Dispersion approach in two-loop calculations

The higher-order corrections become increasingly important with experiments reaching the subpercent 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 Moller 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 subloop 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 subloop insertions into self-energy, vertex and box topology.