Differential equations from unitarity cuts: nonplanar hexa-box integrals

DOI10.1007/JHEP01(2019)006zbMATH Open1409.81157arXiv1807.11522OpenAlexW2887099765WikidataQ128685321 ScholiaQ128685321MaRDI QIDQ667037

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Publication date: 12 March 2019

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Abstract: We compute $epsilon$-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.

Full work available at URL: https://arxiv.org/abs/1807.11522

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