The Last of the Finite Loop Amplitudes in QCD

Abstract

We use on-shell recursion relations to determine the one-loop QCD scattering amplitudes with a massless external quark pair and an arbitrary number (n-2) of positive-helicity gluons. These amplitudes are the last of the unknown infrared- and ultraviolet-finite loop amplitudes of QCD. The recursion relations are similar to ones applied at tree level, but contain new non-trivial features corresponding to poles present for complex momentum arguments but absent for real momenta. We present the relations and the compact solutions to them, valid for all n. We also present compact forms for the previously-computed one-loop n-gluon amplitudes with a single negative helicity and the rest positive helicity.

45 pages, revtex, 7 figures, v2 minor corrections

References in corpus (33)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Recursion Relations for Tree Amplitudes of Gluons
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Multi-Parton Amplitudes in Gauge Theories
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• One-Loop Amplitudes Of Gluons In SQCD
• Gauge Theory Amplitudes In Twistor Space And Holomorphic Anomaly
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory
• Non-Supersymmetric Loop Amplitudes and MHV Vertices
• Non-MHV Tree Amplitudes in Gauge Theory
• MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos
• Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity Cuts
• Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
• Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
• A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
• All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• One-Loop MHV Amplitudes in Supersymmetric Gauge Theories
• One-Loop Gluon Scattering Amplitudes in Theories with $N<4$ Supersymmetries
• Recursion Relations for Tree Amplitudes in Super Gauge Theories
• N=1 Supersymmetric One-loop Amplitudes and the Holomorphic Anomaly of Unitarity Cuts
• Dissolving N=4 loop amplitudes into QCD tree amplitudes
• MHV Rules for Higgs Plus Multi-Parton Amplitudes
• Twistor-Inspired Construction of Electroweak Vector Boson Currents
• Loops in Twistor Space
• All Split Helicity Tree-Level Gluon Amplitudes
• Compact Formulas for Tree Amplitudes of Six Partons
• Twistor Space Structure of the Box Coefficients of N=1 One-loop Amplitudes
• MHV Vertices and Scattering Amplitudes in Gauge Theory
• Multigluon amplitudes, $\mathcal{N}=4$ constraints and the WZW model

Cited by in corpus (88)

• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• On Tree Amplitudes in Gauge Theory and Gravity
• On-Shell Methods in Perturbative QCD
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• D-dimensional unitarity cut method
• Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
• Towards a Basis for Planar Two-Loop Integrals
• A direct proof of the CSW rules
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• Masses, fermions and generalized D-dimensional unitarity
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• Numerical evaluation of virtual corrections to multi-jet production in massless QCD
• The Cut-Constructible Part of QCD Amplitudes
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Next-to-Leading Order QCD Predictions for Z,gamma^*+3-Jet Distributions at the Tevatron
• Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
• Feynman Rules for the Rational Part of the QCD 1-loop amplitudes
• Direct Extraction Of One Loop Rational Terms
• Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
• Basics of Generalized Unitarity
• Taming Tree Amplitudes In General Relativity
• QCD corrections to tri-boson production
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Recursion Relations for Gauge Theory Amplitudes with Massive Vector Bosons and Fermions
• The No-Triangle Hypothesis for N=8 Supergravity
• Generalized Unitarity and Six-Dimensional Helicity
• Recursive Calculation of One-Loop QCD Integral Coefficients
• Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
• On Triple-Cut of Scattering Amplitudes
• On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
• NGluon: A Package to Calculate One-loop Multi-gluon Amplitudes
• Algebraic evaluation of rational polynomials in one-loop amplitudes
• MHV-Vertices for Gravity Amplitudes
• One-loop phi-MHV amplitudes using the unitarity bootstrap
• Integral Coefficients for One-Loop Amplitudes
• Analytic one-loop amplitudes for a Higgs boson plus four partons
• All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
• All-Multiplicity Amplitudes with Massive Scalars
• From Trees to Loops and Back
• Amplitudes in the beta-deformed Conformal Yang-Mills
• Recursive Construction of Higgs-Plus-Multiparton Loop Amplitudes: The Last of the Phi-nite Loop Amplitudes
• On-shell recursion relations for all Born QCD amplitudes
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case
• An Introduction to On-shell Recursion Relations
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• The one-loop amplitude for six-gluon scattering
• All-Multiplicity One-Loop Corrections to MHV Amplitudes in QCD
• The rational parts of one-loop QCD amplitudes I: The general formalism
• MHV Techniques for QED Processes
• Scattering Amplitudes in Quantum Field Theory
• Polynomial Structures in One-Loop Amplitudes
• Susy Theories and QCD: Numerical Approaches
• Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
• One-Loop Helicity Amplitudes for ttbar Production at Hadron Colliders
• Feynman rules for the rational part of the Electroweak 1-loop amplitudes in the R_xi gauge and in the Unitary gauge
• Tree-Level Formalism
• Scattering amplitudes with massive fermions using BCFW recursion
• The rational parts of one-loop QCD amplitudes III: The six-gluon case
• NLO QCD corrections to the production of t-tbar-Z in gluon fusion
• S-Matrix Equivalence Theorem Evasion and Dimensional Regularisation with the Canonical MHV Lagrangian
• Recursion Relations for One-Loop Gravity Amplitudes
• R2SM: a package for the analytic computation of the R2 Rational terms in the Standard Model of the Electroweak interactions
• The rational parts of one-loop QCD amplitudes II: The five-gluon case
• One-Loop NMHV Amplitudes involving Gluinos and Scalars in N=4 Gauge Theory
• Unitarity Method with Spurious Pole
• One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized Unitarity
• Seven parton amplitudes from recursion relations
• Massive Quark-Gluon Scattering Amplitudes at Tree Level
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
• One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds
• On-Shell Unitarity Bootstrap for QCD Amplitudes
• Recursion relations, Helicity Amplitudes and Dimensional Regularization
• The MHV Lagrangian for a spontaneously broken gauge theory
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Automated calculations for multi-leg processes
• The last of the seven-parton tree amplitudes
• Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
• MHV Lagrangians for Yang--Mills and QCD
• Numerical evaluation of one-loop QCD amplitudes
• On perturbative field theory and twistor string theory
• One-Loop Amplitudes in Supersymmetric QCD from MHV Vertices
• Recursive relations for a quiver gauge theory
• Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD
• A Tale Of Two Amplitudes In High Energy Physics