Effects of bottom quark induced processes on polarized $W^+W^-$ production at the LHC at NLO

Duc Ninh Le; Thi Nhung Dao

REVIEW 2 major objections 3 minor 18 references

Effects of bottom quark induced processes on polarized $W^+W^-$ production at the LHC at NLO

T0 review · 2 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Bottom quarks lift the doubly-longitudinal WW fraction by up to 10.5%

desk verdict A clear, honest proceedings summary of the authors' own published NLO calculation; the central LL-enhancement claim is plausible but rests on details deferred to [17], and the report should be read as a status report rather than a self-contained result. read the letter →

arxiv 2505.23234 v1 pith:XHQOQESO submitted 2025-05-29 hep-ph hep-ex

Duc Ninh Le , Thi Nhung Dao This is my paper

classification hep-phhep-ex

keywords polarizedW+W-productionbottom-quarkinducedprocessestop-quarksubtractiondouble-poleapproximationNLOQCD+EWcorrectionslongitudinalpolarizationLHCfive-flavorscheme

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that bottom-quark induced processes, once the on-shell top-quark contribution is subtracted, have a noticeably larger effect on the doubly-longitudinal polarization of W+W- pairs at the LHC than on the unpolarized cross section. Using NLO QCD plus electroweak accuracy, the authors show that including these bottom-induced processes raises the $W_L^+ W_L^-$ polarization fraction from 6.6% to 7.1% with a jet veto and from 5.7% to 6.3% without one, corresponding to relative increases of about 7.6% and 10.5%. The result matters because polarization fractions are extracted from templates, and missing bottom-induced contributions would bias the measured longitudinal polarization fraction.

What carries the argument

The double-pole approximation (DPA), which maps off-shell momenta onto on-shell $W$ momenta so that production and decay amplitudes are separately gauge invariant, is used to define polarized amplitudes. The top-quark contribution at NLO is identified with the on-shell tW mechanism, and its contribution is computed and subtracted separately for each polarization mode in order to match the experimental signal definition. This per-polarization subtraction is the element that makes the reported bottom-induced shifts in the longitudinal fraction well defined.

What would settle it

Repeat the NLO calculation with a different on-shell projection or with a full off-shell treatment of the top-quark background; if the extracted $W_L^+ W_L^-$ fraction changes by more than the quoted scale uncertainty when the subtraction scheme is varied, the reported 7.6% and 10.5% enhancements are scheme-dependent rather than physical.

Watch

Extended reading notes

Core claim

The central claim is that, after subtracting the on-shell top-quark (tW) contribution, bottom-quark induced processes increase the doubly-longitudinal $W^+W^-$ polarization fraction more than other polarization channels. Concretely, the $W_L^+ W_L^-$ fraction changes from 6.6% to 7.1% under a jet veto (YesVeto) and from 5.7% to 6.3% without a veto (NoVeto), while the transverse-transverse fraction decreases modestly. The paper presents this as the first NLO QCD+EW result where the top-quark subtraction is performed separately for each polarization state, as required for a consistent definition of the inclusive polarized $W^+W^-$ signal in the five-flavor scheme.

Load-bearing premise

The result relies on the assumption that the on-shell top-quark contribution can be unambiguously identified with the tW mechanism and subtracted separately for each polarization without leaving a large scheme-dependent remainder.

