Dispersion Approach in Two-Loop Calculations

Abstract: The higher-order corrections become increasingly important with experiments reaching sub-percent level of uncertainty as they look for physics beyond the Standard Model. Our goal is to address the full set of two-loop electroweak corrections to M{\o}ller or electron-proton scattering. It is a demanding task which requires an application of various approaches where two-loop calculations can be automatized. We choose to employ dispersive sub-loop insertion approach and develop two-loop integrals using two-point functions basis. In that basis, we introduce a partial tensor reduction for many-point Passarino-Veltman functions, which later could be used in computer algebra packages. In this paper, we have considered self-energy, triangle and box sub-loop insertions into self-energy, vertex and box topology.