Built on

F. V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions
1981
Earlier work this paper cites.
K. G. Chetyrkin and F. V. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops
1981
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions
2000
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations
2000
Earlier work this paper cites.
C. W. Bauer, A. Frink, and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language
2000
Earlier work this paper cites.
C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations
2004
Earlier work this paper cites.
J. Vollinga, GiNaC: Symbolic computation with C++
2006
Earlier work this paper cites.
A. V. Smirnov, Algorithm FIRE – Feynman Integral REduction
Original
2008
Earlier work this paper cites.
M. Kauers, Fast solvers for dense linear systems
2008
Earlier work this paper cites.
C. Studerus, Reduze-Feynman Integral Reduction in C++
Original
2010
Earlier work this paper cites.
M. Czakon, P. Fiedler, and A. Mitov, Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through O ⁡ ( α s 4 ) O(\alpha_{s}^{4})
Original
2013
Earlier work this paper cites.
A. V. Smirnov and V. A. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations
Original
2013
Earlier work this paper cites.
R. N. Lee and A. A. Pomeransky, Critical points and number of master integrals
Original
2013
Earlier work this paper cites.
J. von zur Gathen, and J. Gerhard, Modern Computer Algebra (3rd ed.)
2013
Earlier work this paper cites.

Similar

T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierhöfer, A. von Manteuffel, S. Pozzorini, D. Rathlev, and L. Tancredi, W + W − W^{+}W^{-} Production at Hadron Colliders in Next to Next to Leading Order QCD
Original
2014
Cited alongside, same era.
F. Cascioli, T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierhöfer, A. von Manteuffel, S. Pozzorini, D. Rathlev, L. Tancredi, and E. Weihs, ZZ production at hadron colliders in NNLO QCD
Original
2014
Cited alongside, same era.
P. Kant, Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach
Original
2014
Cited alongside, same era.
R. N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals
Original
2014
Cited alongside, same era.
M. Assadsolimani, P. Kant, B. Tausk, and P. Uwer, Calculation of two-loop QCD corrections for hadronic single top-quark production in the t t channel

Then

S. Borowka, N. Greiner, G. Heinrich, S. Jones, M. Kerner, J. Schlenk, U. Schubert, and T. Zirke, Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence
Original
2016
Later among the works it cites.
A. Gehrmann-De Ridder, T. Gehrmann, E. W. N. Glover, A. Huss, and T. A. Morgan, Precise QCD predictions for the production of a Z boson in association with a hadronic jet
Original
2016
Later among the works it cites.
R. Boughezal, J. M. Campbell, R. K. Ellis, C. Focke, W. T. Giele, X. Liu, and F. Petriello, Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
Original
2016
Later among the works it cites.
M. Grazzini, S. Kallweit, D. Rathlev, and M. Wiesemann, W ± Z W^{\pm}Z production at hadron colliders in NNLO QCD
Original
2016
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2017

Kira - A Feynman Integral Reduction Program

Maierhoefer, Philipp, Usovitsch, Johann, Uwer, Peter

Understand

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.

Built on

F. V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions
1981
Earlier work this paper cites.
K. G. Chetyrkin and F. V. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops
1981
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions
2000
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations
2000
Earlier work this paper cites.
C. W. Bauer, A. Frink, and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language
2000
Earlier work this paper cites.
C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations
2004
Earlier work this paper cites.
J. Vollinga, GiNaC: Symbolic computation with C++
2006
Earlier work this paper cites.
A. V. Smirnov, Algorithm FIRE – Feynman Integral REduction
Original
2008
Earlier work this paper cites.
M. Kauers, Fast solvers for dense linear systems
2008
Earlier work this paper cites.
C. Studerus, Reduze-Feynman Integral Reduction in C++
Original
2010
Earlier work this paper cites.
M. Czakon, P. Fiedler, and A. Mitov, Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through O ⁡ ( α s 4 ) O(\alpha_{s}^{4})
Original
2013
Earlier work this paper cites.
A. V. Smirnov and V. A. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations
Original
2013
Earlier work this paper cites.
R. N. Lee and A. A. Pomeransky, Critical points and number of master integrals
Original
2013
Earlier work this paper cites.
J. von zur Gathen, and J. Gerhard, Modern Computer Algebra (3rd ed.)
2013
Earlier work this paper cites.