Tensor integrand reduction via Laurent expansion

TL;DR

This paper presents a novel tensor integrand reduction method using Laurent expansion, implemented in Ninja, which improves speed and stability in one-loop calculations and interfaces seamlessly with existing matrix element generators.

Contribution

The authors introduce a new Laurent expansion-based integrand reduction technique for one-loop calculations, implemented in Ninja, enhancing performance and compatibility with various matrix element generators.

Findings

Ninja outperforms other tools in speed and stability

The method scales well with process complexity

Ninja's performance is comparable to tensor integral reduction tools

Abstract

We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja's performance scales well with both the rank and multiplicity of the considered process.