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OpenLoops 2
High Energy Physics - Phenomenology · Submitted 30 Jul 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting significant speed and stability improvements are especially relevant for challenging NLO multi-leg calculations and for NNLO applications.
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The abstract, sentence by sentence
We present the new version of OpenLoops, an automated generator of tree and one-loop scattering amplitudes based on the open-loop recursion. One main novelty of OpenLoops 2 is the extension of the original algorithm from NLO QCD to the full Standard Model, including electroweak (EW) corrections from gauge, Higgs and Yukawa interactions. In this context, among several new features, we discuss the systematic bookkeeping of QCD-EW interferences, a flexible implementation of the complex-mass scheme for processes with on-shell and off-shell unstable particles, a special treatment of on-shell and off-shell external photons, and efficient scale variations. The other main novelty is the implementation of the recently proposed on-the-fly reduction algorithm, which supersedes the usage of external reduction libraries for the calculation of tree-loop interferences. This new algorithm is equipped with an automated system that avoids Gram-determinant instabilities through analytic methods in combination with a new hybrid-precision approach based on a highly targeted usage of quadruple precision with minimal CPU overhead. The resulting significant speed and stability improvements are especially relevant for challenging NLO multi-leg calculations and for NNLO applications.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present the new version of OpenLoops, an automated generator of tree and one-loop scattering amplitudes based on the open-loop recursion. | contribution 1.00 | 0.91 | 0.15 | asserted 1.00 |
| s1 | One main novelty of OpenLoops 2 is the extension of the original algorithm from NLO QCD to the full Standard Model, including electroweak (EW) corrections from gauge, Higgs and Yukawa interactions. | contribution 1.00 | 0.88 | 0.22 | asserted 1.00 |
| s2 | In this context, among several new features, we discuss the systematic bookkeeping of QCD-EW interferences, a flexible implementation of the complex-mass scheme for processes with on-shell and off-shell unstable particles, a special treatment of on-shell and off-shell external photons, and efficient scale variations. | contribution 0.84 | 0.87 | 0.07 | asserted 0.97 |
| s3 | The other main novelty is the implementation of the recently proposed on-the-fly reduction algorithm, which supersedes the usage of external reduction libraries for the calculation of tree-loop interferences. | contribution 0.97 | 0.91 | 0.12 | asserted 1.00 |
| s4 | This new algorithm is equipped with an automated system that avoids Gram-determinant instabilities through analytic methods in combination with a new hybrid-precision approach based on a highly targeted usage of quadruple precision with minimal CPU overhead. | method 0.92 | 0.88 | 0.10 | asserted 1.00 |
| s5 | The resulting significant speed and stability improvements are especially relevant for challenging NLO multi-leg calculations and for NNLO applications. | interpretation 0.57 | 0.82 | 0.45 | asserted 0.99 |
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The paper
Original abstract
We present the new version of OpenLoops, an automated generator of tree and one-loop scattering amplitudes based on the open-loop recursion. One main novelty of OpenLoops 2 is the extension of the original algorithm from NLO QCD to the full Standard Model, including electroweak (EW) corrections from gauge, Higgs and Yukawa interactions. In this context, among several new features, we discuss the systematic bookkeeping of QCD-EW interferences, a flexible implementation of the complex-mass scheme for processes with on-shell and off-shell unstable particles, a special treatment of on-shell and off-shell external photons, and efficient scale variations. The other main novelty is the implementation of the recently proposed on-the-fly reduction algorithm, which supersedes the usage of external reduction libraries for the calculation of tree-loop interferences. This new algorithm is equipped with an automated system that avoids Gram-determinant instabilities through analytic methods in combination with a new hybrid-precision approach based on a highly targeted usage of quadruple precision with minimal CPU overhead. The resulting significant speed and stability improvements are especially relevant for challenging NLO multi-leg calculations and for NNLO applications.
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References
How the literature uses it
340 arXiv papers cite this in 456 sentences
Papers citing it · 80 sentences without a confident label
Builds on it 1 paper
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The latter have been computed [ref] using the two-loop integrals of [ref] , as well as OpenLoops [ref] and Package-X [ref] for the one-loop amplitudes.
