# Dimensional Regularization and Dispersive Two-Loop Calculations

## TL;DR

This paper advances the calculation of two-loop Feynman diagrams by analytically extracting UV divergences using a dispersive approach, facilitating more precise theoretical predictions in particle physics.

## Contribution

It introduces a method to analytically extract UV-divergent poles of Passarino-Veltman functions within a dispersive framework, extending previous work to complex multi-point functions.

## Key findings

- Analytical expressions for UV-divergent poles of Passarino-Veltman functions.
- Representation of dispersive sub-loop insertions for various diagram types.
- Enhanced precision in two-loop calculations for particle physics.

## Abstract

The two-loop contributions are now often required by the precision experiments, yet are hard to express analytically while keeping precision. One way to approach this challenging task is via the dispersive approach, allowing to replace sub-loop diagram by effective propagator. This paper builds on our previous work, where we developed a general approach based on representation of many-point Passarino-Veltman functions in two-point function basis. In this work, we have extracted the UV-divergent poles of the Passarino-Veltman functions analytically and presented them as the dimensionally-regularized and multiply-subtracted dispersive sub-loop insertions, including self-energy, triangle, box and pentagon type.