Finite quantum field quantities are measurable and contain rich information, such as physical cross sections and massive scattering amplitudes in conformal theories.Traditional methods of doing loop calculations often introduce infrared divergences that obscure the physical properties manifest in 4d. Performing loop calculation that avoids infrared divergences is an open problem. In this talk I will present two recent projects where we worked on two classes of infrared finite observables: event shapes and angle-dependent cusp anomalous dimension.In these work we develop novel methods to extract physical results directly from the knowledge of finite Feynman integrals.The methods are particularly suitable to the systematic computation of finite quantities at higher loop order. We applied these new ideas to cutting edge problems of three-loop energy-energy correlator in N=4 sYM and four-loop full-angle dependent cusp anomalous dimension in QED where we removed the important bottlenecks of the state-of-the-art techniques.
