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 2 and FIRE 5. In our benchmarks we find that Kira is highly competitive with these existing tools.

Triple-real contribution to the quark beam function in QCD at next-to-next-to-next-to-leading order

“…Nevertheless, performing the IBP reduction and accounting for additional identities that originate from the partial fractioning, we find that all diagrams can be expressed in terms of 91 master integrals which are drawn from 19 different topologies, see Table 1. We performed the reduction to master integrals using Reduze [50] and KIRA [51], both of which support the generation and solution of IBPs for Feynman integrals with cut propagators, and we verified that the results of the two reduction codes are equivalent. We use the following notation for the master integrals…”

Two-Loop QCD Corrections to the Higgs Plus Three-parton Amplitudes with Top Mass Correction

“…The scalar function f 0 is a function rational in s ij and polynomial in the dimension parameter D, which can be directly reduced using IBP reduction with e.g. public codes [79][80][81][82]. As shown in the r.h.s.…”

Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space

“…The algorithm works by imposing an ordering on the different integral families and solving recursively. There exist multiple public and private implementations of this approach [32,[36][37][38][39][40][41], which usually generates a large linear system to be solved.…”