Two-Loop QCD Helicity Amplitudes for $e^{+}{e}^{-}\to 3$~Jets

Abstract

We compute the two-loop QCD helicity amplitudes for the process e^+e^- --> q bar{q} g. The amplitudes are extracted in a scheme-independent manner from the coefficients appearing in the general tensorial structure for this process. The tensor coefficients are derived from the Feynman graph amplitudes by means of projectors, within the conventional dimensional regularization scheme. The actual calculation of the loop integrals is then performed by reducing all of them to a small set of known master integrals. The infrared pole structure of the renormalized helicity amplitudes agrees with the prediction made by Catani using an infrared factorization formula. We use this formula to structure our results for the finite part into terms arising from the expansion of the pole coefficients and a genuine finite remainder, which is independent of the scheme used to define the helicity amplitudes. The analytic result for the finite parts of the amplitudes is expressed in terms of one- and two-dimensional harmonic polylogarithms.

Misprints corrected in eqs. (2.17) and (2.38), Note added about recent independent confirmation of part of the results; files with FORM expressions for the amplitudes (Omega1.out, Omega2.out) are included unchanged

References in corpus (49)

• Harmonic Polylogarithms
• Differential Equations for Two-Loop Four-Point Functions
• New features of FORM
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• An automatized algorithm to compute infrared divergent multi-loop integrals
• One-Loop Amplitudes for e^+ e^- to Four Partons
• TESLA Technical Design Report Part III: Physics at an e+e- Linear Collider
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• 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
• Numerical Evaluation of Harmonic Polylogarithms
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• Double Unresolved Approximations to Multiparton Scattering Amplitudes
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Virtual corrections to gg -> H to two loops in the heavy top limit
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Two-loop QCD corrections to gluon-gluon scattering
• Collinear Factorization and Splitting Functions for Next-to-next-to-leading Order QCD Calculations
• All-Order Collinear Behavior in Gauge Theories
• Determination of the QCD Coupling ${\alpha }_s$
• The Two-Loop QCD Matrix Element for $e^{+}{e}^{-}\to 3$ Jets
• Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms
• Two-Loop Amplitudes for Gluon Fusion into Two Photons
• 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
• Two-Loop Correction to Bhabha Scattering
• Two-loop QED and QCD corrections to massless fermion-boson scattering
• A complete $\mathcal{O}(\alpha {\alpha }_s)$ calculation of the Photon + 1 Jet rate in $e^{+}{e}^{-}$ annihilation
• The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
• Symbolic Expansion of Transcendental Functions
• Analytic Continuation of Massless Two-Loop Four-Point Functions
• The One-loop QCD Corrections for gamma^* to q qbar gg
• The on-shell massless planar double box diagram with an irreducible numerator
• Two-loop corrections to Light-by-Light scattering in Supersymmetric QED
• Complete Order alpha_s^3 Results for e^+ e^- to (gamma,Z) to Four Jets
• Using differential equations to compute two-loop box integrals
• Analytical Result for Dimensionally Regularized Massless Master Double Box with One Leg off Shell
• Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell
• Radiative Corrections to the Photon + 1 Jet Rate at LEP
• Three-Jet Event Orientation in e+e- Annihilation: New Tests of the Standard Model

Cited by in corpus (130)

