Two-loop splitting functions in QCD

Abstract

We present the universal two-loop splitting functions that describe the limits of two-loop $n$-point amplitudes of massless particles when two of the momenta are collinear. To derive the splitting amplitudes, we take the collinear limits of explicit two-loop four-point helicity amplitudes computed in the 't Hooft-Veltman scheme. The $g\to gg$ splitting amplitude has recently been computed using the unitarity sewing method and we find complete agreement with the results of Ref. \cite{Bern:2lsplit}. The two-loop $q\to qg$ and $g\to q\bar{q}$ splitting functions are new results. We also provide an expression for the two-loop soft splitting function.

28 pages, 3 encapsulated postscript figures, JHEP3 class

References in corpus (67)

• A General Algorithm for Calculating Jet Cross Sections in NLO QCD
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Differential Equations for Two-Loop Four-Point Functions
• Three-jet cross sections to next-to-leading order
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• New features of FORM
• Multi-Parton Amplitudes in Gauge Theories
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Soft-gluon resummation for Higgs boson production at hadron colliders
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Multi-loop Amplitudes and Resummation
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• Calculating Scattering Amplitudes Efficiently
• Massive Loop Amplitudes from Unitarity
• Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond
• Progress in One-Loop QCD Computations
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• One-Loop Splitting Amplitudes in Gauge Theory
• The soft-gluon current at one-loop order
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• Double Unresolved Approximations to Multiparton Scattering Amplitudes
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Factorization in One-Loop Gauge Theory
• A new method for real radiation at NNLO
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• 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
• Infrared Structure of $e^{+}{e}^{-}\to 2$ jets at NNLO
• Collinear Factorization and Splitting Functions for Next-to-next-to-leading Order QCD Calculations
• All-Order Collinear Behavior in Gauge Theories
• NNLO evolution of deep-inelastic structure functions: the singlet case
• Two-Loop QCD Helicity Amplitudes for $e^{+}{e}^{-}\to 3$~Jets
• The Two-Loop QCD Matrix Element for $e^{+}{e}^{-}\to 3$ Jets
• NNLO evolution of deep-inelastic structure functions: the non-singlet case
• Numerical evaluation of phase space integrals by sector decomposition
• Two-Loop Amplitudes for Gluon Fusion into Two Photons
• 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
• Subtraction terms at NNLO
• 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
• 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
• Subtraction terms for one-loop amplitudes with one unresolved parton
• H-->ggg(gqqbar) at Two Loops in the Large-M_t Limit
• Real radiation at NNLO: e^+e^- to 2 jets through O(alpha_s^2)
• Two-loop QCD helicity amplitudes for massless quark-massless gauge boson scattering
• The triple collinear limit of one-loop QCD amplitudes
• Two-loop corrections to Light-by-Light scattering in Supersymmetric QED
• Two-loop QCD helicity amplitudes for massless quark-quark scattering
• Non-Singlet Structure Functions at Three Loops: Fermionic Contributions
• A numerical method for NNLO calculations
• Four jet event shapes in electron-positron annihilation
• All-Orders Singular Emission in Gauge Theories
• Evolution Kernels from Splitting Amplitudes

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