# Building bases of loop integrands

@article{Bourjaily2020BuildingBO,
title={Building bases of loop integrands},
author={Jacob L. Bourjaily and Enrico Herrmann and Cameron Langer and Jaroslav Trnka},
journal={Journal of High Energy Physics},
year={2020}
}
• Published 27 July 2020
• Mathematics
• Journal of High Energy Physics
Abstract We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of ‘power-counting’ for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In…
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