Built on

G. Passarino and M. J. G. Veltman, One Loop Corrections for e+ e- Annihilation Into mu+ mu- in the Weinberg Model , Nucl. Phys. B160
1979
Earlier work this paper cites.
F. A. Berends and W. T. Giele, Recursive Calculations for Processes with n Gluons , Nucl. Phys. B306
1988
Earlier work this paper cites.
A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200 , Fortsch. Phys. 41
Original
1993
Earlier work this paper cites.
J. A. M. Vermaseren, Axodraw , Comput. Phys. Commun. 83
1994
Earlier work this paper cites.
S. Badger, B. Biedermann, P. Uwer and V. Yundin, Numerical evaluation of virtual corrections to multi-jet production in massless QCD , Comput. Phys. Commun. 184
Original
1998
Earlier work this paper cites.
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3 , Comput. Phys. Commun. 140
2001
Earlier work this paper cites.
A. Denner and S. Dittmaier, Reduction of one-loop tensor 5-point integrals , Nucl. Phys. B658
2003
Earlier work this paper cites.
F. del Aguila and R. Pittau, Recursive numerical calculus of one-loop tensor integrals , JHEP 07
2004
Earlier work this paper cites.
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills , Nucl. Phys. B725
2005
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, Bootstrapping multi-parton loop amplitudes in QCD , Phys. Rev. D73
2006
Earlier work this paper cites.
A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals , Nucl. Phys. B734
2006
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level , Nucl. Phys. B763
2007
Earlier work this paper cites.
D. Forde, Direct extraction of one-loop integral coefficients , Phys. Rev. D75
Original
2007
Earlier work this paper cites.
W. T. Giele, Z. Kunszt and K. Melnikov, Full one-loop amplitudes from tree amplitudes , JHEP 04
Original
2008
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, CutTools: A Program implementing the OPP reduction method to compute one-loop amplitudes , JHEP 03
Original
2008
Earlier work this paper cites.
C. F. Berger, Z. Bern, L. J. Dixon, F. Febres Cordero, D. Forde, H. Ita et al., An Automated Implementation of On-Shell Methods for One-Loop Amplitudes , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
G. Ossola, C. G. Papadopoulos and R. Pittau, On the Rational Terms of the one-loop amplitudes , JHEP 05
Original
2008
Earlier work this paper cites.
A. van Hameren, Multi-gluon one-loop amplitudes using tensor integrals , JHEP 07
Original
2009
Earlier work this paper cites.
A. van Hameren, C. G. Papadopoulos and R. Pittau, Automated one-loop calculations: A Proof of concept , JHEP 09
Original
2009
Earlier work this paper cites.
T. Gleisberg, S. Hoeche, F. Krauss, M. Schonherr, S. Schumann, F. Siegert et al., Event generation with SHERPA 1.1 , JHEP 02
Original
2009
Earlier work this paper cites.
P. Draggiotis, M. V. Garzelli, C. G. Papadopoulos and R. Pittau, Feynman Rules for the Rational Part of the QCD 1-loop amplitudes , JHEP 04
Original
2009
Earlier work this paper cites.

Similar

P. Mastrolia, G. Ossola, T. Reiter and F. Tramontano, Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level , JHEP 08
Original
2010
Cited alongside, same era.
S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX , JHEP 06
Original
2010
Cited alongside, same era.
A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD Corrections to Top Anti-Top Bottom Anti-Bottom Production at the LHC: 2. full hadronic results , JHEP 03
Original
2010
Cited alongside, same era.
M. V. Garzelli, I. Malamos and R. Pittau, Feynman rules for the rational part of the Electroweak 1-loop amplitudes , JHEP 01
Original
2010
Cited alongside, same era.
V. Hirschi, R. Frederix, S. Frixione, M. V. Garzelli, F. Maltoni and R. Pittau, Automation of one-loop QCD corrections , JHEP 05

Then

F. Cascioli, T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierhöfer et al., ZZ production at hadron colliders in NNLO QCD , Phys.Lett. B735
Original
2014
Later among the works it cites.
T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierhöfer, A. von Manteuffel et al., W + W − W^{+}W^{-} Production at Hadron Colliders in Next to Next to Leading Order QCD , Phys.Rev.Lett. 113
Original
2014
Later among the works it cites.
R. N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals , J. Phys. Conf. Ser. 523
Original
2014
Later among the works it cites.
T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten et al., An Introduction to PYTHIA 8.2 , Comput. Phys. Commun. 191
Original
2015
Later among the works it cites.
C. Weiss, B. Chokoufe Nejad, W. Kilian and J. Reuter, Automated NLO QCD Corrections with WHIZARD , PoS EPS-HEP2015

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

On-the-fly reduction of open loops

Buccioni, Federico, Pozzorini, Stefano, Zoller, Max

Understand

Building on the open-loop algorithm we introduce a new method for the automated construction of one-loop amplitudes and their reduction to scalar integrals.

The key idea is that the factorisation of one-loop integrands in a product of loop segments makes it possible to perform various operations on-the-fly while constructing the integrand.
Reducing the integrand on-the-fly, after each segment multiplication, the construction of loop diagrams and their reduction are unified in a single numerical recursion.
In this way we entirely avoid objects with high tensor rank, thereby reducing the complexity of the calculations in a drastic way.