tables, 2 appendices, ancillary files at https://zenodo.org/records/13254698

References in corpus (67)

• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Amplituhedron
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Local Integrals for Planar Scattering Amplitudes
• Structure functions for large $x$ and renormalization of Wilson loops
• A novel approach to integration by parts reduction
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Towards a Basis for Planar Two-Loop Integrals
• A Systematic and Efficient Method to Compute Multi-loop Master Integrals
• Reducing differential equations for multiloop master integrals
• Three-Loop Four-Point Correlator in N=4 SYM
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Pentagon functions for massless planar scattering amplitudes
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• The super-correlator/super-amplitude duality: Part I
• From correlation functions to scattering amplitudes
• Pulling the straps of polygons
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Unwinding the Amplituhedron in Binary
• epsilon: A tool to find a canonical basis of master integrals
• Pentagon Functions for Scattering of Five Massless Particles
• Positive Amplitudes In The Amplituhedron
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• Libra: a package for transformation of differential systems for multiloop integrals
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• Two-Loop Integrals for Planar Five-Point One-Mass Processes
• More on the duality correlators/amplitudes
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Cluster algebras for Feynman integrals
• Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• Gauge Invariance and Anomalous Dimensions of a Light-Cone Wilson Loop in Light-Like Axial Gauge
• Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
• Baikov representations, intersection theory, and canonical Feynman integrals
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Constructing Canonical Feynman Integrals with Intersection Theory
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
• Correlation function of null polygonal Wilson loops with local operators
• Two-Loop Master Integrals for Leading-Color $pp\to t\bar{t}H$ Amplitudes with a Light-Quark Loop
• Principal Landau Determinants
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• Symbol Alphabets from the Landau Singular Locus
• Two-loop master integrals for a planar topology contributing to $pp\to t\bar{t}j$
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Perturbative correlation functions of null Wilson loops and local operators
• Intersection theory rules symbology
• Two-Loop Five-Point Two-Mass Planar Integrals and Double Lagrangian Insertions in a Wilson Loop
• Higher loop mixed correlators in N=4 SYM
• Integrated negative geometries in ABJM
• The recursive structure of Baikov representations I: generics and application to symbology
• Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron

Cited by in corpus (7)

• Full-colour double-virtual amplitudes for associated production of a Higgs boson with a bottom-quark pair at the LHC
• Two-Loop Five-Point Two-Mass Planar Integrals and Double Lagrangian Insertions in a Wilson Loop
• Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
• SOFIA: Singularities of Feynman Integrals Automatized
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• A first computation of three-loop master integrals for the production of two off-shell vector bosons with different masses
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons