Direct extraction of one-loop integral coefficients

By D. Forde. 2007

313 citations recorded by the source corpus.

We present a general procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted by considering two-particle and triple unitarity cuts of the corresponding bubble and triangle integral functions. After choosing a specific parameterization of the cut loop momentum we can uniquely identify the coefficients of the desired integral functions simply by examining the behavior of the cut integrand as the unconstrained parameters of the cut loop momentum approach infinity. In this way we can produce compact forms for scalar integral coefficients. Applications of this method are presented for both QCD and electroweak processes, including an alternative form for the recently computed three-mass triangle coefficient in the six-photon amplitude A{sub 6}(1{sup -}, 2{sup +}, 3{sup -}, 4{sup +}, 5{sup -}, 6{sup +}). The direct nature of this extraction procedure allows for a very straightforward automation of the procedure.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/33a771f857e957e0560295d6910d0833b5e4da8b

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In Nuclear and High Energy Physics

Citations in the corpus

Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report (2016, methodology): “This approach can be seen as an extension of the generalised unitarity methods of Britto, Cachazo and Feng [48] and Forde [50].”
Direct extraction of one loop rational terms (2008, methodology): “The traditional Feynman approach to such calculations is extremely computationally intensive due to the rapid growth in the number of diagrams with the number of external legs.”
One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts (2011, methodology): “[29] and we also derive them in what follows.”
The simplest massive S-matrix: from minimal coupling to black holes (2018, methodology): “This problem was beautifully solved by Forde [40], which parameterize the loop momenta in terms of four complex variables, and can be fixed as propagators go on-shell.”
A brief introduction to modern amplitude methods (2013, unknown): “In the next subsection we sketch a method [38, 35] for determining the triangle coefficients.”
A two-loop five-gluon helicity amplitude in QCD (2013, methodology): “For the ∆ [6] g -contribution we get for instance”
Loop amplitudes in gauge theories: modern analytic approaches (2010, background): “Forde’s parametrization of loop momentum allows the extraction of triangle coefficients from triple cuts [38], for the case of massless propagators.”
Integrand reduction of one-loop scattering amplitudes through Laurent series expansion (2012, methodology): “– 26 – [19] C. Berger, Z. Bern, L. Dixon, F. Febres Cordero, D. Forde, et. al., An Automated Implementation of On-Shell Methods for One-Loop Amplitudes, Phys.”