Interpolation of Dense and Sparse Rational Functions and other Improvements in $\texttt{FireFly}$

Abstract

We present the main improvements and new features in version 2.0 of the open-source C++ library FireFly for the interpolation of rational functions. This includes algorithmic improvements, e.g. a hybrid algorithm for dense and sparse rational functions and an algorithm to identify and remove univariate factors. The new version is applied to a Feynman-integral reduction to showcase the runtime improvements achieved. Moreover, FireFly now supports parallelization with MPI and offers new tools like a parser for expressions or an executable for the insertion of replacement tables.

Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC

“…[49]. The analytical results for the amplitude are obtained by interpolating the finite-field samples using the library FireFly [51]. We refer the reader to ref.…”

Two-loop leading-color helicity amplitudes for three-photon production at the LHC

“…In this work we follow an alternative strategy for the evaluation of the coefficients G e are then passed to the FireFly library [82] in order to reconstruct the exact analytical expressions for the coefficients G (n) e . We have created an automated framework which is designed to calculate simultaneously multiple amplitudes (that have the same kinematics) following the finite-field evaluation approach just described.…”

Resummation methods for Master Integrals

“…Many packages have been developed [6][7][8] based on Laporta's algorithm [9] that implement the method of reduction to MI via IBP relations. Nevertheless, the procedure of reduction still remains a difficult problem from a computational point of view for families with many loops and/or many kinematic invariants, leading to the search for new methods [10][11][12][13][14][15][16][17][18]. The method of DE lived through a revolution in recent years with the introduction of the concept of universally transcendental and pure functions and the so-called canonical form of the DE [19].…”