Editorial extensions

If this is right

If the result is correct, experimental extractions of the $W_L^+ W_L^-$ fraction at the LHC should include bottom-induced contributions in the signal templates, otherwise the longitudinal fraction is underestimated by roughly 7-10 percent at NLO.
The per-polarization top-quark subtraction established here provides a template for defining other inclusive diboson signals where top-quark backgrounds overlap with resonant production.
The jet-veto setup, which treats the bottom jet like any other jet, is shown to reduce the impact of bottom-induced effects on the longitudinal fraction, guiding experimental choices between veto and no-veto analyses.
The accidental cancellation of scale uncertainties around a 35 GeV jet-veto threshold should be treated with caution, as the paper notes these uncertainties are likely underestimated.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The 7.6% and 10.5% shifts in the longitudinal fraction likely translate into a similar bias in fits of longitudinal polarization fractions from kinematic distributions, meaning that current templates that omit bottom-induced processes could lead to a systematically low $f_{LL}$ in ATLAS and CMS measurements.
A full off-shell calculation or a different on-shell projection scheme could test the robustness of the subtraction; if the scheme dependence exceeds the quoted scale uncertainty, the precise numerical shift is not yet fully settled.
The method could be extended to NNLO QCD, where top-pair mediated contributions enter; at that order the subtraction of the on-shell top contribution becomes more involved and the reported NLO shift is a lower-bound estimate of the bottom-induced effect.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know this is not a standalone research paper. It is a proceedings contribution in which the authors summarize their own recent NLO QCD+EW calculation of polarized W+W- production in the five-flavor scheme, with the key numbers taken from [17]. The physics content is real: the bottom-induced effects after subtracting the on-shell tW contribution shift the doubly-longitudinal fraction by 7.6% (YesVeto) and 10.5% (NoVeto), and that is a nontrivial correction for polarization measurements at the LHC.

What the report does well: the discussion of the 5FS signal definition is genuinely useful. The authors clearly explain why the inclusive measured W+W- cross section requires subtracting the top-quark contribution, why that subtraction must be done separately for each polarization, and how their approach connects to the experimental jet-veto and b-tagging strategy. They are also honest about the limitations: they explicitly state that the YesVeto scale uncertainties are likely underestimated.

The soft spots are real but not disqualifying. The report is not self-contained. The subtraction scheme is defined only at the diagram level, and the reader is directed to [17] for the actual implementation. In particular, the question of how the tW interference with the non-tW bottom diagrams is assigned is not addressed here, which means the 7.6% and 10.5% numbers come without an estimate of scheme dependence. The authors also quote the LL fractions without any uncertainty on the shift, which is a concrete deficiency.

That said, the stress-test concern about gauge invariance, while legitimate in principle, does not land as a fatal blow here. The authors are explicitly summarizing a peer-reviewed calculation, and the definitions they sketch are standard in the W+W- field. The absence of details in a proceedings write-up is expected, not evidence of a flaw. The right question is whether the reader should go to [17] for the full derivation, and the answer is yes.

Bottom line: this report is for someone who wants a readable overview of the 5FS signal definition and a quick look at the bottom-quark effects on the LL polarization. It is not the paper you cite for the numbers; you cite [17]. But the report deserves to be published in the proceedings, and a serious editor should not desk reject it. I would send it to a referee who can verify internal consistency with [17] and the clarity of the polarization definition. My own verdict: useful, honest, but strictly a companion to the main paper.

Referee Report

2 major / 3 minor

Summary. This paper, a contribution to the proceedings of the PIAS workshop 2024, discusses the definition of the inclusive polarized W+W- production signal at the LHC and presents NLO QCD+EW results for the effects of bottom-quark induced processes. The calculation, reported in the authors' recent paper [17], uses the five-flavor scheme and subtracts the on-shell top-quark (tW) contribution from the inclusive cross section for each polarization. The central numerical result is that the bottom-induced contribution increases the doubly-longitudinal (W_L+ W_L-) polarization fraction from 6.6% to 7.1% (with a jet veto, YesVeto) and from 5.7% to 6.3% (without a jet veto, NoVeto), i.e., relative increases of 7.6% and 10.5%.

Significance. If the subtraction scheme is well defined and the effect is robust, the observation that bottom-induced effects are more sizable for the doubly-longitudinal polarization is a nontrivial and useful result for the design of LHC polarization measurements. The paper clearly lays out the conceptual difference between the 4FS and 5FS definitions of the WW signal and correctly emphasizes that the tW interference is part of the measured signal. It also provides a pedagogical discussion of the on-shell projection needed for polarized amplitudes. The underlying calculation in [17] has been peer-reviewed, which lends credibility to the numbers presented. However, the manuscript itself does not provide enough information to assess the robustness of the central claim, and it explicitly warns about underestimated scale uncertainties in the YesVeto case.

major comments (2)

