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arxiv: 2607.01174 · v1 · pith:KQEBKVKGnew · submitted 2026-07-01 · ✦ hep-ph · hep-ex

The cleanest of them all: NLO electroweak corrections to vector-boson scattering into doubly polarised ZZ pairs at the LHC

Ansgar Denner , Robert Franken , Santiago Lopez Portillo Chavez , Daniele Lombardi , Giovanni Pelliccioli This is my paper

Pith reviewed 2026-07-02 09:37 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords vector boson scatteringelectroweak correctionspolarised Z bosonsdouble pole approximationZZ productionLHC phenomenology
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0 comments X

The pith

Next-to-leading-order electroweak corrections to vector-boson scattering into doubly polarised ZZ pairs are computed for the first time.

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

The paper performs the first calculation of NLO electroweak corrections to vector-boson scattering producing pairs of doubly polarised Z bosons at the LHC, restricted to the fully leptonic decay channel. Production and decay are treated together in the double-pole approximation, with polarisation states separated already at the amplitude level and with factorisable real and virtual corrections included. Results for doubly polarised signals are compared to unpolarised and fully off-shell cases inside a realistic CMS-inspired fiducial region at both integrated and differential level. A reader would care because the work supplies the precise theoretical predictions required to interpret polarisation observables in upcoming LHC measurements.

Core claim

We present the first calculation of the next-to-leading-order electroweak corrections to vector-boson scattering into doubly polarised Z bosons at the LHC in the fully leptonic decay channel. The production and decay of the two polarised Z bosons are consistently modelled in the double-pole approximation, separating polarisation states at the amplitude level and including factorisable real and virtual electroweak corrections. Doubly polarised and unpolarised signals are investigated and confronted with off-shell results in a realistic, CMS-inspired fiducial setup.

What carries the argument

The double-pole approximation, used to model production and decay consistently while separating polarisation states directly at the amplitude level for the ZZ final state.

If this is right

  • Doubly polarised signals can be extracted and compared to unpolarised and off-shell predictions at both integrated and differential levels.
  • The calculation supplies the first NLO electroweak input for vector-boson scattering into polarised ZZ pairs in a realistic LHC fiducial setup.
  • The results support phenomenological studies and experimental analyses planned for LHC Run-3 and High-Luminosity data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same double-pole framework could be applied to other final states or to higher-order corrections to check consistency of polarisation separation.
  • Differential distributions in the fiducial region may highlight where off-shell effects most strongly affect polarisation observables.
  • Experimental measurements of these polarised signals could constrain parameters in the electroweak sector once the NLO corrections are accounted for.

Load-bearing premise

The double-pole approximation remains accurate enough to separate polarisation states at the amplitude level while consistently treating both production and decay for the ZZ final state inside the chosen fiducial region.

What would settle it

A numerical comparison of the double-pole results against a complete off-shell calculation for identical fiducial cuts and observables would directly test whether the approximation introduces unacceptable errors in the polarised cross sections.

read the original abstract

We present the first calculation of the next-to-leading-order electroweak corrections to vector-boson scattering into doubly polarised Z bosons at the LHC in the fully leptonic decay channel. The production and decay of the two polarised Z bosons are consistently modelled in the double-pole approximation, separating polarisation states at the amplitude level and including factorisable real and virtual electroweak corrections. Doubly polarised and unpolarised signals are investigated and confronted with off-shell results. A broad analysis, including results at integrated and differential level, is carried out in a realistic, CMS-inspired fiducial setup. Our study paves the way to upcoming analyses with LHC Run-3 and High-Luminosity data as well as to further phenomenological investigations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript presents the first calculation of next-to-leading-order electroweak corrections to vector-boson scattering into doubly polarised ZZ pairs at the LHC in the fully leptonic decay channel. Production and decay of the polarised Z bosons are modelled consistently in the double-pole approximation, with polarisation states separated at the amplitude level and factorisable real and virtual EW corrections included. Doubly polarised and unpolarised signals are compared to off-shell results at both integrated and differential levels inside a CMS-inspired fiducial region.

