Ninja: Automated Integrand Reduction via Laurent Expansion for One-Loop Amplitudes

TL;DR

The paper presents Ninja, a public C++ library that implements Integrand Reduction via Laurent Expansion to compute one-loop amplitudes with many external legs and multiple mass scales. It introduces a semi-numerical Laurent expansion framework that identifies residue coefficients and Master-Integral contributions by diagonalizing coefficient equations while avoiding explicit computations of pentagon contributions. Ninja provides a flexible Master-Integral interface (OneLoop, LoopTools) and includes NinjaNumGen to generate numerators, with extensions to higher-rank numerators beyond renormalizable theories. The approach demonstrates improved performance and numerical stability for complex processes and supports multi-threaded usage, interfacing with existing one-loop packages and enabling broad applicability in NLO computations.

Abstract

We present the public C++ library Ninja, which implements the Integrand Reduction via Laurent Expansion method for the computation of one-loop integrals. The algorithm is suited for applications to complex one-loop processes.

Figures (2)

• Figure 1: Phase space point and output for the example in 4photons.cc. It shows the computed finite part and poles of an all-plus four-photon helicity amplitude, using a complex fermion mass $m_f=10.0-1.0 i$.
• Figure 2: Diagram contributing to $gg \rightarrow H t \bar{t}$. This picture has been generated using GoSam.