[Section 2 and Table 1] The central quantitative claim of the paper—that bottom-induced effects increase the LL polarization fraction by 7.6% (YesVeto) and 10.5% (NoVeto)—depends on the definition of the 'on-shell top-quark contribution' that is subtracted. The text states that the subtraction has to be done for individual polarized cross sections and that at NLO the top-quark contribution includes only the tW mechanism, but it does not specify whether the subtracted term is the squared tW amplitude, the full tW subprocess including the interference with the non-tW bottom diagrams of Fig. 2(c), or an on-shell projected version of either. Because the tW and non-tW amplitudes interfere, the assignment of this interference is a convention that can change the NoTW-minus-NoB difference and hence the reported fractions. The reader is referred to [17] for details, but the numerical results of Table 1 are presented here without the scheme definition; the paper should either define the subtraction explicitly or cite the relevant equations from [17] and quantify the scheme dependence.
[Table 1 and Section 3] No uncertainty is quoted for the shifts in the LL fraction. The individual scale uncertainties (YesVeto LL: +1.8%/-2.6% for NoB, +1.2%/-2.2% for NoTW) are comparable to the claimed 7.6% relative increase, and the paper itself warns that the YesVeto scale uncertainties are likely underestimated because of an accidental cancellation near the jet-veto threshold. Without a correlated uncertainty on the difference (NoTW - NoB) or on the fraction differences, the significance of the 7.6% and 10.5% effects is not established. The authors should provide the uncertainty on the differences, ideally from a correlated scale variation, or at least discuss how the admitted underestimation affects the central claim.

minor comments (3)

[Section 3] The paper does not list the input parameters (PDF set, central scale, top-quark mass, electroweak scheme) used for the numerical results; since the results are taken from [17], at least a reference to the parameter tables of that paper should be given.
[Figure 3 caption] The definition of cosθ_e^WW is given only in the body text, with the caption saying 'see text'; for self-containedness, the definition should be restated in the caption itself.
[Table 1 caption] The caption contains a typographical error ('T able 1'), and in the rendered text the polarization labels for the NoVeto rows are missing; please check the table formatting so that all four polarization rows are clearly labeled.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a proceedings summary whose numerical results are explicitly taken from an independent fixed-order NLO calculation, not fitted or definitionally forced.

full rationale

The paper does not fit any parameter to data and does not define the claimed result into existence. Its central numerical claims (Table 1: the LL fraction increasing from 6.6% to 7.1% in YesVeto and from 5.7% to 6.3% in NoVeto) are explicitly attributed to the authors' published calculation [17], with the text stating 'These results are taken from [17]'. That cited calculation is a parameter-free perturbative QCD+EW computation with stated assumptions (NLO accuracy, five-flavor scheme, DPA on-shell projection) that do not include the target conclusion; it is therefore independent support under the reviewing rule, even though the citation is self-referential. The 'on-shell top-quark contribution' subtraction is a definitional element of the signal, but the reported enhancement of the doubly-longitudinal polarization is a computed consequence of that definition, not an identity: the paper does not exhibit any equation in which the LL fraction equals the subtraction term by construction. The DPA framework is grounded in earlier external work [8,9]. Scheme dependence of the tW subtraction would be a robustness or correctness concern, not circularity. No load-bearing step reduces to its own input, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

This report contains no data-driven fit; the inputs are SM parameters, PDFs, and factorization assumptions. All numerical results are inherited from [17], so the ledger records the modeling assumptions that the central claim depends on.

assumptions (5)

domain assumption The Standard Model and collinear QCD factorization hold for pp -> W+W- plus anything.
Invoked in Section 1 and throughout; the calculation is a fixed-order SM prediction built on factorized proton PDFs.
domain assumption The double-pole approximation and the on-shell W-boson projection give an accurate decomposition of polarized W+W- production.
Section 2 states that the on-shell condition q_i^2 = M_W^2 is 'crucial for the separation' and that gauge invariance is guaranteed in this limit; non-doubly-resonant diagrams are omitted.
domain assumption The on-shell top-quark contribution, identified with the tW mechanism at NLO, can be computed and subtracted separately for each polarization.
Section 2: 'This subtraction has to be done for individual polarized cross sections... the top-quark contribution includes only the tW mechanism.' The scheme dependence is not quantified in this report.
domain assumption The five-flavor scheme with massless bottom quarks and b jets included in the inclusive definition matches the experimental W+W- signal definition.
Section 2: 'b jets are included in the definition... the 5FS definition is used for the signal cross section.' This is a modeling choice consistent with ATLAS and CMS analyses.
standard math Polarization interference vanishes for fully inclusive integrated cross sections and can be separated as a template otherwise.
Eqs. (9)-(11) and the statement attributed to [8] that the interference term vanishes when decay products are fully inclusive; for differential bins it must be fitted.

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Cite this review

Pith. "Pith review of Effects of bottom quark induced processes on polarized $W^+W^-$ production at the LHC at NLO." pith.science (2026). https://pith.science/paper/XHQOQESO

@misc{pith2026250523234,
  author       = {Pith},
  title        = {Pith review of: Effects of bottom quark induced processes on polarized $W^+W^-$ production at the LHC at NLO},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHQOQESO}},
  note         = {Machine review of arXiv:2505.23234}
}

abstract

In this report we discuss the definition of the polarized cross sections of the inclusive $W^+W^-$ production at the LHC. Results at the level of next-to-leading order (NLO) QCD+EW accuracy, published in our recent paper, are presented to highlight the effects of bottom-quark induced processes. Compared to the unpolarized case, the bottom-induced effects after the subtraction of the on-shell top-quark contribution are more sizable for the doubly-longitudinal polarization.

Figures

Figures reproduced from arXiv: 2505.23234 by the authors.

**Figure 1.** Tree-level Feynman diagrams describing a W +W− resonant signal process at the LHC. A W boson can decay into leptons (33%) or quarks (67%). The hadronic final state has a higher rate, but suffers from a much larger background than the leptonic mode. We therefore only consider the fully leptonic decays of the W bosons in this work. The two intermediate W bosons are required to be on-shell, namely their momenta satisfy… view at source ↗

**Figure 2.** Various types of bottom-induced contributions to the inclusive W +W− production. (a,b,c) are of non-tW origin, while (d) is of tW origin. The top-quark interference (or tW interference) is the interference between (c) and (d). Moreover, the top-quark interference (i.e the signal-background interference) is part of the signal in the measurement result. This term is missing in the 4FS definition. This point is illustr… view at source ↗

**Figure 3.** Differential polarized cross sections in cos θWW e (see text) for YesVeto and NoVeto cut setups. Results are taken from [17] [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [17]

T. N. Dao and D. N. Le,PolarizedW +W − pairs at the LHC: Effects from bottom-quark induced processes at NLO QCD + EW,Eur. Phys. J. C85(2025) 108 [2409.06396]

arXiv 2025

[2] [5]

Hoppe, M

M. Hoppe, M. Sch¨ onherr and F. Siegert,Polarised cross sections for vector boson production with SHERPA, 2310.14803

arXiv

[3] [6]

Pelliccioli and G

G. Pelliccioli and G. Zanderighi,Polarised-boson pairs at the LHC with NLOPS accuracy,Eur. Phys. J. C 84(2024) 16 [2311.05220]

arXiv 2024

[4] [7]

Javurkova, R

M. Javurkova, R. Ruiz, R. C. L. de S´ a and J. Sandesara,Polarized ZZ pairs in gluon fusion and vector boson fusion at the LHC,Phys. Lett. B855(2024) 138787 [2401.17365]

arXiv 2024

[5] [8]

Denner and G

A. Denner and G. Pelliccioli,Polarized electroweak bosons inW +W − production at the LHC including NLO QCD effects,JHEP09(2020) 164 [2006.14867]

arXiv 2020

[6] [9]

Denner and G

A. Denner and G. Pelliccioli,NLO EW and QCD corrections to polarized ZZ production in the four-charged-lepton channel at the LHC,JHEP10(2021) 097 [2107.06579]

arXiv 2021

[7] [10]

D. N. Le and J. Baglio,Doubly-polarized WZ hadronic cross sections at NLO QCD + EW accuracy,Eur. Phys. J. C82(2022) 917 [2203.01470]

arXiv 2022

[8] [11]

D. N. Le, J. Baglio and T. N. Dao,Doubly-polarized WZ hadronic production at NLO QCD+EW: calculation method and further results,Eur. Phys. J. C82(2022) 1103 [2208.09232]

arXiv 2022