Dispersion Approach in Two-Loop Calculations

TL;DR

This paper develops a dispersive approach for automating two-loop electroweak corrections in particle scattering processes, enhancing precision calculations relevant for beyond Standard Model physics.

Contribution

It introduces a dispersive sub-loop insertion method and a tensor reduction technique for two-loop integrals, facilitating automation in complex electroweak correction calculations.

Findings

Developed a dispersive approach for two-loop calculations.

Implemented tensor reduction for multi-point Passarino-Veltman functions.

Applied method to self-energy, triangle, and box sub-loop insertions.

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.