# Extracting analytical one-loop amplitudes from numerical evaluations

## TL;DR

This paper introduces a numerical method to derive analytical expressions for one-loop amplitude coefficients, utilizing high-precision computations to analyze singularities and simplify complex parts, demonstrated on six-gluon amplitudes.

## Contribution

The paper presents a novel approach combining numerical evaluations and high-precision arithmetic to obtain analytical loop amplitude coefficients, improving efficiency and manageability.

## Key findings

- Successfully derived analytical expressions for all helicity configurations of six-gluon one-loop amplitudes.
- Demonstrated the method's effectiveness in handling complex singularity structures.
- Provided a new tool for analytical calculations in quantum field theory.

## Abstract

In this article we present a method to generate analytic expressions for the integral coefficients of loop amplitudes using numerical evaluations only. We use high-precision arithmetic to explore the singularity structure of the coefficients and decompose them into parts of manageable complexity. To illustrate the usability of our method we provide analytical expressions for all helicity configurations of the colour-ordered six-point gluon amplitudes at one loop with a gluon in the loop.