Integrated unitarity for scattering amplitudes and the four-loop ladder Feynman integral

A bstract We consider multi-loop scattering amplitudes in dimensionally regularized Quantum Field Theory. We present an algorithmic way of reconstructing them from their cuts. We rely on combining modern computational methods with formal developments in discontinuities and dispersion relations. Our approach extends Generalized Unitarity by constraining not only the integrand of the amplitude but also its full integrated form. We validated our method by reproducing the four-gluon amplitude in two-loop massless Quantum Chromodynamics. Moreover, since our approach improves the performance of the calculation, we provide 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.