I present a new method for computing multi-loop scattering amplitudes in Quantum Field Theory. It extends the Generalized Unitarity method by constraining not only the integrand of the amplitude but also its full integrated form. I exploit the relation between cuts and discontinuities of the amplitude. Explicitly, by the virtue of analyticity and unitarity of the S-matrix, the amplitude can be expressed in terms of lower-loop on-shell amplitudes dispersively integrated along cuts. As both cuts and discontinuities can be computed systematically in dimensional regularization, I validated the method by reproducing the four-gluon amplitude in two-loop massless Quantum Chromodynamics. Moreover, since my approach improves the performance of the calculation, I present a new result for the four-loop four-point massless planar ladder Feynman integral. It is expressed in terms of Harmonic Polylogarithms with letters 0 and 1.
