REVIEW
An update on vector boson pair production at hadron colliders
High Energy Physics - Phenomenology · Submitted 18 May 1999 · 26 references
Pith's verdict: The paper that made diboson backgrounds quantitative — the NLO-plus-decay-correlations numbers in Tables 3–6 are the ones the experiments actually subtracted, and the external validation against Frixione-Nason-Mele-Ridolfi holds up.
T0 · AI review
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Referee report
The paper
The paper claims
The paper computes the full one-loop QCD corrections to W and Z pair production at hadron colliders, keeping the spin correlations of the decaying bosons so that experimental cuts can be applied to the final leptons.
The reading
What carries the argument
The load-bearing object is a next-to-leading-order Monte Carlo (MCFM) built on the dipole subtraction formalism of Catani and Seymour, fed by the six- and seven-particle helicity amplitudes of Dixon, Kunszt and Signer for the doubly-resonant diagrams plus a new set of sub-amplitudes $B^{tree,a}_7$ and $B^{tree,b}_7$ for the singly-resonant ones, which are obtained by relabelling the external legs of the same functions. Two further pieces carry weight. The propagator factors $P_{ij} = s_{ij}/(s_{ij}-M_{ij}^2)$ organize which diagrams are resonant, and the finite width is introduced not by modifying each propagator independently but by computing with $1/(q^2-M^2)$ and then multiplying the whole amplitude by $prod (q^2-M^2)/(q^2-M^2+iMGamma)$ over the resonant propagators, a prescription that preserves gauge invariance by construction. That trick is what allows the singly-resonant diagrams to be included at all, and it is also the source of the paper's main internal approximation.
Extended reading notes
Core claim
The central claim is that a full $O(alpha_s)$ calculation of $qbar q to V_1 V_2 to$ four leptons, with helicity amplitudes that keep every spin correlation through the decay, gives diboson cross sections that are meaningfully different from what the older literature and the existing event generators provide. At the Tevatron the $K$-factor is about $1.3$ for each channel and at the LHC it runs from about $1.3$ for $Z$ pairs to $1.7$ for $Z W^-$, so the QCD corrections are not a small perturbation on the Born rates. Two consequences are drawn out. First, the authors go beyond the zero-width approximation by including singly-resonant diagrams alongside the doubly-resonant ones, and they show in the trilepton channel that the off-shell photon contribution dominates the low dilepton-mass region, so analyses that included only the $Z$ (as the event generators then did) underestimate the Standard Model background in exactly the signal window used for supersymmetry. Second, applying the same machinery to a Higgs search in the $H to W^{(*)}W^{(*)}$ channel, they find all diboson backgrounds larger than a comparable PYTHIA-based study, by roughly a factor of two for the $WZ$-class events, while the signal itself is also about 20% larger, so the net effect on $S/sqrt{B}$ may be modest.
Load-bearing premise
The finite-width treatment multiplies the entire amplitude, singly-resonant diagrams included, by a product of Breit-Wigner ratios, and the authors state plainly that this is correct only for the doubly-resonant piece and mistreats the singly-resonant diagrams near $q^2 approx M^2$, with no numerical estimate of the size of that error anywhere in the paper.
Editorial extensions
If this is right
- Experimental searches at Run II and the LHC get a set of NLO diboson background numbers with the same lepton acceptance cuts they apply, replacing leading-order or parton-level estimates that were typically 30% low at the Tevatron.
- The $W Z/gamma^*$ channel, not $WZ$ alone, must be counted as background to trilepton supersymmetry searches, because the off-shell photon dominates the low invariant-mass region where the signal was defined.
- The residual scale dependence at next-to-leading order is small enough that the spread between modern parton distribution sets, about 3% at Run II and 6% at the LHC, becomes a leading theory uncertainty on these cross sections.
- Higgs searches in the $140$-$190$ GeV window have their dominant background fixed by the $W^+W^-$ rate, which the paper puts at $13.0$ pb total and $185$ fb after the di-lepton cuts of the analysis it compares to.
- Because the singly-resonant diagrams are included, the calculation can be used to model the high-mass tails of the Breit-Wigner distributions that matter when a new-physics signal sits far off the $Z$ peak.
Reading between the lines
- If the multiplicative width prescription misestimates the singly-resonant diagrams at the several-percent level, that error lands preferentially in the off-shell regions that new-physics searches use as signal windows, so the practical size of the effect is worth more than its formal status as an all-orders ambiguity.
