Maximal Unitarity at Two Loops
arXiv:1108.1180 · doi:10.1103/PhysRevD.85.045017
Abstract
We show how to compute the coefficients of the double box basis integrals in a massless four-point amplitude in terms of tree amplitudes. We show how to choose suitable multidimensional contours for performing the required cuts, and derive consistency equations from the requirement that integrals of total derivatives vanish. Our formulae for the coefficients can be used either analytically or numerically.
42 pages, 9 figures; several misprints corrected and one figure added, extraneous figures removed, final journal version with one added reference
References in corpus (35)
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- Algorithm FIRE -- Feynman Integral REduction
- An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
- 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
- The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
- Direct extraction of one-loop integral coefficients
- Full one-loop amplitudes from tree amplitudes
- 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
- NNLO corrections to 3-jet observables in electron-positron annihilation
- Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
- The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
- Direct Extraction Of One Loop Rational Terms
- Infrared structure of e+e- --> 3 jets at NNLO
- Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
- On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
- On Triple-Cut of Scattering Amplitudes
- Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e- annihilations
- On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
- Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
- Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
- Optimizing the Reduction of One-Loop Amplitudes
- Integral Coefficients for One-Loop Amplitudes
- Closed-Form Decomposition of One-Loop Massive Amplitudes
- Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
- One-loop amplitudes for W+3 jet production in hadron collisions
- Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
- The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
- Polynomial Structures in One-Loop Amplitudes
- Analytic Structure of Three-Mass Triangle Coefficients
- On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes
Cited by in corpus (69)
- Scattering amplitudes over finite fields and multivariate functional reconstruction
- The elliptic dilogarithm for the sunset graph
- A Systematic and Efficient Method to Compute Multi-loop Master Integrals
- Two-loop Integrand Decomposition into Master Integrals and Surface Terms
- Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
- Two-loop planar master integrals for Higgs partons with full heavy-quark mass dependence
- A Two-Loop Five-Gluon Helicity Amplitude in QCD
- Ultraviolet Properties of N = 8 Supergravity at Five Loops
- To , or not to : Recent developments and comparisons of regularization schemes
- Hepta-Cuts of Two-Loop Scattering Amplitudes
- The -form of the differential equations for Feynman integrals in the elliptic case
- The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations
- A first look at two-loop five-gluon scattering in QCD
- Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
- Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
- Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
- Decomposition of Feynman Integrals by Multivariate Intersection Numbers
- A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
- The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
- Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
- The unequal mass sunrise integral expressed through iterated integrals on
- Azurite: An algebraic geometry based package for finding bases of loop integrals
- Prescriptive Unitarity
- Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
- The two-loop five-point amplitude in supergravity
- Determine Arbitrary Feynman Integrals by Vacuum Integrals
- Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
- Two-Loop Maximal Unitarity with External Masses
- On Genera of Curves from High-loop Generalized Unitarity Cuts
- Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
- Elliptic Functions and Maximal Unitarity
- The classification of two-loop integrand basis in pure four-dimension
- Multivariate Residues and Maximal Unitarity
- Integrands of loop amplitudes within loop-tree duality
- Getting more flavour out of one-flavour QCD
- Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
- Generalized unitarity and the worldsheet S matrix in AdS_n x S^n x M^(10-2n)
- Numerical multi-loop integrals and applications
- Maximal Unitarity for the Four-Mass Double Box
- Correlation functions of local composite operators from generalized unitarity
- MultivariateResidues: a Mathematica package for computing multivariate residues
- Building Bases of Loop Integrands
- Kinematic Numerators and a Double-Copy Formula for N = 4 Super-Yang-Mills Residues
- Cross-Order Integral Relations from Maximal Cuts
- Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
- Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
- Global Poles of the Two-Loop Six-Point N=4 SYM integrand
- Imaginary parts and discontinuities of Wilson line correlators
- Multi-loop Integrand Reduction with Computational Algebraic Geometry
- Position-space cuts for Wilson line correlators
- Integration-by-parts identities from the viewpoint of differential geometry
- Deciphering the Maximal Transcendentality Principle via Bootstrap
- Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
- Gluonic evanescent operators: two-loop anomalous dimensions
- Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
- Generalized unitarity method for unstable particles
- The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector
- Automated computation of scattering amplitudes
- Scattering amplitudes in gauge theories with and without supersymmetry
- MultivariateResidues - a Mathematica package for computing multivariate residues
- Multi-loop calculations: numerical methods and applications
- Automation of One-Loop Calculations with GoSam: Present Status and Future Outlook
- Gluon Fusion Processes at One-loop within the Standard Model and Beyond
- Differential equations for Feynman integrals beyond multiple polylogarithms
- From elliptic curves to Feynman integrals
- Hidden Analytic Structure of Higgs Amplitudes and Maximal Transcendentality Principle
- Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
- Recent new methods and applications of the differential equation approach to master integrals