Kira - A Feynman Integral Reduction Program

Abstract

In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals-appearing in quantum field theoretic calculations-to a set of master integrals. We extend existing approaches by using an additional algorithm based on modular arithmetic to remove linearly dependent equations from the system of equations arising from integration-by-parts and Lorentz identities. Furthermore, the algebraic manipulations required in the back substitution are optimized. We describe in detail the implementation as well as the usage of the program. In addition, we show benchmarks for concrete examples and compare the performance to Reduze. The algorithmic improvements lead to a significant increase in the performance with respect to previously available programs