• Antenna Subtraction at NNLO
• QCD and strongly coupled gauge theories: challenges and perspectives
• Numerical evaluation of multiple polylogarithms
• Multi-loop Amplitudes and Resummation
• Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning
• Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
• Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Precise QCD predictions for the production of a Z boson in association with a hadronic jet
• NNLO corrections to event shapes in $e^{+}{e}^{-}$ annihilation
• Numerical evaluation of multi-loop integrals by sector decomposition
• Feynman Diagrams and Differential Equations
• NNLO corrections to 3-jet observables in electron-positron annihilation
• On the NNLO QCD corrections to single-top production at the LHC
• Infrared Structure of $e^{+}{e}^{-}\to 2$ jets at NNLO
• Gluon-Gluon Antenna Functions from Higgs Boson Decay
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• Quark-Gluon Antenna Functions from Neutralino Decay
• Two-Loop QCD Corrections to the Helicity Amplitudes for $H\to$ 3 partons
• Second-order QCD corrections to the thrust distribution
• Numerical evaluation of phase space integrals by sector decomposition
• Antenna subtraction at NNLO with hadronic initial states: initial-final configurations
• Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• Four-Particle Phase Space Integrals in Massless QCD
• Physics at the e+ e- Linear Collider
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Event shapes and jet rates in electron-positron annihilation at NNLO
• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• A subtraction scheme for NNLO computations
• Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations
• Jet rates in electron-positron annihilation at O(α_s^3) in QCD
• Subleading Power Corrections for N-Jettiness Subtractions
• Three-jet production in electron-positron collisions using the CoLoRFulNNLO method
• Subtraction terms at NNLO
• Infrared structure of e+e- --> 3 jets at NNLO
• The two-loop soft current in dimensional regularization
• Two-loop splitting functions in QCD
• The gluon jet function at two-loop order
• First determination of the strong coupling constant using NNLO predictions for hadronic event shapes in e^+e^- annihilations
• Single soft gluon emission at two loops
• 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
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e- annihilations
• A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
• NNLO moments of event shapes in e+e- annihilation
• The three-loop form factor in N=4 super Yang-Mills
• Two-loop QCD helicity amplitudes for $q\bar{q}\to W^{\pm }\gamma$ and $q\bar{q}\to Z^0\gamma$
• Subtraction terms for one-loop amplitudes with one unresolved parton
• The transverse momentum spectrum of weak gauge bosons at N${}^3$LL+NNLO
• NNLO QCD corrections to the transverse momentum distribution of weak gauge bosons
• NNLO QCD corrections to jet production in deep inelastic scattering
• 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
• Theoretical uncertainties on alpha_s from event-shape variables in e+e- annihilations
• Di-lepton Rapidity Distribution in Drell-Yan Production to Third Order in QCD
• A Complete Basis of Helicity Operators for Subleading Factorization
• Two-loop QCD helicity amplitudes for massless quark-quark scattering
• Fiducial Drell-Yan production at the LHC improved by transverse-momentum resummation at N${}^4$LL+N${}^3$LO
• Tensor decomposition for bosonic and fermionic scattering amplitudes
• Progress in NNLO calculations for scattering processes
• Precise QCD predictions for the production of dijet final states in deep inelastic scattering
• Master Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs
• Two-loop amplitudes with nested sums: Fermionic contributions to e+ e- --> q qbar g
• Three-loop master integrals for ladder-box diagrams with one massive leg
• Numerical evaluation of loop integrals
• The infrared structure of e+ e- --> 3 jets at NNLO reloaded
• Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box
• The one-loop gluon amplitude for heavy-quark production at NNLO
• Precision direct photon and W-boson spectra at high p_T and comparison to LHC data
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• Electroweak corrections to monojet production at the Tevatron and the LHC
• Two-loop leading colour QCD corrections to $q\bar{q}\to \gamma \gamma g$ and $qg\to \gamma \gamma q$
• The Soft Quark Sudakov
• Moments of event shapes in electron-positron annihilation at NNLO
• Transverse-momentum spectra of electroweak bosons near threshold at NNLO
• Two-loop QCD helicity amplitudes for $gg\to Zg$ and $gg\to Z\gamma$
• The electron self-energy in QED at two loops revisited
• Muon-electron scattering at NNLO
• Jet cross sections at the LHC and the quest for higher precision
• Electroweak Sudakov effects in W, Z and gamma production at large transverse momentum
• NNLO soft function for electroweak boson production at large transverse momentum
• Employing Helicity Amplitudes for Resummation
• $Z\gamma$ production at NNLO including anomalous couplings
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• Two-Loop Tensor Integrals in Quantum Field Theory
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• Jet algorithms in electron-positron annihilation: Perturbative higher order predictions
• NNLO corrections to 2-jet observables in electron-positron annihilation
• NNLO QCD corrections to event orientation in e+e- annihilation
• Evolution Kernels from Splitting Amplitudes
• s-channel Single Top Quark Production and Decay at NNLO in QCD
• The LBK theorem to all orders
• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
• Third order QCD predictions for fiducial W-boson production
• Calculations for deep inelastic scattering using fast interpolation grid techniques at NNLO in QCD and the extraction of ${\alpha }_s$ from HERA data
• Towards e+e- --> 3 jets at NNLO by sector decomposition
• Dijet production in diffractive deep-inelastic scattering in next-to-next-to-leading order QCD
• NNLO QCD Corrections to Jet Production in Charged Current Deep Inelastic Scattering
• Two-Loop QCD Helicity Amplitudes for (2+1)-Jet Production in Deep Inelastic Scattering
• Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?
• General massive one-loop off-shell three-point functions
• Reduction of Feynman Integrals in the Parametric Representation II: Reduction of Tensor Integrals
• Recent Progress in Perturbative Quantum Field Theory
• One-loop N-point equivalence among negative-dimensional, Mellin-Barnes and Feynman parametrization approaches to Feynman integrals
• Vector Bosons and Jets in Proton Collisions
• Full One-loop Electro-Weak Corrections to Three-jet Observables at the Z pole and Beyond
• Weak Corrections to Three-Jet Production in Electron-Positron Annihilations: 1) The Factorisable Contributions
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• The sector decomposition approach to real radiation at NNLO
• Two-loop QCD corrections to the $V\to q\bar{q}g$ helicity amplitudes with axial-vector couplings
• Status of jet cross sections to NNLO
• Two-Loop Diagrammatics in a Self-Dual Background
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• Jet production at electron-positron colliders at next-to-next-to-next-to-leading order in QCD
• Jet Physics at Two-Loop Accuracy
• Two-loop mixed QCD-electroweak amplitudes for $Z+$jet production at the LHC: bosonic corrections
• QCD: Theoretical Developments
• EERAD3 version 2: QCD corrections in hadronic colour-singlet decays
• Jet physics at hadron colliders
• Effective Field Theories for the LHC
• Infrared finite cross sections at NNLO
• QCD Beyond Leading Power
• Monte Carlo Event Generators for Future Lepton Colliders
• Two-loop corrections to $gg\to \gamma \gamma$
• Theoretical Developments on Hard QCD Processes at Colliders