Differential equations from unitarity cuts: nonplanar hexa-box integrals

Samuel Abreu (Physikalisches Institut, Albert-Ludwigs-Universitat Freiburg, Hermann-Herder-Straße 3, Freiburg, D-79104, Germany) ; Ben Page (Physikalisches Institut, Albert-Ludwigs-Universitat Freiburg, Hermann-Herder-Straße 3, Freiburg, D-79104, Germany) ; Mao Zeng (Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, 475 Portola Plaza, Los Angeles, CA, 90095, U.S.A.)

We compute ϵ-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is presented. For 5-point planar topologies, Gram determinants which vanish in 4 dimensions are used to build compact expressions for pure integrals. Using unitarity cuts and computational algebraic geometry, we obtain a compact IBP system which can be solved in 8 hours on a single CPU core, overcoming a major bottleneck for deriving the differential equations. Alternatively, assuming prior knowledge of the alphabet of the nonplanar hexa-box, we reconstruct analytic differential equations from 30 numerical phase-space points, making the computation almost trivial with current techniques. We solve the differential equations to obtain the values of the master integrals at the symbol level. Full results for the differential equations and solutions are included as supplementary material.

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      "surname": "Page", 
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      "surname": "Zeng", 
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      "value": "We compute \u03f5-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is presented. For 5-point planar topologies, Gram determinants which vanish in 4 dimensions are used to build compact expressions for pure integrals. Using unitarity cuts and computational algebraic geometry, we obtain a compact IBP system which can be solved in 8 hours on a single CPU core, overcoming a major bottleneck for deriving the differential equations. Alternatively, assuming prior knowledge of the alphabet of the nonplanar hexa-box, we reconstruct analytic differential equations from 30 numerical phase-space points, making the computation almost trivial with current techniques. We solve the differential equations to obtain the values of the master integrals at the symbol level. Full results for the differential equations and solutions are included as supplementary material."
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Published on:
14 June 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 1
Pages 1-32
DOI:
https://doi.org/10.1007/JHEP01(2019)006
arXiv:
1807.11522
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: