Abstract
We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations in the block-triangular form, very efficient for numerical calculations. Our results are crucial for complete next-to-next-to-leading order quantum chromodynamics calculations for three-jet, photon, and/or hadron production at hadron colliders. To determine the block-triangular relations, we develop an efficient and general method, which may provide a practical solution to the bottleneck problem of reducing multiloop multiscale integrals.
Highlights
Owing to the good performance of the Large Hadron Collider (LHC), we have entered the era of precision high energy physics
Our results are expressed as systems of linear relations in the block-triangular form, very efficient for numerical calculations
Our results are expressed as systems of linear relations in the block-triangular form, which are very efficient for numerical calculations
Summary
Owing to the good performance of the Large Hadron Collider (LHC), we have entered the era of precision high energy physics. The non-planar contribution of two-loop three-photon production at the LHC cannot be calculated, owing to the lack of such reduction for nonplanar integrals [19]. To reconstruct the fully analytical two-loop five-gluon all-plus helicity amplitude [17], one needs to run the numerical computation of the IBP for nearly half a million times 1. If one uses the same method to reconstruct analytical one-minus or maximal-helicity-violation amplitude, many more IBP calculation runs may be needed, which becomes prohibitive. [52] is sufficiently good for reducing integrals with integrands having only denominators, the method is very time-consuming for physical problems that contain integrands with numerators. Our work constitutes an important step towards the complete NNLO QCD calculation for three-jet, photon, or hadron production at the LHC. Is efficient and general, it can be straightforwardly applied to any other process, providing a practical solution for the bottleneck problem of reducing Feynman integrals
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