Two-loop QCD helicity amplitudes for massless quark-quark scattering

Abstract

We present the two-loop helicity amplitudes for the scattering of massless quarks in QCD. We use projector techniques to compute the coefficients of the general four-quark amplitude at up to two-loops in conventional dimensional regularisation and use these coefficients to derive the helicity amplitudes in the 't Hooft-Veltman scheme. The structure of the infrared divergences agrees with that predicted by Catani while expressions for the finite remainders for $q\bar{q}\to Q\bar{Q}$ and the processes related by crossing symmetry are given in terms of logarithms and polylogarithms that are real in the physical region. We have checked that the interference of tree and two-loop helicity amplitudes, summed over helicities and colours, reproduces the previous results for the finite remainders for interference of tree and two-loop amplitudes given in Refs. [1,2].

Latex, JHEP3 class, 68 pages, typos corrected, reference added

References in corpus (62)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Differential Equations for Two-Loop Four-Point Functions
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• New features of FORM
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Soft-gluon resummation for Higgs boson production at hadron colliders
• Higher Order Corrections to Jet Cross Sections in Hadron Colliders
• Multi-loop Amplitudes and Resummation
• One-Loop Corrections to Five-Gluon Amplitudes
• NNLO global parton analysis
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Evolution of Color Exchange in QCD Hard Scattering
• One-Loop Splitting Amplitudes in Gauge Theory
• The soft-gluon current at one-loop order
• The 3-loop QCD calculation of the moments of deep inelastic structure functions
• One-Loop Corrections to Two-Quark Three-Gluon Amplitudes
• A new method for real radiation at NNLO
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• Two-loop QCD corrections to gluon-gluon scattering
• NNLO evolution of deep-inelastic structure functions: the singlet case
• Two-Loop QCD Helicity Amplitudes for $e^{+}{e}^{-}\to 3$~Jets
• NNLO evolution of deep-inelastic structure functions: the non-singlet case
• One-loop helicity amplitudes for all 2 -> 2 processes in QCD and N=1 supersymmetric Yang-Mills theory
• Two-Loop Amplitudes for Gluon Fusion into Two Photons
• Some higher moments of deep inelastic structure functions at next-to-next-to leading order of perturbative QCD
• Four-Particle Phase Space Integrals in Massless QCD
• A Two-Loop Four-Gluon Helicity Amplitude in QCD
• Two-loop QCD corrections to the scattering of massless distinct quarks
• QCD and QED Corrections to Light-by-Light Scattering
• Two-loop QCD corrections to massless quark-gluon scattering
• Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
• Subtraction terms at NNLO
• Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering
• Two-Loop Correction to Bhabha Scattering
• 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
• The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
• One-loop radiative corrections to the helicity amplitudes of QCD processes involving four quarks and one gluon
• Improved Approximations for the Three-Loop Splitting Functions in QCD
• Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
• Antenna Factorization in Strongly-Ordered Limits
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• Scalar One-Loop Integrals using the Negative-Dimension Approach
• The two-loop scalar and tensor pentabox graph with light-like legs
• The on-shell massless planar double box diagram with an irreducible numerator
• Two-loop QCD helicity amplitudes for massless quark-massless gauge boson scattering
• Application of the negative-dimension approach to massless scalar box integrals
• Two-loop corrections to Light-by-Light scattering in Supersymmetric QED
• Progress in NNLO calculations for scattering processes
• All-Orders Singular Emission in Gauge Theories
• Estimating the effect of NNLO contributions on global parton analyses
• Higher Orders in A(α_s)/[1-x]_+ of Non-Singlet Partonic Splitting Functions
• The QCD/SM Working Group: Summary Report
• The Inclusive Two Jet Triply Differential Cross Section
• One-loop QCD corrections to quark scattering at NNLO
• One-loop QCD corrections to gluon-gluon scattering at NNLO
• Evolution Kernels from Splitting Amplitudes
• First results for three-loop deep-inelastic structure functions in QCD
• Jet Physics at Two-Loop Accuracy

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