Cristal and Azurite: new tools for integration-by-parts reductions

TL;DR

This paper introduces Azurite, a tool for identifying basis integrals in loop amplitude calculations, and Cristal, a future tool for complete integration-by-parts reductions, advancing computational methods in quantum field theory.

Contribution

The paper presents Azurite and Cristal, new computational tools that improve the process of basis determination and reduction in loop integral calculations.

Findings

Azurite effectively finds bases of loop integrals.

Cristal aims to produce complete IBP reductions.

Tools are publicly available for the community.

Abstract

Scattering amplitudes computed at a fixed loop order, along with any other object computed in perturbative quantum field theory, can be expressed as a linear combination of a finite basis of loop integrals. To compute loop amplitudes in practice, such a basis of integrals must be determined. We discuss Azurite (A ZURich-bred method for finding master InTEgrals), a publicly available package for finding bases of loop integrals. We also discuss Cristal (Complete Reduction of IntegralS Through All Loops), a future package that produces the complete integration-by-parts reductions.