Tensor integrand reduction via Laurent expansion

Hirschi, Valentin; Peraro, Tiziano

doi:10.1007/JHEP06(2016)060

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:

Hirschi, Valentin ^[1]; Peraro, Tiziano ^[2]

SLAC National Accelerator Lab., Menlo Park, CA (United States)
The Univ. of Edinburgh, Scotland (United Kingdom)

Publication Date:: Thu Jun 09 00:00:00 EDT 2016

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.

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                    Hirschi, Valentin, & Peraro, Tiziano. Tensor integrand reduction via Laurent expansion.  United States.  https://doi.org/10.1007/JHEP06(2016)060

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                    Hirschi, Valentin, and Peraro, Tiziano. Thu .  
"Tensor integrand reduction via Laurent expansion".  United States.  https://doi.org/10.1007/JHEP06(2016)060.  https://www.osti.gov/servlets/purl/1281026.

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@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         = {Thu Jun 09 00:00:00 EDT 2016},

  month        = {Thu Jun 09 00:00:00 EDT 2016}

}

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Works referenced in this record:

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Title: Tensor integrand reduction via Laurent expansion

Abstract

Citation Formats

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

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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

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

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

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

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

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Adaptive Integrand Decomposition in parallel and orthogonal space text, January 2016

The complete NLO corrections to dijet hadroproduction text, January 2016

NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers text, January 2017

Top-quark pair hadroproduction in association with a heavy boson at NLO+NNLL including EW corrections text, January 2019

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Reducing full one-loop amplitudes to scalar integrals at the integrand level
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A numerical unitarity formalism for evaluating one-loop amplitudes
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Full one-loop amplitudes from tree amplitudes
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OneLOop: For the evaluation of one-loop scalar functions
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golem95: A numerical program to calculate one-loop tensor integrals with up to six external legs
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Tools for NLO automation: Extension of the golem95C integral library
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Automated one-loop calculations in four and D dimensions
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Scalar one-loop integrals for QCD
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`CutTools` : a program implementing the `OPP` reduction method to compute one-loop amplitudes
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Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level
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Automated one-loop calculations: a proof of concept
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Helac-Nlo
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Automated one-loop calculations with GoSam
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Tensorial reconstruction at the integrand level
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journal, November 1979

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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

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

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

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

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

Next-to-Leading-Order QCD Corrections to $t \bar{t} + jet$ Production at Hadron Colliders
journal, June 2007

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

A framework for Higgs characterisation
journal, November 2013

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

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

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

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

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

Precise predictions for same-sign W-boson scattering at the LHC
text, January 2018

Automated simulations beyond the Standard Model: supersymmetry
text, January 2019

Precise predictions for same-sign W-boson scattering at the LHC
journal, August 2018

Precise predictions for same-sign W-boson scattering at the LHC
text, January 2018

Adaptive Integrand Decomposition in parallel and orthogonal space
text, January 2016

The complete NLO corrections to dijet hadroproduction
text, January 2016

NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers
text, January 2017

Top-quark pair hadroproduction in association with a heavy boson at NLO+NNLL including EW corrections
text, January 2019

Automated simulations beyond the Standard Model: supersymmetry
text, January 2019