Progress in Two-Loop Master Integrals Computation

Over the last years, master integral families at one, two and three loops, with up to five external particles, including off-shell legs and internal masses have been computed analytically based on the Simplified Differential Equations approach. In this presentation we focus on the latest results for two-loop five-point Feynman Integrals with one off-shell leg. The three planar and one of the non-planar families have been fully expressed in terms of Goncharov polylogarithms. For the other two non-planar families, we introduce a new approach to obtain the boundary terms and establish a one-dimensional integral representation of the master integrals in terms of generalised polylogarithms, when the alphabet contains non-factorizable square roots. The results are relevant to the study of NNLO QCD corrections for $W,Z$ and Higgs-boson production in association with two hadronic jets.