TL;DR
This paper explores advanced complex analysis techniques for calculating one-loop scattering amplitudes, introducing methods that leverage spinor-variable contour integrals and discrete Fourier transforms to improve tensor integral reduction.
Contribution
It presents two novel techniques: a spinor-variable contour integration method and a Fourier transform approach for tensor integral reduction in scattering amplitude calculations.
Findings
Enhanced efficiency in tensor integral reduction
New contour integral formulation for loop calculations
Potential for broader application in amplitude computations
Abstract
The use of complex analysis for computing one-loop scattering amplitudes is naturally induced by generalised unitarity-cut conditions, fulfilled by complex values of the loop variable. We report on two techniques: the cut-integration with spinor-variables as contour integrals of rational functions; and the use of the Discrete Fourier Transform to optimize the reduction of tensor-integrals to master scalar integrals.
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