- The comparison with PYTHIA-based studies suggests a general lesson beyond this paper: any search background quoted from a parton-shower generator that omits photon-mediated diboson diagrams and interference should be re-derived, since the missing piece is concentrated in the low-mass sidebands where background-suppression cuts often sit.
- The fact that the signal and the background both grew by comparable factors relative to the earlier analysis implies that $S/sqrt{B}$ is a blunt instrument for judging whether a background update matters; the shape of the dilepton mass distribution carries more information than the total rate.
- Having the full spin correlations in the decay means the same machinery could be re-run with arbitrary polarization or angular observables imposed on the leptons, which is where anomalous triple-gauge-coupling searches would look for deviations from these Standard Model predictions.
Original abstract
We present numerical results (including full one-loop QCD corrections) for the processes p p-bar and pp -> W+ W-, W+/- Z/gamma* and Z/gamma* Z/gamma* followed by the decay of the massive vector bosons into leptons. In addition to their intrinsic importance as tests of the standard model, these processes are also backgrounds to conjectured non-standard model processes. Because of the small cross sections at the Tevatron, full experimental control of these backgrounds will be hard to achieve. This accentuates the need for up-to-date theoretical information. A comparison is made with earlier work and cross section results are presented for p p-bar collisions at sqrt{s}=2 TeV and pp collisions at sqrt{s}=14 TeV. Practical examples of the use of our calculations are presented.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We present numerical results (including full one-loop QCD corrections) for the processes p p-bar and pp -> W+ W-, W+/- Z/gamma* and Z/gamma* Z/gamma* followed by the decay of the massive vector bosons into leptons. In addition to their intrinsic importance as tests of the standard model, these processes are also backgrounds to conjectured non-standard model processes. Because of the small cross sections at the Tevatron, full experimental control of these backgrounds will be hard to achieve. This accentuates the need for up-to-date theoretical information. A comparison is made with earlier work and cross section results are presented for p p-bar collisions at sqrt{s}=2 TeV and pp collisions at sqrt{s}=14 TeV. Practical examples of the use of our calculations are presented.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present numerical results (including full one-loop QCD corrections) for the processes p p-bar and pp -> W+ W-, W+/- Z/gamma* and Z/gamma* Z/gamma* followed by the decay of the massive vector bosons into leptons. | contribution 0.99 | 0.96 | 0.17 | asserted 1.00 |
| s1 | In addition to their intrinsic importance as tests of the standard model, these processes are also backgrounds to conjectured non-standard model processes. | background 0.93 | 0.07 | 0.05 | asserted 0.97 |
| s2 | Because of the small cross sections at the Tevatron, full experimental control of these backgrounds will be hard to achieve. | background 0.88 | 0.24 | 0.07 | hedged possibility 0.56 |
| s3 | This accentuates the need for up-to-date theoretical information. | background 0.52 | 0.08 | 0.11 | asserted 0.98 |
| s4 | A comparison is made with earlier work and cross section results are presented for p p-bar collisions at sqrt{s}=2 TeV and pp collisions at sqrt{s}=14 TeV. | result 0.71 | 0.89 | 0.13 | asserted 1.00 |
| s5 | Practical examples of the use of our calculations are presented. | contribution 0.98 | 0.86 | 0.07 | asserted 0.98 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:hep-ph/9905386 by the authors.
References
How later papers used it
246 later papers cite it
21 later papers by other authors are listed below: 13 used its method or tool, 6 used its data or values and 2 compared their own results with it. 1 more paper by the same authors is listed: 1 used its method or tool.
Uses its method or tool 14 of 102 papers with this label · 1 by the same authors
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Calculated the inclusive cross section for p p-bar to c c-bar plus X using the Monte-Carlo program MCFM.
Parton Model Calculation of Inclusive Charm Production by a Low-energy Antiproton Beam (2009) · 1.00 · paraphrased: the licence does not allow quoting
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Considered the invariant mass spectrum of the t t-bar pair calculated up to next-to-leading order as implemented in MCFM.
Top pair invariant mass distribution: a window on new physics (2007) · 1.00 · paraphrased: the licence does not allow quoting
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Calculated the W+ and W- cross sections and their uncertainties at 7 TeV using MCFM v5.8.
A New Method for Indirect Mass Measurements using the Integral Charge Asymmetry at the LHC (2014) · 1.00 · paraphrased: the licence does not allow quoting
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Calculated the cross-sections for W or Z bosons associated with jets at next-to-leading order using the MCFM Monte Carlo program.
Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in $pp$ collisions at ${\sqrt{s}}$ = 7 TeV with the ATLAS detector (2014) · 1.00 · paraphrased: the licence does not allow quoting
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Used the strict NLO parton level tools MCFM (6.3) and VBFNLO (2.6.0) with their built-in analysis routines.
NLO tools and the background to $H\rightarrow WW$ (2012) · 1.00 · paraphrased: the licence does not allow quoting
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Used the MCFM code for these pT-integrated results.
Constraints for the nuclear parton distributions from Z and W production at the LHC (2010) · 1.00 · paraphrased: the licence does not allow quoting
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The acceptance correction is computed at NLO for the $Z$ plus jet process ($O(α_S^2)$, where $α_S$ is the strong coupling constant), using the MCFM v6.8 program [ref] , interfaced to APPLGRID [ref] .
Defiducialization: Providing Experimental Measurements for Accurate Fixed-Order Predictions (2020) · Introduction · 1.00
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Gave the NLO normalization of these rates by MCFM or PROSPINO2.
Measuring Supersymmetry with Heavy Scalars (2010) · 1.00 · paraphrased: the licence does not allow quoting
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The grids were generated using the [ref] generator.
Parton Distribution Functions of the Charged Pion Within The xFitter Framework (2020) · Cross-section calculation · 1.00
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Computed the W, Z, t t-bar and gg to H total NLO cross sections for LHC kinematics at 14 TeV using the MCFM code.
Deviations from NLO QCD evolution in inclusive HERA data (2009) · 1.00 · paraphrased: the licence does not allow quoting
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Used the original 6.6 implementation in the scheme.
Matching NLO QCD with parton shower in Monte Carlo scheme - the KrkNLO method (2015) · 0.98 · paraphrased: the licence does not allow quoting
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Calculated the theoretical predictions for the data at NLO using the program.
Measurement of double-differential cross sections for top quark pair production in pp collisions at sqrt(s) = 8 TeV and impact on parton distribution functions (2017) · 0.98 · paraphrased: the licence does not allow quoting
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Did the NLO Standard Model expectation of top quark pair production with this paper and the next-to-leading order generator.
Properties of the Top Quark (2010) · 0.97 · paraphrased: the licence does not allow quoting
By the same authors
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Performed a parton-level analysis of all the major background processes using the general purpose NLO program MCFM.
Next-to-leading order predictions for WW + 1 jet distributions at the LHC (2007) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Uses its data or values 6 of 31 papers with this label
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Obtained the total asymmetries with good approximation by summing the Standard Model values to its own new-physics contributions.
Simple models for the top asymmetry: constraints and predictions (2011) · 1.00 · paraphrased: the licence does not allow quoting
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Took the NLO cross sections for the Standard Model W+W- and ZZ background processes from this paper.
LHC phenomenology of a two-Higgs-doublet neutrino mass model (2010) · 0.99 · paraphrased: the licence does not allow quoting
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The associated production of vector bosons ($$ production) is simulated at LO using , and normalized to the cross sections at NNLO precision for $$ production [ref] , and at NLO precision for $$ and $$ production [ref] .
Search for dark matter produced in association with a dark Higgs boson decaying into a bottom quark-antiquark pair in proton-proton collisions at $\sqrt{s}$ = 13 TeV (2026) · Simulated samples · 0.92
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The samples are normalised to NLO accuracy cross-sections in QCD [ref] .
Measurements of inclusive and differential cross-sections of combined $t\bar{t}\gamma$ and $tW\gamma$ production in the $e\mkern-2mu\mu$ channel at 13 TeV with the ATLAS detector (2020) · Signal and background modelling · 0.89
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The theoretical NLO cross-section for events with one lepton is $29.4±1.5$ [ref] .
Measurement of single top-quark production in association with a $W$ boson in the single-lepton channel at $\sqrt{s} = 8$ TeV with the ATLAS detector (2020) · Data and simulated event samples · 0.84
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The diboson and $tt̅$ samples are inclusive and their normalizations use total cross sections calculated at NLO [ref] and next-to-next-to-leading order [ref] , respectively.
Measurement of the charge asymmetry of electrons from the decays of $W$ bosons produced in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV (2021) · Backgrounds · 0.95
Compares with it 2 of 21 papers with this label
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Found its own LO and NLO QCD corrected cross sections in the Standard Model in good agreement with this paper's within the integration errors.
Revisiting the large extra dimension effects on $W$-pair production at the LHC in NLO QCD (2011) · 1.00 · paraphrased: the licence does not allow quoting
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Compared its results for top-pair production with those of MCFM.
Automation of one-loop QCD corrections (2011) · 1.00 · paraphrased: the licence does not allow quoting
How the literature uses it
229 arXiv papers cite this in 282 sentences
Papers citing it · 79 sentences without a confident label
Builds on it 3 papers
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It is the goal of this study to extend our previous setup [ref] , publicly available in [ref] , and which provides finite $m_t$ effects in the region $p_t≪2m_t$, to predictions with a finite $m_t$ for $p_T≫2 m_t$.
NLO Higgs+jet at large transverse momenta including top quark mass effects · Introduction · 0.98
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In this letter, we report on an extension of the well-known NLO parton-level program ~ [ref] , which allows the one-loop matrix elements in to be accessed using the Binoth Les Houches Accord (BLHA)~ [ref] via a direct C++ interface The source code is available at https://gitlab.com/mcfm-team/releasesgitlab.com/mcfm-team/releases. footnote.
Accelerating LHC phenomenology with analytic one-loop amplitudes: A C++ interface to MCFM · Introduction · 0.85
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[ref] – and the $gg$ process is included for five massless flavours.
Vector boson pair production at the LHC · Description of the calculation · 0.97
Uses its method or tool 100 papers
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We took the matrix elements for the Born, real and virtual amplitudes from the calculations of Ref. [ref] , borrowing heavily from their implementation in the package [ref] .
W+W-, WZ and ZZ production in the POWHEG BOX · Description of the implementation · 0.89
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For the calculation of W/Z+jets at , we used LoopSim together with [ref] and independently with + ntuples.
Simulated NNLO for high-pT observables in vector boson + jets production at the LHC · Details of the calculation · 1.00
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The inclusive cross section for $p̅ p →c c̅+X$ is calculated using the Monte-Carlo program MCFM [ref] .
Parton Model Calculation of Inclusive Charm Production by a Low-energy Antiproton Beam · Introduction · 1.00
Uses its data or values 25 papers
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The uncertainties shown include theoretical uncertainties in the production cross sections of the processes [ref] .
Measurement of the inclusive $t\bar{t}$ production cross section in the lepton+jets channel in $pp$ collisions at $\sqrt{s}$= 7 TeV with the ATLAS detector using support vector machines · Signal and background classes · 0.90
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The background from $WW$ events is normalized to NLO calculations from [ref] .
Evidence for WZ and ZZ production in final states with b-tagged jets · Summary of Contributing Analyses · 0.84
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The signal cross-sections are scaled by a $K$-factor of 1.25 to match the cross-section values predicted by an NLO perturbative QCD calculation using MCFM [ref] with the CT10 PDF set [ref] as quoted in section [ref].
Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in $pp$ collisions at ${\sqrt{s}}$ = 7 TeV with the ATLAS detector · Data sample and Monte Carlo simulation · 0.89
Compares with it 19 papers
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We also compare our analytic results for the $(α_s)$ NLP power corrections with the full nonsingular spectrum obtained numerically from the LO $V+$jet and $H+$jet calculations in MCFM8 [ref] .
Power Corrections for N-Jettiness Subtractions at ${\cal O}(\alpha_s)$ · Numerical Results · 0.92
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This measurement is consistent with the NLO SM prediction of $σ(VZ)=±$ pb [ref] .
Evidence for WZ and ZZ production in final states with b-tagged jets · Measurement of the $WZ+ZZ$ Cross Section · 0.97
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It shows that our LO and NLO QCD corrected cross sections in the SM are in good agreement with those in Ref. [ref] within the integration errors.
Revisiting the large extra dimension effects on $W$-pair production at the LHC in NLO QCD · Numerical results and discussions · 1.00
Cites it as background 33 papers
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Results at fixed next-to-leading-order (NLO) in QCD for W/Z in association with up to 2 jets are available from [ref] , up to 3 jets from [ref] , and up to 4 jets (5 in the case of W) from [ref] + [ref] .
Simulated NNLO for high-pT observables in vector boson + jets production at the LHC · Introduction · 0.93
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The helicity amplitudes for the process including decays have been calculated in [ref] , followed by phenomenological studies in [ref] .
Anomalous coupling, top-mass and parton-shower effects in ${W^+W^-}$ production · Introduction · 0.96
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First steps towards this direction have been taken by calculating two-loop contributions [ref] , the full α corrections to the and decay widths [ref] , the α EW corrections to $/+$ production [ref] , and the QCD corrections to $/+$ production [ref] .
Mixed QCD-electroweak O(\alpha_s\alpha) corrections to Drell-Yan processes in the resonance region: pole approximation and non-factorizable corrections · Introduction · 0.81
Discussion
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