A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes

R. K. Ellis; W. T. Giele; Z. Kunszt

doi:10.1088/1126-6708/2008/03/003

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arXiv · 0708.2398

A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes

R. K. Ellis·W. T. Giele·Z. Kunszt

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Abstract

Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and implement the method in a numerical procedure. Our technique can be applied to any one-loop scattering amplitude and offers the possibility that one-loop calculations can be performed in an automatic fashion, as tree-level amplitudes are currently done. Instead of individual Feynman diagrams, the ingredients for our one-loop evaluation are tree-level amplitudes, which are often already known. To study the practicality of this method we evaluate the cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically, using the analytically known 4, 5 and 6 gluon tree-level amplitudes. Comparisons with analytic answers are performed to ascertain the numerical accuracy of the method.

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R. K. Ellis, W. T. Giele, Z. Kunszt. 2007-08-24. A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes. https://doi.org/10.1088/1126-6708%2F2008%2F03%2F003

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