472 research outputs found
Reconstructing Rational Functions with
We present the open-source library for the
reconstruction of multivariate rational functions over finite fields. We
discuss the involved algorithms and their implementation. As an application, we
use in the context of integration-by-parts reductions and
compare runtime and memory consumption to a fully algebraic approach with the
program .Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio
Rational Tracer: a Tool for Faster Rational Function Reconstruction
Rational Tracer (Ratracer) is a tool to simplify complicated arithmetic
expressions using modular arithmetics and rational function reconstruction,
with the main idea of separating the construction of expressions (via tracing,
i.e. recording the list of operations) and their subsequent evaluation during
rational reconstruction. Ratracer can simplify arithmetic expressions (provided
as text files), solutions of linear equation systems (specifically targeting
Integration-by-Parts (IBP) relations between Feynman integrals), and even more
generally: arbitrary sequences of rational operations, defined in C++ using the
provided library ratracer.h. Any of these can also be automatically expanded
into series prior to reconstruction. This paper describes the usage of Ratracer
specifically focusing on IBP reduction, and demonstrates its performance
benefits by comparing with Kira+FireFly and Fire6. Specifically, Ratracer
achieves a typical ~10x probe time and ~5x overall time speedup over
Kira+FireFly, and even higher if only a few terms in need to be
reconstructed
Integral Reduction with Kira 2.0 and Finite Field Methods
We present the new version 2.0 of the Feynman integral reduction program Kira
and describe the new features. The primary new feature is the reconstruction of
the final coefficients in integration-by-parts reductions by means of finite
field methods with the help of FireFly. This procedure can be parallelized on
computer clusters with MPI. Furthermore, the support for user-provided systems
of equations has been significantly improved. This mode provides the
flexibility to integrate Kira into projects that employ specialized reduction
formulas, direct reduction of amplitudes, or to problems involving linear
system of equations not limited to relations among standard Feynman integrals.
We show examples from state-of-the-art Feynman integral reduction problems and
provide benchmarks of the new features, demonstrating significantly reduced
main memory usage and improved performance w.r.t. previous versions of Kira
Balancing act: multivariate rational reconstruction for IBP
We address the problem of unambiguous reconstruction of rational functions of
many variables. This is particularly relevant for recovery of exact expansion
coefficients in integration-by-parts identites (IBPs) based on modular
arithmetic. These IBPs are indispensable in modern approaches to evaluation of
multiloop Feynman integrals by means of differential equations. Modular
arithmetic is far more superior to algebraic implementations when one deals
with high-multiplicity situations involving a large number of Lorentz
invariants. We introduce a new method based on balanced relations which allows
one to achieve the goal of a robust functional restoration with minimal data
input. The technique is implemented as a Mathematica package Reconstruction.m
in the FIRE6 environment and thus successfully demonstrates a proof of concept.Comment: 15 pages, 10 ancillary files with code, scripts and demo; download
code @ https://bitbucket.org/feynmanIntegrals/fire/src/master/FIRE6/mm
Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finite remainders from numerical evaluations over finite fields including all colour contributions. Compact expressions are found using the pentagon function basis. We provide a fast and stable implementation for the colour- and helicity-summed interference between the one-loop and two-loop finite remainders in C++ as part of the NJet library
Massive form factors at O(a)
We report on our recent calculation of massive quark form factors using a semi-numerical approach based on series expansions of the master integrals around singular and regular kinematic points and numerical matching. The methods allows to cover the whole kinematic range of negative and positive values of the virtuality with at least seven significant digits accuracy
Massive form factors at O(a)
We report on our recent calculation of massive quark form factors using a semi-numerical approach based on series expansions of the master integrals around singular and regular kinematic points and numerical matching. The methods allows to cover the whole kinematic range of negative and positive values of the virtuality with at least seven significant digits accuracy
Massive form factors at
We report on our recent calculation of massive quark form factors using a
semi-numerical approach based on series expansions of the master integrals
around singular and regular kinematic points and numerical matching. The
methods allows to cover the whole kinematic range of negative and positive
values of the virtuality with at least seven significant digits accuracy.Comment: 9 pages, 3 figures, contribution to the proceedings of Loops and Legs
in Quantum Field Theory (LL2022), Ettal, German
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