Feynman Rules for the Rational Part of the QCD 1-loop amplitudes

Abstract

We compute the complete set of Feynman Rules producing the Rational Terms of kind R_2 needed to perform any QCD 1-loop calculation. We also explicitly check that in order to account for the entire R_2 contribution, even in case of processes with more than four external legs, only up to four-point vertices are needed. Our results are expressed both in the 't Hooft Veltman regularization scheme and in the Four Dimensional Helicity scheme, using explicit color configurations as well as the color connection language.

18 pages, 11 figures. Misprints corrected in Appendix A. Version to be published in JHEP

References in corpus (20)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Full one-loop amplitudes from tree amplitudes
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• On the Rational Terms of the one-loop amplitudes
• D-dimensional unitarity cut method
• Techniques for the calculation of electroweak radiative corrections at the one-loop level and results for W-physics at LEP200
• Helac-Phegas: a generator for all parton level processes
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Numerical Evaluation of Six-Photon Amplitudes
• Optimizing the Reduction of One-Loop Amplitudes
• Integral Coefficients for One-Loop Amplitudes
• Closed-Form Decomposition of One-Loop Massive Amplitudes
• The NLO multileg working group: summary report
• The rational parts of one-loop QCD amplitudes I: The general formalism
• A complete reduction of one-loop tensor 5- and 6-point integrals
• One-loop Integral Coefficients from Generalized Unitarity
• Multi-gluon one-loop amplitudes numerically
• The rational parts of one-loop QCD amplitudes II: The five-gluon case
• Formulae for a numerical computation of one-loop tensor integrals

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