skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Tensor integrand reduction via Laurent expansion

Abstract

We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem95. We find that Ninja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than Ninja. Lastly, we considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.

Authors:
 [1];  [2]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. The Univ. of Edinburgh, Scotland (United Kingdom)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1281026
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 6; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; scattering amplitudes; perturbative QCD

Citation Formats

Hirschi, Valentin, and Peraro, Tiziano. Tensor integrand reduction via Laurent expansion. United States: N. p., 2016. Web. doi:10.1007/JHEP06(2016)060.
Hirschi, Valentin, & Peraro, Tiziano. Tensor integrand reduction via Laurent expansion. United States. doi:10.1007/JHEP06(2016)060.
Hirschi, Valentin, and Peraro, Tiziano. Thu . "Tensor integrand reduction via Laurent expansion". United States. doi:10.1007/JHEP06(2016)060. https://www.osti.gov/servlets/purl/1281026.
@article{osti_1281026,
title = {Tensor integrand reduction via Laurent expansion},
author = {Hirschi, Valentin and Peraro, Tiziano},
abstractNote = {We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem95. We find that Ninja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than Ninja. Lastly, we considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.},
doi = {10.1007/JHEP06(2016)060},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2016,
place = {United States},
year = {2016},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 15 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Reducing full one-loop amplitudes to scalar integrals at the integrand level
journal, February 2007


A numerical unitarity formalism for evaluating one-loop amplitudes
journal, March 2008


Full one-loop amplitudes from tree amplitudes
journal, April 2008


OneLOop: For the evaluation of one-loop scalar functions
journal, November 2011


golem95: A numerical program to calculate one-loop tensor integrals with up to six external legs
journal, November 2009

  • Binoth, T.; Guillet, J. -Ph.; Heinrich, G.
  • Computer Physics Communications, Vol. 180, Issue 11
  • DOI: 10.1016/j.cpc.2009.06.024

Tools for NLO automation: Extension of the golem95C integral library
journal, June 2014

  • Guillet, J. Ph.; Heinrich, G.; von Soden-Fraunhofen, J. F.
  • Computer Physics Communications, Vol. 185, Issue 6
  • DOI: 10.1016/j.cpc.2014.03.009

Automated one-loop calculations in four and D dimensions
journal, May 1999


Scalar one-loop integrals for QCD
journal, February 2008


FF — a package to evaluate one-loop Feynman diagrams
journal, July 1991


CutTools : a program implementing the OPP reduction method to compute one-loop amplitudes
journal, March 2008

  • Ossola, Giovanni; Papadopoulos, Costas G.; Pittau, Roberto
  • Journal of High Energy Physics, Vol. 2008, Issue 03
  • DOI: 10.1088/1126-6708/2008/03/042

Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level
journal, August 2010

  • Mastrolia, P.; Ossola, G.; Reiter, T.
  • Journal of High Energy Physics, Vol. 2010, Issue 8
  • DOI: 10.1007/JHEP08(2010)080

Automated one-loop calculations: a proof of concept
journal, September 2009


Helac-Nlo
journal, March 2013

  • Bevilacqua, G.; Czakon, M.; Garzelli, M. V.
  • Computer Physics Communications, Vol. 184, Issue 3
  • DOI: 10.1016/j.cpc.2012.10.033

Automated one-loop calculations with GoSam
journal, March 2012


Scattering Amplitudes with Open Loops
journal, March 2012


NGluon: A package to calculate one-loop multi-gluon amplitudes
journal, August 2011


Numerical evaluation of virtual corrections to multi-jet production in massless QCD
journal, August 2013

  • Badger, Simon; Biedermann, Benedikt; Uwer, Peter
  • Computer Physics Communications, Vol. 184, Issue 8
  • DOI: 10.1016/j.cpc.2013.03.018

Tensorial reconstruction at the integrand level
journal, October 2010

  • Heinrich, G.; Ossola, G.; Reiter, T.
  • Journal of High Energy Physics, Vol. 2010, Issue 10
  • DOI: 10.1007/JHEP10(2010)105

Automation of one-loop QCD computations
journal, May 2011

  • Hirschi, Valentin; Frederix, Rikkert; Frixione, Stefano
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)044

The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
journal, July 2014

  • Alwall, J.; Frederix, R.; Frixione, S.
  • Journal of High Energy Physics, Vol. 2014, Issue 7
  • DOI: 10.1007/JHEP07(2014)079

One-loop corrections for e+e− annihilation into μ+μ− in the Weinberg model
journal, November 1979


