Two-loop five-point massless QCD amplitudes within the IBP approach

Abstract

We solve the integration-by-parts (IBP) identities needed for the computation of any planar two-loop five-point massless amplitude in QCD. We also derive some new results for the most complicated non-planar topology with irreducible numerators of power as high as six. We do this by applying a new strategy for solving the IBP identities which scales better for problems with a large number of scales and/or master integrals. Our results are a proof of principle that the remaining non-planar contributions for all two-loop five-point massless QCD amplitudes can be computed in analytic form.

arXiv comment6 pages, 1 ancillary file, results available from "http://www.precision.hep.phy.cam.ac.uk/results/amplitudes/". v2 (published version): added references

References in corpus (49)

• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• Differential Equations for Feynman Graph Amplitudes
• Algorithm FIRE -- Feynman Integral REduction
• Connection between Feynman integrals having different values of the space-time dimension
• FIRE5: a C++ implementation of Feynman Integral REduction
• Kira - A Feynman Integral Reduction Program
• Reduze - Feynman Integral Reduction in C++
• JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes
• The five-loop beta function of Yang-Mills theory with fermions
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• Lectures on differential equations for Feynman integrals
• Calculation of the quark and gluon form factors to three loops in QCD
• A novel approach to integration by parts reduction
• Towards a Basis for Planar Two-Loop Integrals
• Feynman Diagrams and Differential Equations
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Integration-by-parts reductions from unitarity cuts and algebraic geometry
• Two-loop QCD corrections to gluon-gluon scattering
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Two-loop QCD corrections to the scattering of massless distinct quarks
• Two-loop QCD corrections to massless quark-gluon scattering
• Critical points and number of master integrals
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations
• A first look at two-loop five-gluon scattering in QCD
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• Complete renormalization of QCD at five loops
• A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Bootstrapping pentagon functions
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators
• A practical criterion of irreducibility of multi--loop Feynman integrals
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• Integration by parts: An introduction
• Three-loop master integrals for ladder-box diagrams with one massive leg
• Two-loop five-point all plus helicity Yang-Mills amplitude
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• The $n_f^2$ contributions to fermionic four-loop form factors
• Direct Solution of Integration-by-Parts Systems
• Simplified differential equations approach for Master Integrals
• Master integrals for the four-loop Sudakov form factor
• Analytic all-plus-helicity gluon amplitudes in QCD
• Amplitudes from superconformal Ward identities

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