The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole

Abstract

We extend the resummation of dimensionally-regulated amplitudes to next-to-next-to-leading poles. This requires the calculation of two-loop anomalous dimension matrices for color mixing through soft gluon exchange. Remarkably, we find that they are proportional to the corresponding one-loop matrices. Using the color generator notation, we reproduce the two-loop single-pole quantities H^(2) introduced by Catani for quark and gluon elastic scattering. Our results also make possible threshold and a variety of other resummations at next-to-next-to leading logarithm. All of these considerations apply to 2 to n processes with massless external lines.

52 pages, revtex, 4 eps figures

References in corpus (39)

• A General Algorithm for Calculating Jet Cross Sections in NLO QCD
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• The Dipole Formalism for the Calculation of QCD Jet Cross Sections at Next-to-Leading Order
• Resummation of non-global QCD observables
• Multi-loop Amplitudes and Resummation
• Factorization and high-energy effective action
• Evolution of Color Exchange in QCD Hard Scattering
• Three-Loop Results for Quark and Gluon Form Factors
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• Virtual corrections to gg -> H to two loops in the heavy top limit
• The Quark Form Factor at Higher Orders
• Two-loop QCD corrections to gluon-gluon scattering
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Threshold Resummation for Dijet Cross Sections
• Two-Loop QCD Helicity Amplitudes for $e^{+}{e}^{-}\to 3$~Jets
• The Two-Loop QCD Matrix Element for $e^{+}{e}^{-}\to 3$ Jets
• Effects of Higher-Order Threshold Corrections in High-E_T Jet Production
• Two-loop QCD corrections to the scattering of massless distinct quarks
• Two-loop QCD corrections to massless quark-gluon scattering
• Resummed event shapes at hadron-hadron colliders
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Sudakov resummation of multiparton QCD cross sections
• High energy scattering in QCD and cross singularities of Wilson loops
• Two-loop QCD corrections to massless identical quark scattering
• Two-loop corrections to Higgs boson production
• Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• Soft gluons at large angles in hadron collisions
• Two-Loop Electroweak Logarithms in Four-Fermion Processes at High Energy
• Two-loop QCD helicity amplitudes for massless quark-quark scattering
• Analytic resummation for the quark form factor in QCD
• Higher Orders in A(α_s)/[1-x]_+ of Non-Singlet Partonic Splitting Functions
• The colour evolution of the process q q -> q q g
• Hadron collisions and the fifth form factor
• Symmetry of Anomalous Dimension Matrices for Colour Evolution of Hard Scattering Processes
• The resummed quark form factor in dimensional regularization
• Scattering Amplitudes in High Energy QCD

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