The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges

TL;DR

This paper calculates three master integrals for a specific two-loop Feynman diagram with equal-mass exchanges, using differential equations and series expansions for high-precision numerical results, and finds a relation to the equal-mass sunrise diagram.

Contribution

It provides a detailed computation of master integrals for the crossed ladder diagram with two equal-mass exchanges, including series expansion methods and numerical validation.

Findings

High-precision numerical values for the master integrals

Identification of a relation with the equal-mass sunrise diagram

Agreement with previous large momentum expansion results

Abstract

We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.