D-dimensional unitarity cut method

Abstract

We develop a unitarity method to compute one-loop amplitudes with massless propagators in d=4-2*epsilon dimensions. We compute double cuts of the loop amplitudes via a decomposition into a four-dimensional and a -2*epsilon-dimensional integration. The four-dimensional integration is performed using spinor integration or other efficient techniques. The remaining integral in -2*epsilon dimensions is cast in terms of bubble, triangle, box, and pentagon master integrals using dimensional shift identities. The method yields results valid for arbitrary values of epsilon.

4 pages. v2: references changed

References in corpus (28)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• Higgs boson production at hadron colliders in NNLO QCD
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Dimensionally Regulated Pentagon Integrals
• Connection between Feynman integrals having different values of the space-time dimension
• Massive Loop Amplitudes from Unitarity
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• Dimensionally Regulated One-Loop Integrals
• Progress in One-Loop QCD Computations
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• One-Loop Self-Dual and N=4 Super Yang-Mills
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• One-Loop Amplitudes Of Gluons In SQCD
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• Gauge Theory Amplitudes In Twistor Space And Holomorphic Anomaly
• Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory
• The Cut-Constructible Part of QCD Amplitudes
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
• The Last of the Finite Loop Amplitudes in QCD
• Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity Cuts
• Loops in Twistor Space
• A Calculational Formalism for One-Loop Integrals
• Numerical Evaluation of One-Loop Diagrams Near Exceptional Momentum Configurations

