Abstract
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.
Highlights
A problem that has recently attracted much attention is the calculation of massless two-loop five-point amplitudes
We focus on the application of the approach to the construction of a system of differential equations for the nonplanar hexa-box topology shown in figure 1, which has so far not been achieved through more standard techniques
We have presented a completely generic method for constructing differential equations of Feynman integrals using unitarity-compatible IBP relations
Summary
A crucial step in constructing differential equations for a Feynman integral is obtaining the associated set of integration-by-parts (IBP) relations These are required to rewrite the derivatives of the integrals in terms of a set of master integrals. We focus on the application of the approach to the construction of a system of differential equations for the nonplanar hexa-box topology shown, which has so far not been achieved through more standard techniques. This serves as an illustration of the potential of our approach, which is completely generic and applicable beyond this example
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