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Title: 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 unitarity-compatible IBP reduction. For the one-loop box, our method directly produces the final DEs without any integration-by-parts reduction. We further illustrate the method by deriving maximal-cut level differential equations for two-loop nonplanar five-point integrals, whose exact expressions are yet unknown. Finally, we speed up the computation using finite field techniques and rational function reconstruction.
Authors:
ORCiD logo [1]
  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 1029-8479
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 unitarity-compatible IBP reduction. For the one-loop box, our method directly produces the final DEs without any integration-by-parts reduction. We further illustrate the method by deriving maximal-cut level differential equations for two-loop nonplanar five-point 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}
}