Progress in One-Loop QCD Computations

Abstract

We review progress in calculating one-loop scattering amplitudes required for next-to-leading-order corrections to QCD processes. The underlying technical developments include the spinor helicity formalism, color decompositions, supersymmetry, string theory, factorization and unitarity. We provide explicit examples illustrating these techniques.

To appear in Annual Reviews of Nuclear and Particle Science (1996)

References in corpus (1)

• Multi-Parton Amplitudes in Gauge Theories

Cited by in corpus (244)

• New Relations for Gauge-Theory Amplitudes
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• MHV Vertices And Tree Amplitudes In Gauge Theory
• What is the Simplest Quantum Field Theory?
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• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
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• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data
• Hard Interactions of Quarks and Gluons: a Primer for LHC Physics
• Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Three-Loop Superfiniteness of N=8 Supergravity
• On-Shell Methods in Perturbative QCD
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• On the Tree-Level S-Matrix of Yang-Mills Theory
• One-Loop Splitting Amplitudes in Gauge Theory
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• The elliptic dilogarithm for the sunset graph
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• D-dimensional unitarity cut method
• One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Towards a Basis for Planar Two-Loop Integrals
• Perturbative Quantum Gravity and its Relation to Gauge Theory
• 50 Years of Quantum Chromodynamics
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
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• An algebraic/numerical formalism for one-loop multi-leg amplitudes
• Two-loop QCD corrections to gluon-gluon scattering
• One-Loop Amplitudes Of Gluons In SQCD
• Collinear Factorization and Splitting Functions for Next-to-next-to-leading Order QCD Calculations
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• Uniqueness of two-loop master contours
• All-Order Collinear Behavior in Gauge Theories
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Is N = 8 Supergravity Ultraviolet Finite?
• A new approach to multi-jet calculations in hadron collisions
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• The Cut-Constructible Part of QCD Amplitudes
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• NLO QCD corrections to top quark pair production in association with one hard jet at hadron colliders
• Color-Kinematics Duality for 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
• Neutralino Annihilation into Two Photons
• Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
• Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• A Feynman integral via higher normal functions
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• Basics of Generalized Unitarity
• Next-to-Leading Order W + 5-Jet Production at the LHC
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• On the Coupling of Gravitons to Matter
• MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos
• $Apart: A Generalized Mathematica Apart Function
• The Last of the Finite Loop Amplitudes in QCD
• Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
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• Maximal Unitarity at Two Loops
• Next-to-leading order QCD predictions for W+W+jj production at the LHC
• QCD corrections to top quark pair production in association with a photon at hadron colliders
• Two-loop splitting functions in QCD
• All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Multiple Singular Emission in Gauge Theories
• The Heisenberg-Euler Effective Action: 75 years on
• The Googly Amplitudes in Gauge Theory
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
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• Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory
• 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
• Generalized Unitarity and Six-Dimensional Helicity
• Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
• Quark-gluon vertex in arbitrary gauge and dimension
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
• Regularization Scheme Independence and Unitarity in QCD Cross Sections
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Algebraic evaluation of rational polynomials in one-loop amplitudes
• Cubic Twistorial String Field Theory
• The One-loop QCD Corrections for gamma^* to q qbar gg
• An Approach Toward the Numerical Evaluation of Multi-Loop Feynman Diagrams
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Prescriptive Unitarity
• How Far Are We from the Quantum Theory of Gravity?
• On the U(1) duality anomaly and the S-matrix of N=4 supergravity
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Loops in Twistor Space
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• H-->ggg(gqqbar) at Two Loops in the Large-M_t Limit
• Multi-Gluon Collinear Limits from MHV diagrams
• Self-dual Yang--Mills Theory and One-Loop Maximally Helicity Violating Multi-Gluon Amplitudes
• Double Copy from Homotopy Algebras
• Integral Coefficients for One-Loop Amplitudes
• One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity
• All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
• One-loop amplitudes for W+3 jet production in hadron collisions
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• All-Multiplicity Amplitudes with Massive Scalars
• NLO QCD corrections for W^+W^- pair production in association with two jets at hadron colliders
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Double-Copy Constructions and Unitarity Cuts
• Next-to-Leading Order Calculation of Four-Jet Shape Variables
• The Form Factors of the Gauge-Invariant Three-Gluon Vertex
• All Split Helicity Tree-Level Gluon Amplitudes
• Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
• On BCFW shifts of integrands and integrals
• Recursive Construction of Higgs-Plus-Multiparton Loop Amplitudes: The Last of the Phi-nite Loop Amplitudes
• All-Orders Singular Emission in Gauge Theories
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• Simplifying Algebra in Feynman Graphs, Part II: Spinor Helicity from the Spacecone
