Single-scale diagrams and multiple binomial sums

TL;DR

This paper computes the epsilon-expansion of complex two-loop self-energy diagrams with thresholds, reducing on-shell results to multiple binomial sums and providing their analytical values.

Contribution

It introduces a method to express two-loop self-energy diagrams' epsilon-expansion as multiple binomial sums with explicit analytical solutions.

Findings

Explicit analytical forms for the sums are provided.

The epsilon-expansion results are applicable to diagrams with different thresholds.

The approach simplifies complex two-loop calculations.

Abstract

The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.