Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators

Abstract

We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms $\Li{a}{-t/s}$, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.

LaTeX, 16 pages; misprints in ff. (8), (24), (30) corrected; some explanations added

References in corpus (1)

• Analytical Result for Dimensionally Regularized Massless On-shell Double Box

Cited by in corpus (105)

• Differential Equations for Two-Loop Four-Point Functions
• Coherent Exclusive Exponentiation For Precision Monte Carlo Calculations
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Magic identities for conformal four-point integrals
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Automatized analytic continuation of Mellin-Barnes integrals
• Multi-loop Amplitudes and Resummation
• Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Towards a Basis for Planar Two-Loop Integrals
• Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• 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
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• 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
• Collider Physics at the Precision Frontier
• Hepta-Cuts of Two-Loop Scattering Amplitudes
• Isolating a light Higgs boson from the di-photon background at the LHC
• Two-Loop Correction to Bhabha Scattering
• A quasi-finite basis for multi-loop Feynman integrals
• Two-loop QCD corrections to massless identical quark scattering
• Multiple Singular Emission in Gauge Theories
• Two-loop QED and QCD corrections to massless fermion-boson scattering
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Three-mass triangle integrals and single-valued polylogarithms
• The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• Analytic Continuation of Massless Two-Loop Four-Point Functions
• An Approach Toward the Numerical Evaluation of Multi-Loop Feynman Diagrams
• An analytic solution for the equal-mass banana graph
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Multi-loop Feynman integrals and conformal quantum mechanics
• The on-shell massless planar double box diagram with an irreducible numerator
• Two-loop QCD helicity amplitudes for massless quark-massless gauge boson scattering
• Two-loop corrections to Light-by-Light scattering in Supersymmetric QED
• A practical criterion of irreducibility of multi--loop Feynman integrals
• 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
• Using differential equations to compute two-loop box integrals
• Application and explicit solution of recurrence relations with respect to space-time dimension
• Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box
• Planar box diagram for the (N_F = 1) 2-loop QED virtual corrections to Bhabha scattering
• Double-Higgs boson production in the high-energy limit: planar master integrals
• Removing infrared divergences from two-loop integrals
• Two-loop QED Operator Matrix Elements with Massive External Fermion Lines
• Master integrals for the four-loop Sudakov form factor
• Duality between Wilson loops and gluon amplitudes
• Higgs boson contribution to the leading two-loop Yukawa corrections to $gg\to HH$
• Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order
• The Two-Loop Four-Graviton Scattering Amplitudes
• Multivariate Residues and Maximal Unitarity
• Differential equations on unitarity cut surfaces
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• 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
• Unitarity Cuts of Integrals with Doubled Propagators
• An all order identity between ABJM and N=4 SYM four-point amplitudes
• The Leading Power Regge Asymptotic Behaviour of Dimensionally Regularized Massless On-Shell Planar Triple Box
• Global Residues and Two-Loop Hepta-Cuts
• Towards All Loop Supergravity Amplitudes on $Ad{S}_5\times S^5$
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• Evaluating multiloop Feynman integrals by Mellin-Barnes representation
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions
• Reduction and evaluation of two-loop graphs with arbitrary masses
• Progress towards 2 to 2 scattering at two-loops
• General massive one-loop off-shell three-point functions
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• Evaluating Two-Loop massive Operator Matrix Elements with Mellin-Barnes Integrals
• N=4 Super-Yang-Mills Theory, QCD and Collider Physics
• Recent Progress in Perturbative Quantum Field Theory
• Radiative Corrections to the Azimuthal Asymmetry in Transversely Polarized Moller Scattering
• The Two-Loop Infrared Structure of Amplitudes with Mixed Gauge Groups
• Some recent results on evaluating Feynman integrals
• Evaluating double and triple (?) boxes
• Two-Loop Diagrammatics in a Self-Dual Background
• Some methods to evaluate complicated Feynman integrals
• Non-planar double-box, massive and massless pentabox Feynman integrals in negative dimensional approach
• Jet Physics at Two-Loop Accuracy
• Exact non-factorizable O(alpha_s g^2) two-loop contribution to Z -> b bbar
• Two-Loop QCD-EW Master Integrals for Z Plus Jet Production at Large Transverse Momentum
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• (Quasi)elastic electron--muon large-angle scattering to a two-loop approximation: vertex contributions
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Two-loop Splitting Amplitudes
• Two-loop corrections to $gg\to \gamma \gamma$