Recent progress on two-loop massless pentabox integrals with one off-shell leg

Abstract

Analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg are presented. The Simplified Differential Equations approach is the only known way to fulfil this task due to its unique factorisation property of the symbols of the canonical differential equation. The results are relevant to the study of many $2\to 3$ scattering processes of interest at the LHC.