# A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop

## TL;DR

This paper introduces a numerical routine for efficiently evaluating the two master integrals of the crossed vertex diagram with a massive top-quark loop, enabling precise calculations across all phase space regions.

## Contribution

It provides a new numerical method using differential equations and power series expansions for the crossed vertex diagram with massive particles, facilitating fast and accurate integral evaluations.

## Key findings

- High-precision numerical evaluations achieved
- Method applicable across all phase space regions
- Routine simplifies complex integral calculations

## Abstract

We present an evaluation of the two master integrals for the crossed vertex diagram with a closed loop of top quarks that allows for an easy numerical implementation. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular points. The different series are then matched numerically with high accuracy in intermediate points. The expansions allow a fast and precise numerical calculation of the two master integrals in all the regions of the phase space. A numerical routine that implements these expansions is presented.