Impact of NNLO QED corrections on lepton-proton scattering at MUSE · Calculation · 0.82
Uses its method or tool 258 papers
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The exact fixed-order NLO EW results have been obtained with the + [ref] framework, allowing for a fully automated calculation of cross sections and observables at next-to-leading order in the electroweak coupling.
Four lepton production and the accuracy of QED FSR · Computational methods · 0.99
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A stable and fast implementation of the delicate real-virtual matrix element was possible by combining OpenLoops [ref] with NTS stabilisation [ref] .
Muon-electron scattering at NNLO · Conclusions and outlook · 1.00
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The one-loop-squared amplitudes for the $pp→H$, $pp→Hj$, and $pp→Hjj$ processes are computed through [ref] .
Higgs-boson production in the full theory at NNLO+PS · Outline of the calculation · 1.00
Uses its data or values 1 paper
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The NLO squared amplitudes come from the interference between tree-level and one-loop amplitudes, which can be obtained from the literature as well as various program packages [ref] .
Two-loop QCD amplitudes for $t\bar{t}H$ production from boosted limit · Numeric results · 0.80
Compares with it 39 papers
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Our private build of 2 [ref] was checked on the amplitude level against the private version of used in [ref] for various DPA setups.
NNLO QCD study of polarised $W^+ W^-$ production at the LHC · Tools used in the calculation · 0.93
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We will compare our approximations to OpenLoops [ref] running in quadruple precision mode [ref] .
Universal structure of radiative QED amplitudes at one loop · Validation · 0.87
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The amplitudes with axial vector coupling in the gluonic channel are again a new result and we found agreement for all helicity amplitudes with the numerical result from OpenLoops 2 [ref] .
Two-loop helicity amplitudes for $V+$jet production including axial vector couplings to higher orders in $\epsilon$ · Checks and results · 1.00
Cites it as background 11 papers
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In particular, such corrections have been implemented in Monte Carlo generators and they have been even automated [ref] , at different levels in the different frameworks, using various one-loop matrix-element providers [ref] .
One-loop electroweak Sudakov logarithms: a revisitation and automation · Introduction · 0.81
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In the literature, logarithmic electroweak corrections at the leading power have been intensively studied [ref] , and have been recently implemented in [ref] .
Analytic two-loop electroweak corrections at high energies · Introduction · 0.95
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The past two decades have seen the fast development of automation programs for the calculation of QCD and EW corrections for various scattering processes at one loop accuracy [ref] .
Electroweak corrections to Higgs boson production via W W fusion at the future LHeC · Introduction · 0.93
What it cites · 84 sentences without a confident label
Uses the method or tool of 34 papers
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The on-the-fly reduction methods [ref] implemented in are supplemented by a new stability system, which is based on the analysis of the analytic structure of spurious singularities in the employed reduction identities.
On-the-fly reduction of open loops · On-the-fly stability system · 0.80
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In this section we outline two variants of this procedure: the original open-loop method [ref] , which was used throughout in and is still used for loop-induced processes in , and the new on-the-fly method [ref] used for tree–loop interferences in .
Scattering Amplitudes with Open Loops · The algorithm · 0.91
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In , as detailed below, numerical instabilities are avoided by means of the library [ref] in combination with a stability rescue system that makes use of [ref] in qp.
CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes · Numerical stability · 1.00
Cites as background 22 papers
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[This type of recursion was first proposed in the context of off-shell recurrence relations for colour-ordered gluon-scattering amplitudes [ref] .]
Multi-gluon one-loop amplitudes using tensor integrals · Introduction · 0.94
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Nowadays, thanks to a variety of modern techniques [ref] , one-loop calculations can be carried out with a number of automated and widely applicable programs [ref]
Full one-loop amplitudes from tree amplitudes · Introduction · 0.99
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Nowadays, thanks to a variety of modern techniques [ref] , one-loop calculations can be carried out with a number of automated and widely applicable programs [ref]
An Automated Implementation of On-Shell Methods for One-Loop Amplitudes · Introduction · 0.99
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