Cited by in corpus (170)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• QCD and strongly coupled gauge theories: challenges and perspectives
• CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data
• Direct extraction of one-loop integral coefficients
• Full one-loop amplitudes from tree amplitudes
• On-Shell Methods in Perturbative QCD
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• On the Rational Terms of the one-loop amplitudes
• Automated one-loop calculations: a proof of concept
• Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
• Towards a Basis for Planar Two-Loop Integrals
• Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
• 50 Years of Quantum Chromodynamics
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• Masses, fermions and generalized D-dimensional unitarity
• Electroweak Radiative Corrections for Collider Physics
• Uniqueness of two-loop master contours
• 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
• Basics of Generalized 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
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• Unexpected Cancellations in Gravity Theories
• Maximal Unitarity at Two Loops
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Precise Predictions for Z + 4 Jets at Hadron Colliders
• Supertwistor space for 6D maximal super Yang-Mills
• Generalized Unitarity and Six-Dimensional Helicity
• Decomposition of Feynman Integrals by Multivariate Intersection Numbers
• On Triple-Cut of Scattering Amplitudes
• Loop amplitudes in gauge theories: modern analytic approaches
• NGluon: A Package to Calculate One-loop Multi-gluon Amplitudes
• On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
• All tree-level amplitudes in massless QCD
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Numerical Evaluation of Six-Photon Amplitudes
• Prescriptive Unitarity
• Numerical NLO QCD calculations
• Double-Cut of Scattering Amplitudes and Stokes' Theorem
• Optimizing the Reduction of One-Loop Amplitudes
• One-loop phi-MHV amplitudes using the unitarity bootstrap
• Integral Coefficients for One-Loop Amplitudes
• Closed-Form Decomposition of One-Loop Massive Amplitudes
• Analytic one-loop amplitudes for a Higgs boson plus four partons
• One-loop Higgs plus four gluon amplitudes: Full analytic results
• Duals of Feynman Integrals, I: Differential Equations
• Feynman rules for the rational part of the Electroweak 1-loop amplitudes
• Duals of Feynman Integrals, 2: Generalized Unitarity
• Two-Loop Maximal Unitarity with External Masses
• The one-loop gluon amplitude for heavy-quark production at NNLO
• On Genera of Curves from High-loop Generalized Unitarity Cuts
• Analytic results for the one-loop NMHV Hqqgg amplitude
• Direct Solution of Integration-by-Parts Systems
• Helicity amplitudes for QCD with massive quarks
• Six-Photon Amplitudes
• An Introduction to On-shell Recursion Relations
• One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case
• Cosmology meets cohomology
• One-loop MHV Rules and Pure Yang-Mills
• Simplicity in the Structure of QED and Gravity Amplitudes
• Renormalization Group Evolution from On-shell SMEFT
• Amplitudes in Pure Yang-Mills and MHV Diagrams
• Polynomial Structures in One-Loop Amplitudes
• Susy Theories and QCD: Numerical Approaches
• Analytic Structure of Three-Mass Triangle Coefficients
• The classification of two-loop integrand basis in pure four-dimension
• 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
• MCgrid: projecting cross section calculations on grids
• Multivariate Residues and Maximal Unitarity
• One-loop Amplitudes in Six-Dimensional (1,1) Theories from Generalised Unitarity
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Next-to-Leading Order Gamma Gamma + 2-Jet Production at the LHC
• One-Loop Gluonic Amplitudes from Single Unitarity Cuts
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Decomposition of one-loop QCD amplitudes into primitive amplitudes based on shuffle relations
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• Six-Photon Amplitudes in Scalar QED
• Manifestly Dual-Conformal Loop Integration
• Single Cut Integration
• Relations of loop partial amplitudes in gauge theory by Unitarity cut method
• Counting to one: reducibility of one- and two-loop amplitudes at the integrand level
• Numerical multi-loop integrals and applications
• Maximal Unitarity for the Four-Mass Double Box
• Simplifying $D$-Dimensional Physical-State Sums in Gauge Theory and Gravity
• Unitarity Cuts of Integrals with Doubled Propagators
• UV cancelations in gravity loop integrands
• On General BCJ Relation at One-loop Level in Yang-Mills Theory
• Solving for tadpole coefficients in one-loop amplitudes
• The Unitarity Method using a Canonical Basis Approach
• Augmented Recursion For One-loop Gravity Amplitudes
• Global Residues and Two-Loop Hepta-Cuts
• R2SM: a package for the analytic computation of the R2 Rational terms in the Standard Model of the Electroweak interactions
• One-Loop Calculations with BlackHat
• Non-planarity through unitarity in ABJM
• Prescriptive Unitarity with Elliptic Leading Singularities
• Unitarity Method with Spurious Pole
• Cross-Order Integral Relations from Maximal Cuts
• One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized Unitarity
• The Q-cut Representation of One-loop Integrands and Unitarity Cut Method
• A tale of tails through generalized unitarity
• EFT matching from analyticity and unitarity
• NLO QCD calculations with HELAC-NLO
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity
• One-loop Feynman Integral Reduction by Differential Operators
• Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams
• Generation Function For One-loop Tensor Reduction
• On-shell diagrammatics and the perturbative structure of planar gauge theories
• PV-Reduction of Sunset Topology with Auxiliary Vector
• The BlackHat Library for One-Loop Amplitudes
• On the amplitudes in N=(1,1) D=6 SYM
• Form Factor and Boundary Contribution of Amplitude
• Random polarisations of the dipoles
• A Fully Numerical Approach to One-Loop Amplitudes
• Reduction of General One-loop Integrals Using Auxiliary Vector
• Gravity loop integrands from the ultraviolet
• Dispersion theoretic calculation of the $H\to Z+\gamma$ amplitude
• Reduction with Degenerate Gram matrix for One-loop Integrals
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
• Massive Nonplanar Two-Loop Maximal Unitarity
• BCJ Relations for One-Loop QCD Integral Coefficients
• The n-point MHV one-loop Amplitude in N=4 Supergravity
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• The MHV Lagrangian for a spontaneously broken gauge theory
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
• Position-space cuts for Wilson line correlators
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Emergent unitarity from the amplituhedron
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• Nontrivial One-loop Recursive Reduction Relation
• The $\mathcal{N}=4$ Supergravity NMHV six-point one-loop amplitude
• Reduction of one-loop integrals with higher poles by unitarity cut method
• One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter
• Automated calculations for multi-leg processes
• Studies of Quantum Chromodynamics at the LHC
• Illustrations of Integrand-Basis Building at Two Loops
• Four photon production at the LHC: an application of 2->4 analytic unitarity
• Rational Terms in Theories with Matter
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
• Peaks and cusps: anomalous thresholds and LHC physics
• Augmented Recursion For One-loop Amplitudes
• Unitarity-Cuts and Berry's Phase
• Massive particles and unitarity cuts
• Cuts and coproducts of massive triangle diagrams
• Locally Finite Observables in sYM
• Analytic structure of one-loop coefficients
• All one-loop NMHV gluon amplitudes in N=1 SYM
• Scattering amplitudes in gauge theories with and without supersymmetry
• Application of BCFW-recursion relations and the Feynman-tree theorem to the four gluon amplitude with all plus helicities
• Integrated Unitarity for Scattering Amplitudes
• Automated computation of scattering amplitudes
• Proton structure at the LHC
• Particle Physics in the LHC Era and beyond
• On perturbative field theory and twistor string theory
• Cross Section Evaluation by Spinor Integration I: The massless case in 4D
• A Tale Of Two Amplitudes In High Energy Physics
• Cross Section Evaluation by Spinor Integration II: The massive case in 4D
• On the Cuts of Scattering Amplitudes
• General One-loop Reduction in Generalized Feynman Parametrization Form