Differential equations on unitarity cut surfaces
We reformulate differential equations (DEs) for Feynman integrals to avoid doubled propagators in intermediate steps. External momentum derivatives are dressed with loop momentum derivatives to form tangent vectors to unitarity cut surfaces, in a way inspired by unitaritycompatible IBP reduction. For the oneloop box, our method directly produces the final DEs without any integrationbyparts reduction. We further illustrate the method by deriving maximalcut level differential equations for twoloop nonplanar fivepoint integrals, whose exact expressions are yet unknown. Finally, we speed up the computation using finite field techniques and rational function reconstruction.
 Authors:

^{[1]}
 Univ. of California, Los Angeles, CA (United States). Bhaumik Inst. for Theoretical Physics and Dept. of Physics and Astronomy
 Publication Date:
 Grant/Contract Number:
 SC0009937
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 6; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Univ. of California, Los Angeles, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Perturbative QCD; Scattering Amplitudes
 OSTI Identifier:
 1463882
Zeng, Mao. Differential equations on unitarity cut surfaces. United States: N. p.,
Web. doi:10.1007/JHEP06(2017)121.
Zeng, Mao. Differential equations on unitarity cut surfaces. United States. doi:10.1007/JHEP06(2017)121.
Zeng, Mao. 2017.
"Differential equations on unitarity cut surfaces". United States.
doi:10.1007/JHEP06(2017)121. https://www.osti.gov/servlets/purl/1463882.
@article{osti_1463882,
title = {Differential equations on unitarity cut surfaces},
author = {Zeng, Mao},
abstractNote = {We reformulate differential equations (DEs) for Feynman integrals to avoid doubled propagators in intermediate steps. External momentum derivatives are dressed with loop momentum derivatives to form tangent vectors to unitarity cut surfaces, in a way inspired by unitaritycompatible IBP reduction. For the oneloop box, our method directly produces the final DEs without any integrationbyparts reduction. We further illustrate the method by deriving maximalcut level differential equations for twoloop nonplanar fivepoint integrals, whose exact expressions are yet unknown. Finally, we speed up the computation using finite field techniques and rational function reconstruction.},
doi = {10.1007/JHEP06(2017)121},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2017,
place = {United States},
year = {2017},
month = {6}
}