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We compute all master integrals for massless three-loop four-particlescattering amplitudes required for processes like di-jet or di-photonproduction at the LHC. We present our result in terms of a Laurent expansion ofthe integrals in the dimensional regulator up to 8$^{\text{th}}$ power, withcoefficients expressed in terms of harmonic polylogarithms. As a basis ofmaster integrals we choose integrals with integrands that only have logarithmicpoles - called $d$log forms. This choice greatly facilitates the subsequentcomputation via the method of differential equations. We detail how this basisis obtained via an improved algorithm originally developed by one of theauthors. We provide a public implementation of this algorithm. We explain howthe algorithm is naturally applied in the context of unitarity. In addition, weclassify our $d$log forms according to their soft and collinear properties.

Constructing d-log integrands and computing master integrals for three-loop four-particle scattering