Complex Factorisation and Recursion for One-Loop Amplitudes
Sam D. Alston, David C. Dunbar, Warren B. Perkins
TL;DR
This paper introduces a recursive method for calculating the rational parts of one-loop amplitudes in massless theories, leveraging complex factorisation properties to improve computational efficiency and accuracy.
Contribution
It presents a novel recursive approach based on complex factorisation to determine rational parts of one-loop amplitudes, validated on Yang-Mills and gravity theories.
Findings
Verified Bern et al.'s n-point ansatze for single-minus amplitudes
Constructed scalar contribution to five-graviton MHV amplitude
Demonstrated effectiveness of complex factorisation in amplitude computation
Abstract
We consider the factorisation of one-loop amplitudes at complex kinematic points. By determining the terms that are absent for real kinematics, we can construct a recursive ansatz for the purely rational pieces of one-loop amplitudes in massless theories. We illustrate this method by verifying the Bern et.al. n-point ansatze for the single-minus one-loop amplitudes in Yang-Mills theory and by constructing the scalar contribution to the one-loop five graviton MHV scattering amplitude.
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