Dispersive calculation of the massless multi-loop sunrise diagram

TL;DR

This paper presents a straightforward method for calculating the massless multi-loop sunrise diagram, verifying the results rigorously and discussing distribution-related pitfalls, shedding light on high energy behaviors relevant to complex quantum field calculations.

Contribution

It introduces a simple formal approach to compute the massless multi-loop sunrise diagram and verifies the results with rigorous mathematical methods.

Findings

The method successfully computes the multi-loop sunrise diagram.

The approach reveals high energy behavior of the diagrams.

Distribution pitfalls in calculations are identified and explained.

Abstract

The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.