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

2006/07/31 by Zhiguang Xiao, Zhi-Guang Xiao, Gang Yang +1 · 1 citation
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Dimensional regularization #Feynman diagram #Feynman integral #Formalism (music) #Gluon #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Renormalization #Theoretical physics #hep-ph #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2006.09.008

published as Nucl.Phys. B758 (2006) 1-34 · 49 pages, 8 figure and LaTeX file; minor corrections, references added, to be published in Nucl. Phys. B

arxiv created 2006/09/11 · openalex publication_date 2006/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• String-Based Perturbative Methods for Gauge Theories
• Holomorphic Anomaly Of Unitarity Cuts And One-Loop Gauge Theory Amplitudes
• Bootstrapping one-loop QCD amplitudes with general helicities
• Automatized analytic continuation of Mellin–Barnes integrals
• One-loop self-dual and N = 4 super Yang-Mills
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Inherited twistor-space structure of gravity amplitudes
• Recursive numerical calculus of one-loop tensor integrals
• All next-to-maximally-helicity-violating one-loop gluon amplitudes inN=4super-Yang-Mills theory
• Towards LHC phenomenology at the loop level: A new method for one-loop amplitudes
• Reduction formalism for dimensionally regulated one-loop N-point integrals
• New recursion relations for tree amplitudes of gluons
• Loops in twistor space
• Seminumerical evaluation of one-loop corrections
• From Yang-Mills lagrangian to MHV diagrams
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Loop amplitudes in pure Yang-Mills from generalised unitarity
• Recursion Relations for Tree Amplitudes in Super Gauge Theories
• A Calculational Formalism for One-Loop Integrals
• Next-to-maximal helicity violating amplitudes in gauge theory
• Calculating Scattering Amplitudes Efficiently
• Recursion relations for gauge theory amplitudes with massive particles
• SIX-QUARK AMPLITUDES FROM FERMIONIC MHV VERTICES
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Automated one-loop calculations in four and D dimensions

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