• Two-Loop Maximal Unitarity with External Masses
• Using Dimensional Reduction for Hadronic Collisions
• The one-loop gluon amplitude for heavy-quark production at NNLO
• Direct Solution of Integration-by-Parts Systems
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• String theory and the mapping of gravity into gauge theory
• Landau Singularities from the Amplituhedron
• All-Multiplicity One-Loop Corrections to MHV Amplitudes in QCD
• The rational parts of one-loop QCD amplitudes I: The general formalism
• On the low-energy limit of the QED N-photon amplitudes
• Exact Combinatorics of Bern-Kosower-type Amplitudes for Two-Loop ${\Phi }^3$ Theory
• MHV Vertices and Scattering Amplitudes in Gauge Theory
• Little String Amplitudes (and the Unreasonable Effectiveness of 6D SYM)
• Susy Theories and QCD: Numerical Approaches
• On Form Factors in N=4 SYM Theory and Polytopes
• Collinear Limits in QCD from MHV Rules
• Multigluon amplitudes, $\mathcal{N}=4$ constraints and the WZW model
• A complete reduction of one-loop tensor 5- and 6-point integrals
• Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory
• Generalized string theory mapping relations between gravity and gauge theory
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• String Theory and Noncommutative Field Theories at One Loop
• New structures in scattering amplitudes: a review
• Tree-Level Formalism
• Amplitudes for Multiple M5 Branes
• Twistorial Analyticity and Three Stringy Systems of the Kerr Spinning Particle
• Colour Decompositions of Multi-quark One-loop QCD Amplitudes
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• The rational parts of one-loop QCD amplitudes III: The six-gluon case
• CSW rules for a massive scalar
• Loop-level gluon OPEs in celestial holography
• Next-to-Leading Order Gamma Gamma + 2-Jet Production at the LHC
• Amplitudes at Infinity
• A simple method for multi-leg loop calculations 2: a general algorithm
• Simplifying Algebra in Feynman Graphs, Part I:Spinors
• Maximal Unitarity for the Four-Mass Double Box
• Quark scattering amplitudes at strong coupling
• On Soft Theorems And Form Factors In N=4 SYM Theory
• One-Loop Maximal Helicity Violating Amplitudes in N=4 Super Yang-Mills Theories
• Building Bases of Loop Integrands
• On-shell two-loop three-gluon vertex
• Perturbative Relations between Gravity and Gauge Theory
• Systematics of One-Loop Scattering Amplitudes in N=4 Super Yang-Mills Theories
• One-Loop Calculations with BlackHat
• On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes
• The rational parts of one-loop QCD amplitudes II: The five-gluon case
• Vector Boson + Jets with BlackHat and Sherpa
• Grassmannians and form factors with $q^2=0$ in N=4 SYM theory
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Simplifying Algebra in Feynman Graphs, Part III: Massive Vectors
• Cross-Order Integral Relations from Maximal Cuts
• Scalar field theory limits of bosonic string amplitudes
• Gravity and Form Scattering and Renormalisation of Gravity in Six and Eight Dimensions
• Double-real contribution to the quark beam function at N${}^3$LO QCD
• Multiloop ${\Phi }^3$ Amplitudes from Bosonic String Theory
• Colourful FKS subtraction
• Determination of Boundary Contributions in Recursion Relation
• One-loop corrections to the D3 brane action
• Two-loop Euler-Heisenberg effective actions from charged open strings
• The Pinch Technique Beyond One Loop: The Gauge-Independent Two-Loop Quark Self-Energy
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• On the amplitudes in N=(1,1) D=6 SYM
• Imaginary parts and discontinuities of Wilson line correlators
• N=4 Super-Yang-Mills Theory, QCD and Collider Physics
• A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory
• Recent Progress in Perturbative Quantum Field Theory
• Gravity loop integrands from the ultraviolet
• A compact representation of the 2 photon 3 gluon amplitude
• On the low-energy limit of the QED N-photon amplitudes: part 2
• Challenges of D=6 N=(1,1) SYM Theory
• N=2 Quantum String Scattering
• On Perturbative Gravity and Gauge Theory
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Color structures and permutations
• Hidden Beauty in Multiloop Amplitudes
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Nonlinear dynamics of soft boson excitations in hot QCD plasma I: plasmon-plasmon scattering
• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• Two-Loop ${\varphi }^4$-Diagrams from String Theory
• Four-jet production in $e^{+}{e}^{-}$ annihilation at next-to-leading order
• Position-space cuts for Wilson line correlators
• Six-jet production at lepton colliders
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Systematics of one-loop Yang-Mills diagrams from bosonic string amplitudes
• Integral representations of thermodynamic 1PI Green functions in the world-line formalism
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Dimensional Regularization and Dimensional Reduction in the Light Cone
• Confinement and the Supercritical Pomeron in QCD
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• Rotating Black Hole, Twistor-String and Spinning Particle
• Generalized unitarity method for unstable particles
• Ultra-Violet Infinities and Counterterms in Higher Dimensional Yang-Mills
• ABJM flux-tube and scattering amplitudes
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
• A technique for loop calculations in non-Abelian gauge theories - with application to five gluon amplitude
• How to Integrate Divergent Integrals: a Pure Numerical Approach to Complex Loop Calculations
• Gauge theory one-loop amplitudes and the BCFW recursion relations
• Tree and $1$-loop fundamental BCJ relations from soft theorems
• Bound-state gravity from higher derivatives
• Developments in perturbative QCD
• On Higgs boson plus gluon amplitudes at one loop
• Evaluation of Multi-Box Diagrams in Six Dimensions
• Unitarity methods for Mellin moments of Drell-Yan cross sections
• 1-loop Color structures and sunny diagrams
• Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD
• A Recursive Method to Calculate UV-divergent Parts at One-Loop Level in Dimensional Regularization
• Two-loop Splitting Amplitudes
• Applications of QCD
• Steps towards NNLO QCD calculations: collinear factorization at O(α_S^2)
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• Two-loop corrections to $gg\to \gamma \gamma$