Maximal Unitarity for the Four-Mass Double Box
arXiv:1308.4632 · doi:10.1103/PhysRevD.89.125010
Abstract
We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero- through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals, and show how discrete symmetries of these varieties largely determine the constraints.
25 pages, 3 figures; final journal version
References in corpus (105)
- Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
- Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
- Multiloop integrals in dimensional regularization made simple
- Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
- Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes
- Algorithm FIRE -- Feynman Integral REduction
- An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
- Automation of one-loop QCD corrections
- The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
- The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
- Local Integrals for Planar Scattering Amplitudes
- Reduze - Feynman Integral Reduction in C++
- Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
- A Duality For The S Matrix
- The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
- Automatic Integral Reduction for Higher Order Perturbative Calculations
- Direct extraction of one-loop integral coefficients
- Full one-loop amplitudes from tree amplitudes
- On-Shell Methods in Perturbative QCD
- On the Tree-Level S-Matrix of Yang-Mills Theory
- The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
- Assault on the NLO Wishlist: pp -> tt bb
- Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
- A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
- Precise Predictions for W + 4 Jet Production at the Large Hadron Collider
- D-dimensional unitarity cut method
- Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
- Two-Loop g -> gg Splitting Amplitudes in QCD
- Towards a Basis for Planar Two-Loop Integrals
- Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
- Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
- Precise Predictions for W + 3 Jet Production at Hadron Colliders
- Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
- Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
- NNLO corrections to 3-jet observables in electron-positron annihilation
- One-Loop Amplitudes Of Gluons In SQCD
- Uniqueness of two-loop master contours
- Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
- Two-Loop Amplitudes for Gluon Fusion into Two Photons
- Bootstrapping Multi-Parton Loop Amplitudes in QCD
- The Cut-Constructible Part of QCD Amplitudes
- Next-to-Leading Order QCD Predictions for Z,gamma^*+3-Jet Distributions at the Tevatron
- Unification of Residues and Grassmannian Dualities
- Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
- Direct Extraction Of One Loop Rational Terms
- The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
- Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
- W+3 jet production at the Tevatron
- Hepta-Cuts of Two-Loop Scattering Amplitudes
- Infrared structure of e+e- --> 3 jets at NNLO
- Next-to-Leading Order W + 5-Jet Production at the LHC
- Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
- On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
- Scattering Amplitudes from Multivariate Polynomial Division
- Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity Cuts
- Maximal Unitarity at Two Loops
- Generalized unitarity at work: first NLO QCD results for hadronic W+3jet production
- Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
- Precise Predictions for Z + 4 Jets at Hadron Colliders
- Sharpening The Leading Singularity
- Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
- Generalized Unitarity and Six-Dimensional Helicity
- Recursive Calculation of One-Loop QCD Integral Coefficients
- On Triple-Cut of Scattering Amplitudes
- Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
- One-Loop Gluon Scattering Amplitudes in Theories with Supersymmetries
- On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
- NGluon: A Package to Calculate One-loop Multi-gluon Amplitudes
- Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e- annihilations
- Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
- N=1 Supersymmetric One-loop Amplitudes and the Holomorphic Anomaly of Unitarity Cuts
- Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
- Generic multiloop methods and application to N=4 super-Yang-Mills
- A Note on Polytopes for Scattering Amplitudes
- Optimizing the Reduction of One-Loop Amplitudes
- Precise determination of the strong coupling constant at NNLO in QCD from the three-jet rate in electron--positron annihilation at LEP
- Integral Coefficients for One-Loop Amplitudes
- Closed-Form Decomposition of One-Loop Massive Amplitudes
- Analytic results for two-loop master integrals for Bhabha scattering I
- Calculation of master integrals by difference equations
- One-loop amplitudes for W+3 jet production in hadron collisions
- Scattering Amplitudes and BCFW Recursion in Twistor Space
- N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
- Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
- NLO QCD corrections to multi-jet production at the LHC with a centre-of-mass energy of sqrt(s)=8 TeV
- Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
- Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
- The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
- Two-Loop Maximal Unitarity with External Masses
- W+3 jet production at the LHC as a signal or background
- On Genera of Curves from High-loop Generalized Unitarity Cuts
- Multiloop Integrand Reduction for Dimensionally Regulated Amplitudes
- The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
- Polynomial Structures in One-Loop Amplitudes
- Analytic Structure of Three-Mass Triangle Coefficients
- An Integrand Reconstruction Method for Three-Loop Amplitudes
- The classification of two-loop integrand basis in pure four-dimension
- Multi-Parton Scattering Amplitudes via On-Shell Methods
- Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
- Counting to one: reducibility of one- and two-loop amplitudes at the integrand level
- Global Residues and Two-Loop Hepta-Cuts
- On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes
- The number of master integrals is finite
Cited by in corpus (17)
- Scattering amplitudes over finite fields and multivariate functional reconstruction
- The elliptic dilogarithm for the sunset graph
- A Two-Loop Five-Gluon Helicity Amplitude in QCD
- Ultraviolet Properties of N = 8 Supergravity at Five Loops
- The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
- Azurite: An algebraic geometry based package for finding bases of loop integrals
- Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
- Elliptic Functions and Maximal Unitarity
- Multivariate Residues and Maximal Unitarity
- Building Bases of Loop Integrands
- A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
- Cross-Order Integral Relations from Maximal Cuts
- Integration-by-parts identities from the viewpoint of differential geometry
- Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
- Generalized unitarity method for unstable particles
- Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity