A numerical unitarity formalism for evaluating one-loop amplitudes
By R. Ellis, W. Giele, Z. Kunszt. 2007
263 citations recorded by the source corpus.
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.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/94118711c574a040bffcef02cceafa0284c02fb8
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In Nuclear and High Energy Physics
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Citations in the corpus
- One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts (2011, background): “Giele, that we will refer to as the generalized D-dimensional unitarity [22, 23, 24].”
- Direct extraction of one loop rational terms (2008, background): “In supersymmetric theories performing the on-shell cut in four dimensions is sufficient to reconstruct the full amplitude, whereas in QCD we will be left with additional rational terms.”
- Integrand reduction of one-loop scattering amplitudes through Laurent series expansion (2012, methodology): “The original algorithm [5,7] is based on the solution of a triangular system of equations to be solved top-down, from the determination of the 5-point coefficients to the 1-point coefficients.”
- Constraining anomalous Higgs boson couplings to the heavy flavor fermions using matrix element techniques (2016, methodology): “[70] R.”
- Automation of one-loop QCD computations (2011, methodology): “With some degree of arbitrariness, we may classify the modern procedures alluded to before into two classes, that we call Generalized Unitarity (GU) [20–22] and Integrand Reduction (IR) [2, 6, 23].”