Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
arXiv:hep-ph/0612089 · doi:10.1103/PhysRevD.75.105006
Abstract
In the first part of this paper, we extend the d-dimensional unitarity cut method of hep-ph/0609191 to cases with massive propagators. We present formulas for integral reduction with which one can obtain coefficients of all pentagon, box, triangle and massive bubble integrals. In the second part of this paper, we present a detailed study of the phase space integration for unitarity cuts. We carry out spinor integration in generality and give algebraic expressions for coefficients, intended for automated evaluation.
33 pages. v2: notation modified. v3: typos fixed
References in corpus (32)
- One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
- Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- Connection between Feynman integrals having different values of the space-time dimension
- One-Loop Amplitudes for e^+ e^- to Four Partons
- 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 Self-Dual and N=4 Super Yang-Mills
- D-dimensional unitarity cut method
- Recursion Relations for Gauge Theory Amplitudes with Massive Particles
- 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
- All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills 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
- Recursive numerical calculus of one-loop tensor integrals
- All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
- Lectures on Twistor Strings and Perturbative Yang-Mills Theory
- On Triple-Cut of Scattering Amplitudes
- One-Loop Gluon Scattering Amplitudes in Theories with Supersymmetries
- Algebraic evaluation of rational polynomials in one-loop amplitudes
- Semi-Numerical Evaluation of One-Loop Corrections
- The one-loop amplitude for six-gluon scattering
- The rational parts of one-loop QCD amplitudes I: The general formalism
- The rational parts of one-loop QCD amplitudes III: The six-gluon case
- The rational parts of one-loop QCD amplitudes II: The five-gluon case
- Twistor String Theory and QCD
Cited by in corpus (70)
- 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
- 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
- Masses, fermions and generalized D-dimensional unitarity
- Direct Extraction Of One Loop Rational Terms
- Basics of Generalized Unitarity
- Unexpected Cancellations in Gravity Theories
- Maximal Unitarity at Two Loops
- Generalized Unitarity and Six-Dimensional Helicity
- Loop amplitudes in gauge theories: modern analytic approaches
- On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
- Optimizing the Reduction of One-Loop Amplitudes
- Double-Cut of Scattering Amplitudes and Stokes' Theorem
- One-loop phi-MHV amplitudes using the unitarity bootstrap
- Integral Coefficients for One-Loop Amplitudes
- Closed-Form Decomposition of One-Loop Massive Amplitudes
- Duals of Feynman Integrals, I: Differential Equations
- Duals of Feynman Integrals, 2: Generalized Unitarity
- Two-Loop Maximal Unitarity with External Masses
- Six-Photon Amplitudes
- One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case
- Cosmology meets cohomology
- One-loop MHV Rules and Pure Yang-Mills
- Polynomial Structures in One-Loop Amplitudes
- Analytic Structure of Three-Mass Triangle Coefficients
- One-Loop Helicity Amplitudes for ttbar Production at Hadron Colliders
- Multivariate Residues and Maximal Unitarity
- One-Loop Gluonic Amplitudes from Single Unitarity Cuts
- Six-Photon Amplitudes in Scalar QED
- The one-loop amplitudes for Higgs + 4 partons with full mass effects
- Maximal Unitarity for the Four-Mass Double Box
- Simplifying -Dimensional Physical-State Sums in Gauge Theory and Gravity
- Solving for tadpole coefficients in one-loop amplitudes
- The Unitarity Method using a Canonical Basis Approach
- One-Loop Calculations with BlackHat
- Unitarity Method with Spurious Pole
- A unitarity compatible approach to one-loop amplitudes with massive fermions
- Cross-Order Integral Relations from Maximal Cuts
- The Q-cut Representation of One-loop Integrands and Unitarity Cut Method
- Global Poles of the Two-Loop Six-Point N=4 SYM integrand
- Analytic Tadpole Coefficients of One-loop Integrals
- External leg corrections in the unitarity method
- One-loop Feynman Integral Reduction by Differential Operators
- On-shell diagrammatics and the perturbative structure of planar gauge theories
- Generation Function For One-loop Tensor Reduction
- Generalised Unitarity At One-Loop With Massive Fermions
- Reduction of General One-loop Integrals Using Auxiliary Vector
- Reduction with Degenerate Gram matrix for One-loop Integrals
- The MHV Lagrangian for a spontaneously broken gauge theory
- The Supergravity NMHV six-point one-loop amplitude
- Nontrivial One-loop Recursive Reduction Relation
- Reduction of one-loop integrals with higher poles by unitarity cut method
- Automated calculations for multi-leg processes
- Hard QCD at hadron colliders
- Analytic Computations of Massive One-Loop Amplitudes
- Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
- Augmented Recursion For One-loop Amplitudes
- Light-by-light scattering amplitudes from generalized unitarity in massive QED
- Massive particles and unitarity cuts
- On perturbative field theory and twistor string theory
- Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
- Cross Section Evaluation by Spinor Integration I: The massless case in 4D
- Constructing QCD one-loop amplitudes
- Reduction of one-massless-loop with scalar boxes in dimensions
- On the Cuts of Scattering Amplitudes
- Cross Section Evaluation by Spinor Integration II: The massive case in 4D
- General One-loop Reduction in Generalized Feynman Parametrization Form