Significance. If the double-pole approximation is validated to the required precision, this constitutes a timely and relevant advance for polarised VBS phenomenology, providing the first NLO EW predictions needed to interpret upcoming LHC Run-3 and HL-LHC data on longitudinal and transverse ZZ scattering. The work supplies concrete benchmarks that can be used by experimental collaborations and for further studies of electroweak symmetry breaking.

major comments (2)
  1. [§4] §4 (numerical results) and the associated comparison plots: the manuscript confronts DPA results with full off-shell calculations but does not provide a quantitative bound on the size of neglected non-factorisable contributions and off-shell effects specifically for the extracted doubly-polarised signals. Without such an error estimate (e.g., via dedicated variation or comparison to a higher-order reference), it remains unclear whether the DPA error lies below the percent-level NLO EW corrections reported in the CMS fiducial setup.
  2. [§3.2] §3.2 (double-pole approximation implementation): the claim that polarisation states are separated at the amplitude level while consistently treating production and decay relies on the factorisable approximation; however, the text does not demonstrate that the residual non-factorisable interference terms are negligible compared to the NLO corrections for the chosen fiducial cuts, which is load-bearing for the central result.
minor comments (3)
  1. [Figures 5-6] Figure 5 and 6: axis labels and legend entries for the polarised cross sections should explicitly state the fiducial cuts applied to each distribution to improve readability.
  2. [Table 2] Table 2: the relative size of the NLO EW corrections for the doubly polarised channels is given without an accompanying estimate of the DPA uncertainty; adding a column or footnote with this information would strengthen the presentation.
  3. [References] Reference list: several recent works on polarised VBS at NLO (e.g., on WW and WZ channels) are not cited; including them would better contextualise the novelty of the ZZ case.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive assessment of its significance for polarised VBS phenomenology. We address the two major comments below and will revise the manuscript to strengthen the presentation of the DPA validation.

read point-by-point responses

  1. Referee: [§4] §4 (numerical results) and the associated comparison plots: the manuscript confronts DPA results with full off-shell calculations but does not provide a quantitative bound on the size of neglected non-factorisable contributions and off-shell effects specifically for the extracted doubly-polarised signals. Without such an error estimate (e.g., via dedicated variation or comparison to a higher-order reference), it remains unclear whether the DPA error lies below the percent-level NLO EW corrections reported in the CMS fiducial setup.

    Authors: We agree that an explicit quantitative bound on the neglected contributions for the doubly polarised signals would improve clarity. While Section 4 already presents direct comparisons of DPA and full off-shell results for both integrated cross sections and differential distributions of the polarised signals, showing relative differences typically below the percent level in the fiducial region, we will revise the text to add a dedicated paragraph explicitly extracting and tabulating these differences as an error estimate for the polarised observables and comparing them to the size of the NLO EW corrections. revision: yes

  2. Referee: [§3.2] §3.2 (double-pole approximation implementation): the claim that polarisation states are separated at the amplitude level while consistently treating production and decay relies on the factorisable approximation; however, the text does not demonstrate that the residual non-factorisable interference terms are negligible compared to the NLO corrections for the chosen fiducial cuts, which is load-bearing for the central result.

    Authors: We acknowledge the need for a more explicit demonstration that residual non-factorisable terms remain small relative to the NLO corrections under the chosen cuts. In the revised manuscript we will expand the discussion in Section 3.2 with additional justification based on the process kinematics and fiducial selection, and will cross-reference the Section 4 comparisons (which bound the combined effect of non-factorisable and off-shell contributions) to show that these effects are sub-dominant to the reported corrections. revision: yes

Circularity Check

0 steps flagged

No circularity; direct perturbative computation

full rationale

The paper reports an explicit NLO EW calculation in the double-pole approximation, separating polarisation states at the amplitude level and including factorisable corrections. No equations, parameters, or central results are obtained by fitting to the target observables, by self-definition, or by reduction to prior self-citations. The DPA is invoked as a standard, externally validated approximation whose accuracy is checked against off-shell results rather than assumed by construction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum-field-theory perturbation theory and the double-pole approximation, both of which are domain assumptions rather than new postulates introduced by the paper.

axioms (2)
  • standard math Perturbative expansion of the Standard Model electroweak sector is valid at NLO for this process
    Invoked by the very definition of NLO electroweak corrections.
  • domain assumption Double-pole approximation accurately isolates resonant Z contributions while permitting amplitude-level polarisation separation
    Explicitly used to model production and decay consistently.

pith-pipeline@v0.9.1-grok · 5679 in / 1447 out tokens · 32999 ms · 2026-07-02T09:37:08.581295+00:00 · methodology

discussion (0)

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Reference graph

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