A simple formula for reducing Feynman diagrams to scalar integrals
journal, July 1991


Recent Progress in the Golem Project
journal, August 2010


One-loop tensor Feynman integral reduction with signed minors
journal, June 2012


ALOHA: Automatic libraries of helicity amplitudes for Feynman diagram computations
journal, October 2012

  • de Aquino, Priscila; Link, William; Maltoni, Fabio
  • Computer Physics Communications, Vol. 183, Issue 10
  • DOI: 10.1016/j.cpc.2012.05.004

Integrand reduction of one-loop scattering amplitudes through Laurent series expansion
journal, June 2012

  • Mastrolia, Pierpaolo; Mirabella, Edoardo; Peraro, Tiziano
  • Journal of High Energy Physics, Vol. 2012, Issue 6
  • DOI: 10.1007/JHEP06(2012)095

Direct extraction of one loop rational terms
journal, January 2009


Ninja: Automated integrand reduction via Laurent expansion for one-loop amplitudes
journal, October 2014


Multi-leg one-loop massive amplitudes from integrand reduction via Laurent expansion
journal, March 2014

  • van Deurzen, Hans; Luisoni, Gionata; Mastrolia, Pierpaolo
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)115

The complex-mass scheme for perturbative calculations with unstable particles
journal, October 2006


Feynman rules for the rational part of the QCD 1-loop amplitudes
journal, April 2009


Symmetric Tensors and Symmetric Tensor Rank
journal, January 2008

  • Comon, Pierre; Golub, Gene; Lim, Lek-Heng
  • SIAM Journal on Matrix Analysis and Applications, Vol. 30, Issue 3
  • DOI: 10.1137/060661569

The total cross section for the production of heavy quarks in hadronic collisions
journal, July 1988


Next-to-Leading-Order QCD Corrections to t t ¯ + jet Production at Hadron Colliders
journal, June 2007


Dominant QCD Backgrounds in Higgs Boson Analyses at the LHC: A Study of p p t t ¯ + 2 Jets at Next-to-Leading Order
journal, April 2010


A framework for Higgs characterisation
journal, November 2013

  • Artoisenet, P.; de Aquino, P.; Demartin, F.
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)043

Higgs Production with Large Transverse Momentum in Hadronic Collisions at Next-to-Leading Order
journal, June 1999


Next-to-Leading-Order QCD Corrections to Higgs Boson Production Plus Three Jets in Gluon Fusion
journal, September 2013


NLO QCD corrections to the production of Higgs plus two jets at the LHC
journal, April 2013


Next-to-leading order QCD corrections to the Drell–Yan cross section in models of TeV-scale gravity
journal, May 2005


Automated event generation for loop-induced processes
journal, October 2015

  • Hirschi, Valentin; Mattelaer, Olivier
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)146

Z-boson pair production via gluon fusion
journal, July 1989


Production of γZg and associated processes via gluon fusion at hadron colliders
journal, January 2013

  • Agrawal, Pankaj; Shivaji, Ambresh
  • Journal of High Energy Physics, Vol. 2013, Issue 1
  • DOI: 10.1007/JHEP01(2013)071

Recursive generation of one-loop amplitudes in the Standard Model
journal, April 2013


Reduction schemes for one-loop tensor integrals
journal, January 2006


Scalar one-loop 4-point integrals
journal, March 2011


Parton distributions with LHC data
journal, February 2013


    Works referencing / citing this record:

    VHH production at the high-luminosity LHC
    journal, June 2019


    Precise predictions for single-top production: the impact of EW corrections and QCD shower on the t-channel signature
    journal, September 2019

    • Frederix, Rikkert; Pagani, Davide; Tsinikos, Ioannis
    • Journal of High Energy Physics, Vol. 2019, Issue 9
    • DOI: 10.1007/jhep09(2019)122

    Precise predictions for single-top production: the impact of EW corrections and QCD shower on the t-channel signature
    journal, September 2019

    • Frederix, Rikkert; Pagani, Davide; Tsinikos, Ioannis
    • Journal of High Energy Physics, Vol. 2019, Issue 9
    • DOI: 10.1007/jhep09(2019)122

    Automated simulations beyond the Standard Model: supersymmetry
    journal, December 2019

    • Frixione, Stefano; Fuks, Benjamin; Hirschi, Valentin
    • Journal of High Energy Physics, Vol. 2019, Issue 12
    • DOI: 10.1007/jhep12(2019)008

    VHH production at the high-luminosity LHC
    journal, June 2019