The calculation of 2-loop self-energy diagrams by the sector decomposition

TL;DR

This paper introduces a sector decomposition method to efficiently compute 2-loop self-energy diagrams for scalar particles, separating divergences from finite parts for easier renormalization and computation.

Contribution

The paper presents a novel sector decomposition technique specifically designed for 2-loop self-energy calculations, improving efficiency in divergence separation.

Findings

Effective separation of divergent and finite parts in 2-loop diagrams

Method applicable to both analytical and numerical calculations

Facilitates renormalization of scalar particle self-energies

Abstract

Detailed description of the calculation of the 2-loop self-energy for a scalar particle is presented. By employing a simple sector decomposition method, the ultraviolet divergent part is efficiently separated from the finite part. The resulting expression can be used for both analytic and numerical computation to renormalize the divergence and to provide finite results for physics.