Massive Loop Amplitudes from Unitarity

Abstract

We show, for previously uncalculated examples containing a uniform mass in the loop, that it is possible to obtain complete massive one-loop gauge theory amplitudes solely from unitarity and known ultraviolet or infrared mass singularities. In particular, we calculate four-gluon scattering via massive quark loops in QCD. The contribution of a heavy quark to five-gluon scattering with identical helicities is also presented.

Minor modifications, 27 pages including two figures

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Cited by in corpus (264)

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• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Gravity as the Square of Gauge Theory
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Direct extraction of one-loop integral coefficients
• Full one-loop amplitudes from tree amplitudes
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• 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
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• One-Loop Self-Dual and N=4 Super Yang-Mills
• D-dimensional unitarity cut method
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• On D=5 super Yang-Mills theory and (2,0) theory
• Automated one-loop calculations: a proof of concept
• Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
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• Towards a Basis for Planar Two-Loop Integrals
• Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
• Perturbative Quantum Gravity and its Relation to Gauge Theory
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
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• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
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• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
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• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
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• A Two-Loop Five-Gluon Helicity Amplitude in QCD
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• Next-to-Leading Order QCD Predictions for Z,gamma^*+3-Jet Distributions at the Tevatron
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• Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Feynman Rules for the Rational Part of the QCD 1-loop amplitudes
• Direct Extraction Of One Loop Rational Terms
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Basics of Generalized Unitarity
• Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
• Hepta-Cuts of Two-Loop Scattering Amplitudes
• Four-Jet Production at the Large Hadron Collider at Next-to-Leading Order in QCD
• 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 Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• The Last of the Finite Loop Amplitudes in QCD
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• Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
• Maximal Unitarity at Two Loops
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• More on Soft Theorems: Trees, Loops and Strings
• Recursive numerical calculus of one-loop tensor integrals
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• 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
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• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
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• Loop amplitudes in gauge theories: modern analytic approaches
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• All tree-level amplitudes in massless QCD
• A geometrical angle on Feynman integrals
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• The Sub-Leading Scattering Waveform from Amplitudes
• Infinities within graviton scattering amplitudes
• Integrand reduction of one-loop scattering amplitudes through Laurent series expansion
• Tensorial Reconstruction at the Integrand Level
• On the U(1) duality anomaly and the S-matrix of N=4 supergravity
• Inelastic Exponentiation and Classical Gravitational Scattering at One Loop
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Loops in Twistor Space
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Multi-Gluon Collinear Limits from MHV diagrams
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• One-loop Higgs plus four gluon amplitudes: Full analytic results
• Closed-Form Decomposition of One-Loop Massive Amplitudes
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• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Duals of Feynman Integrals, I: Differential Equations
• Adaptive Integrand Decomposition in parallel and orthogonal space
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• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Automated computation of one-loop integrals in massless theories
• Double-Copy Constructions and Unitarity Cuts
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• Non-renormalization and operator mixing via on-shell methods
• SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks
• Two-Loop Maximal Unitarity with External Masses
• A simple method for multi-leg loop calculations
• The one-loop gluon amplitude for heavy-quark production at NNLO
• Analytic results for the one-loop NMHV Hqqgg amplitude
• Loops on the Celestial Sphere
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• All-Multiplicity One-Loop Corrections to MHV Amplitudes in QCD
• The rational parts of one-loop QCD amplitudes I: The general formalism
• One-loop MHV Rules and Pure Yang-Mills
• Simplicity in the Structure of QED and Gravity Amplitudes
• Scattering Amplitudes in Quantum Field Theory
• Local integrands for two-loop all-plus Yang-Mills amplitudes
• Loop-Level Double-Copy for Massive Quantum Particles
• Susy Theories and QCD: Numerical Approaches
• Analytic Structure of Three-Mass Triangle Coefficients
• Amplitudes in Pure Yang-Mills and MHV Diagrams
• Collinear Limits in QCD from MHV Rules
• 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
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• New structures in scattering amplitudes: a review
• Multivariate Residues and Maximal Unitarity
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• Colour Decompositions of Multi-quark One-loop QCD Amplitudes
• The rational parts of one-loop QCD amplitudes III: The six-gluon case
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• Next-to-Leading Order Gamma Gamma + 2-Jet Production at the LHC
• One-Loop Gluonic Amplitudes from Single Unitarity Cuts
• A simple method for multi-leg loop calculations 2: a general algorithm
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• Building Bases of Loop Integrands
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Solving for tadpole coefficients in one-loop amplitudes
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• Augmented Recursion For One-loop Gravity Amplitudes
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• The Unitarity Method using a Canonical Basis Approach
• From correlation functions to event shapes in QCD
• NLO QCD Predictions for $Wb\bar{b}$ Production in Association with up to Three Light Jets at the LHC
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• The rational parts of one-loop QCD amplitudes II: The five-gluon case
• One-Loop Calculations with BlackHat
• Reduction of multi-leg loop integrals
• A minimal approach to the scattering of physical massless bosons
• Extracting Einstein from the Loop-Level Double-Copy
• Cross-Order Integral Relations from Maximal Cuts
• Unitarity Method with Spurious Pole
• An Elliptic Yangian-Invariant, `Leading Singularity'
• A unitarity compatible approach to one-loop amplitudes with massive fermions
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Gravity and Form Scattering and Renormalisation of Gravity in Six and Eight Dimensions
• The Noncommutative S-Matrix
• One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized Unitarity
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• One-loop corrections to the D3 brane action
• Complex Factorisation and Recursion for One-Loop Amplitudes
• All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity
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• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• External leg corrections in the unitarity method
• Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• The BlackHat Library for One-Loop Amplitudes
• Generalised Unitarity At One-Loop With Massive Fermions
• Precise top-quark mass from the diphoton mass spectrum
• On the amplitudes in N=(1,1) D=6 SYM
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• On Perturbative Gravity and Gauge Theory
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
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• Testing and improving the numerical accuracy of the NLO predictions
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• The $\mathcal{N}=4$ Supergravity NMHV six-point one-loop amplitude
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• Two-Loop Diagrammatics in a Self-Dual Background
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• Illustrations of Integrand-Basis Building at Two Loops
• Quantum Effects for Black Holes with On-Shell Amplitudes
• Rational Terms in Theories with Matter
• Analytic Computations of Massive One-Loop Amplitudes
• Augmented Recursion For One-loop Amplitudes
• Ultra-Violet Infinities and Counterterms in Higher Dimensional Yang-Mills
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
• Generalized unitarity method for unstable particles
• How to Integrate Divergent Integrals: a Pure Numerical Approach to Complex Loop Calculations
• Photon pair production in gluon fusion: Top quark effects at NLO with threshold matching
• On Higgs boson plus gluon amplitudes at one loop
• S-matrix equivalence restored
• Analytic structure of one-loop coefficients
• Automated computation of scattering amplitudes
• Application of BCFW-recursion relations and the Feynman-tree theorem to the four gluon amplitude with all plus helicities
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Coulomb Phase Gluon Scattering at Strong Coupling
• Two-loop Splitting Amplitudes
• Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD
• On the Cuts of Scattering Amplitudes
• Back-to-back heavy quark pair production in Semi-inclusive DIS
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Two-loop corrections to $gg\to \gamma \gamma$
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity