Automated one-loop calculations: a proof of concept

Abstract

An algorithm, based on the OPP reduction method, to automatically compute any one-loop amplitude, for all momentum, color and helicity configurations of the external particles, is presented. It has been implemented using the tree-order matrix element code HELAC and the OPP reduction code CutTools. As a demonstration of the potential of the current implementation, results for all sub-processes included in the 2007 Les Houches wish list for LHC, are presented.

22 pages, published version

References in corpus (29)

• Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions
• WHIZARD: Simulating Multi-Particle Processes at LHC and ILC
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes
• Scalar one-loop integrals for QCD
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Direct extraction of one-loop integral coefficients
• Full one-loop amplitudes from tree amplitudes
• On the Rational Terms of the one-loop amplitudes
• D-dimensional unitarity cut method
• NLO QCD corrections to t tbar + jet production at hadron colliders
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• 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
• Masses, fermions and generalized D-dimensional unitarity
• Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
• Feynman Rules for the Rational Part of the QCD 1-loop amplitudes
• NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 1. quark-antiquark annihilation
• Generalized unitarity at work: first NLO QCD results for hadronic W+3jet production
• On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Numerical Evaluation of Six-Photon Amplitudes
• NLO QCD corrections to WW+jet production at hadron colliders
• One-loop amplitudes for W+3 jet production in hadron collisions
• The NLO multileg working group: summary report
• Multi-gluon one-loop amplitudes numerically
• Automated Evaluation of One-Loop Six-Point Processes for the LHC

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