Planar three-loop master integrals for $2\to 2$ processes with one external massive particle

Abstract

We present analytic results for the two tennis-court integral families relevant to $2\to 2$ scattering processes involving one massive external particle and massless propagators in terms of Goncharov polylogarithms of up to transcendental weight six. We also present analytic results for physical kinematics for the ladder-box family and the two tennis-court families in terms of real-valued polylogarithmic functions, making our solutions well-suited for phenomenological applications.

arXiv commentv2: added appendix on adjacency conditions, added ancillary files, version accepted for publication in JHEP; v1: 17 pages, 1 figure

References in corpus (36)

• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• Numerical evaluation of multiple polylogarithms
• Local Integrals for Planar Scattering Amplitudes
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes
• Integral Reduction with Kira 2.0 and Finite Field Methods
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• From polygons and symbols to polylogarithmic functions
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• FIESTA 4: optimized Feynman integral calculations with GPU support
• PolyLogTools - Polylogs for the masses
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Magnus and Dyson Series for Master Integrals
• Expansion by regions: revealing potential and Glauber regions automatically
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Feynman graph polynomials
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• Collider Physics at the Precision Frontier
• epsilon: A tool to find a canonical basis of master integrals
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the planar graphs
• Cluster algebras for Feynman integrals
• Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
• A Three-Point Form Factor Through Five Loops
• Three-loop master integrals for ladder-box diagrams with one massive leg
• Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• Simplified differential equations approach for Master Integrals
• Three-loop helicity amplitudes for diphoton production in gluon fusion
• Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
• Pentagon integrals to arbitrary order in the dimensional regulator
• Resummation methods for Master Integrals

Cited by in corpus (9)

• 50 Years of Quantum Chromodynamics
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• First look at the evaluation of three-loop non-planar Feynman diagrams for Higgs plus jet production
• Dissecting polytopes: Landau singularities and asymptotic expansions in $2\to 2$ scattering
• $D$-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals
• A first computation of three-loop master integrals for the production of two off-shell vector bosons with different masses
• All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering
• A high-precision result for a full-color three-loop three-point form factor in $\mathcal{N}=4$ SYM
• Three-Loop QCD corrections to the production of a Higgs boson and a Jet