The on-shell massless planar double box diagram with an irreducible numerator

Abstract

Using a Mellin-Barnes representation, we compute the on-shell massless planar double box Feynman diagram with an irreducible scalar product of loop momenta in the numerator. This diagram is needed in calculations of two loop corrections to scattering processes of massless particles, together with the double box without numerator calculated previously by Smirnov. We verify the poles in epsilon of our result by means of a system of differential equations relating the two diagrams, which we present in an explicit form. We verify the finite part with an independent numerical check.

6 pages, latex, npb.sty, 2 figures (one in postscript); contributed to proceedings of "Loops and Legs in Quantum Field Theory", Bastei, Germany, April 9-14, 2000

References in corpus (4)

• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• A Two-Loop Four-Gluon Helicity Amplitude in QCD
• Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
• Application of the negative-dimension approach to massless scalar box integrals

Cited by in corpus (58)

• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Magic identities for conformal four-point integrals
• Multi-loop Amplitudes and Resummation
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Two-loop QCD corrections to gluon-gluon scattering
• Soft triple-real radiation for Higgs production at N3LO
• Uniqueness of two-loop master contours
• Two-Loop QCD Helicity Amplitudes for $e^{+}{e}^{-}\to 3$~Jets
• The Two-Loop QCD Matrix Element for $e^{+}{e}^{-}\to 3$ Jets
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• Four-Particle Phase Space Integrals in Massless QCD
• Two-loop QCD corrections to the scattering of massless distinct quarks
• Two-loop QCD corrections to massless quark-gluon scattering
• Ultraviolet properties of Maximal Supergravity
• Two-Loop Correction to Bhabha Scattering
• A quasi-finite basis for multi-loop Feynman integrals
• Two-loop QCD corrections to massless identical quark scattering
• Two-loop QED and QCD corrections to massless fermion-boson scattering
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• Three-mass triangle integrals and single-valued polylogarithms
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• Analytic Continuation of Massless Two-Loop Four-Point Functions
• An analytic solution for the equal-mass banana graph
• Multi-loop Feynman integrals and conformal quantum mechanics
• Two-loop QCD helicity amplitudes for massless quark-massless gauge boson scattering
• Two-loop corrections to Light-by-Light scattering in Supersymmetric QED
• Analytical Evaluation of Dimensionally Regularized Massive On-Shell Double Boxes
• Two-loop QCD helicity amplitudes for massless quark-quark scattering
• Progress in NNLO calculations for scattering processes
• Master Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs
• Numerical evaluation of loop integrals
• Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
• Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box
• Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell
• Master integrals for the four-loop Sudakov form factor
• Two-Loop Virtual Corrections to Drell-Yan Production at order alpha_s alpha^3
• Duality between Wilson loops and gluon amplitudes
• The Two-Loop Four-Graviton Scattering Amplitudes
• One-loop QCD corrections to quark scattering at NNLO
• Two-loop amplitudes for processes $gg\to Hg,qg\to Hq$ and $q\bar{q}\to Hg$ at large Higgs transverse momentum
• The Four Dimensional Helicity Scheme Beyond One Loop
• The Leading Power Regge Asymptotic Behaviour of Dimensionally Regularized Massless On-Shell Planar Triple Box
• MB Tools reloaded
• Evaluating multiloop Feynman integrals by Mellin-Barnes representation
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• On the amplitudes in N=(1,1) D=6 SYM
• One-loop N-point equivalence among negative-dimensional, Mellin-Barnes and Feynman parametrization approaches to Feynman integrals
• Gravity loop integrands from the ultraviolet
• Hidden Beauty in Multiloop Amplitudes
• Some recent results on evaluating Feynman integrals
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Some methods to evaluate complicated Feynman integrals
• The scalar box integral and the Mellin - Barnes representation
• Evaluation of Multi-Box Diagrams in Six Dimensions
• The canonical form has got baubles