The rational parts of one-loop QCD amplitudes I: The general formalism

Abstract

A general formalism for computing only the rational parts of oneloop QCD amplitudes is developed. Starting from the Feynman integral representation of the one-loop amplitude, we use tensor reduction and recursive relations to compute the rational parts directly. Explicit formulas for the rational parts are given for all bubble and triangle integrals. Formulas are also given for box integrals up to two-masshard boxes which are the needed ingredients to compute up to 6-gluon QCD amplitudes. We use this method to compute explicitly the rational parts of the 5- and 6-gluon QCD amplitudes in two accompanying papers.

49 pages, 8 figure and LaTeX file; minor corrections, references added, to be published in Nucl. Phys. B

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Cited by in corpus (22)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Direct extraction of one-loop integral coefficients
• On the Rational Terms of the one-loop amplitudes
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Numerical Evaluation of Six-Photon Amplitudes
• Optimizing the Reduction of One-Loop Amplitudes
• One-loop phi-MHV amplitudes using the unitarity bootstrap
• Integral Coefficients for One-Loop Amplitudes
• All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
• One-loop MHV Rules and Pure Yang-Mills
• Polynomial Structures in One-Loop Amplitudes
• Self-Dual Supergravity and Twistor Theory
• One-Loop Calculations with BlackHat
• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
• Unitarity Method with Spurious Pole
• A Fully Numerical Approach to One-Loop Amplitudes
• (Non)-supersymmetric Marginal Deformations from Twistor String Theory
• The last of the seven-parton tree amplitudes
• MHV Lagrangians for Yang--Mills and QCD
• Constructing QCD one-loop amplitudes
• A new method for the numerical evaluation of one-loop amplitudes