Numerical NLO QCD calculations

Abstract

We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the integration contour for the loop integration into the complex space. The algorithm is formulated at the amplitude level and does not rely on Feynman graphs. Therefore all required ingredients can be calculated efficiently using recurrence relations. The algorithm applies to massless partons as well as to massive partons.

62 pages, version to be published

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Cited by in corpus (54)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• RECOLA: REcursive Computation of One-Loop Amplitudes
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• Merging Multi-leg NLO Matrix Elements with Parton Showers
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• Recola2: REcursive Computation of One-Loop Amplitudes 2
• Electroweak Radiative Corrections for Collider Physics
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• Physics at the e+ e- Linear Collider
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• Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
• Loop Tree Duality for multi-loop numerical integration
• Four-dimensional unsubtraction with massive particles
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• Four-dimensional unsubtraction from the loop-tree duality
• NLO results for five, six and seven jets in electron-positron annihilation
• Universal four-dimensional representation of $H\to \gamma \gamma$ at two loops through the Loop-Tree Duality
• Removing infrared divergences from two-loop integrals
• Numerical Loop-Tree Duality: contour deformation and subtraction
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
• Efficiency improvements for the numerical computation of NLO corrections
• Direct contour deformation with arbitrary masses in the loop
• Integrands of loop amplitudes within loop-tree duality
• Electroweak corrections to lepton pair production in association with two hard jets at the LHC
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Loop-tree duality from vertices and edges
• Decomposition of one-loop QCD amplitudes into primitive amplitudes based on shuffle relations
• Numerical multi-loop integrals and applications
• Numerical integration of loop integrals through local cancellation of threshold singularities
• Numerical integration of subtraction terms
• Infrared singularities in one-loop amplitudes
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• Two-Loop Rational Terms in Yang-Mills Theories
• Comparing efficient computation methods for massless QCD tree amplitudes: Closed Analytic Formulae versus Berends-Giele Recursion
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Exposing the threshold structure of loop integrals
• On the vanishing of certain cuts or residues of loop integrals with higher powers of the propagators
• Colour Evolution and Infrared Physics
• Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?
• Random polarisations of the dipoles
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Numerical implementation of the Loop-Tree Duality method
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Locally finite two-loop amplitudes for electroweak production through gluon fusion
• Flow-oriented perturbation theory
• Numerical evaluation of multi-loop integrals using subtraction terms
• Direct numerical approach to one-loop amplitudes
• NLO automated tools for QCD and beyond
• QCD and Collider Processes
• Two-Loop Rational Terms for Spontaneously Broken Theories
• Coordinate light-cone-ordered perturbation theory
• A new formulation of the loop-tree duality at higher loops