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arxiv: 2606.19999 · v1 · pith:47SHUFGGnew · submitted 2026-06-18 · ✦ hep-ph · hep-ex

NLO QCD and EW corrections to semileptonic vector-boson scattering at the LHC

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

Pith reviewed 2026-06-26 17:09 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords vector-boson scatteringNLO correctionselectroweakQCDsemileptonicLHCfiducial cross sectionsdifferential distributions
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0 comments X

The pith

Fully off-shell NLO QCD and EW corrections are computed for semileptonic vector-boson scattering at the LHC.

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

This paper computes the next-to-leading order corrections in QCD and the electroweak sector for the semileptonic vector-boson scattering process at the LHC. The calculation is performed in a fully off-shell manner for the process producing a lepton, neutrino and four jets. It focuses on the leading electroweak contribution at order alpha to the sixth power along with its corrections at order alpha to the seventh and the mixed alpha_s alpha to the sixth. Results are presented for cross sections and distributions in two fiducial regions selected for their relevance to vector-boson scattering. Such predictions are essential as experimental measurements of this process become more precise.

Core claim

In a fully off-shell calculation, we provide results for the leading electroweak contribution of O(α^6) and the corresponding corrections of O(α^7) and O(α_s α^6) for fiducial cross sections and a selection of differential distributions in the process pp → ℓ⁺ ν_ℓ + 4j in two different fiducial regions relevant for vector-boson scattering.

What carries the argument

Fully off-shell NLO calculation of electroweak and QCD corrections to the semileptonic vector-boson scattering process pp → ℓ⁺ ν_ℓ + 4j

If this is right

  • The provided NLO results enable more precise comparisons with LHC data on vector-boson scattering.
  • Corrections of O(α^7) and O(α_s α^6) modify the leading O(α^6) predictions for cross sections.
  • Differential distributions in the fiducial regions can be directly compared to experimental measurements.
  • The calculation covers both QCD and electroweak corrections for improved accuracy.

Where Pith is reading between the lines

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

  • The method could be applied to fully leptonic or other decay channels of vector-boson scattering.
  • Including these corrections may reduce theoretical uncertainties in VBS analyses at the LHC.
  • The fiducial region definitions could be optimized based on these theoretical results.

Load-bearing premise

The two chosen fiducial regions sufficiently isolate the vector-boson scattering signal and that the perturbative series truncated at NLO remains a reliable approximation inside those regions.

What would settle it

Experimental measurement of the fiducial cross section or distributions in the two regions that significantly deviates from the NLO theoretical prediction after accounting for these corrections.

read the original abstract

Vector-boson scattering with semileptonic final states has recently been measured at the LHC, and future experiments are expected to further increase the precision of its measurement, calling for adequate theoretical predictions. In this work, we present a calculation of the NLO QCD and electroweak corrections to the process $\text{p}\text{p} \to \ell^+ \nu_\ell + 4\text{j}$ in two different fiducial regions relevant for vector-boson scattering. In a fully off-shell calculation, we provide results for the leading electroweak contribution of $\mathcal{O}\left(\alpha^6\right)$ and the corresponding corrections of $\mathcal{O}\left(\alpha^7\right)$ and $\mathcal{O}\left(\alpha_\text{s} \alpha^6\right)$ for fiducial cross sections and a selection of differential distributions.

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

1 major / 0 minor

Summary. The paper presents a fully off-shell calculation of NLO QCD and electroweak corrections to the semileptonic vector-boson scattering process pp → ℓ⁺ν_ℓ + 4j at the LHC. It computes the leading electroweak contribution at O(α⁶) together with the NLO corrections at O(α⁷) and O(α_s α⁶) for fiducial cross sections and selected differential distributions in two fiducial regions chosen to isolate the VBS signal.

Significance. If the results hold, the work supplies important higher-order predictions for a process that has been measured at the LHC and will be measured with greater precision. The explicit Feynman-diagram evaluation in the Standard Model and the fully off-shell treatment constitute a clear computational strength for this class of calculations.

major comments (1)
  1. [Numerical results section] Numerical results section: the manuscript supplies no explicit check—such as the relative size of the NLO corrections versus LO across the reported distributions or an estimate of missing NNLO pieces—to confirm that the perturbative series truncated at NLO remains reliable inside the chosen fiducial regions. This assumption is load-bearing for the applicability of the central claim.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the positive evaluation of the computational approach and for highlighting the need for explicit checks on perturbative reliability. We address the major comment below.

read point-by-point responses

  1. Referee: [Numerical results section] Numerical results section: the manuscript supplies no explicit check—such as the relative size of the NLO corrections versus LO across the reported distributions or an estimate of missing NNLO pieces—to confirm that the perturbative series truncated at NLO remains reliable inside the chosen fiducial regions. This assumption is load-bearing for the applicability of the central claim.

    Authors: We agree that explicit verification of the size of the NLO corrections is necessary to support the applicability of the results. In the revised manuscript we will add tables and/or figures displaying the relative NLO QCD and EW corrections (K-factors) with respect to the LO predictions for the fiducial cross sections and for all reported differential distributions in both fiducial regions. This will directly quantify the corrections inside the selected phase-space regions. For an estimate of missing NNLO pieces we will include a discussion based on the observed NLO scale uncertainties and on comparisons with existing higher-order studies of related VBS processes; a dedicated NNLO calculation lies outside the scope of the present work. revision: yes

standing simulated objections not resolved
  • A precise quantitative estimate of missing NNLO contributions without performing a full NNLO calculation

Circularity Check

0 steps flagged

No significant circularity; explicit Feynman-diagram computation in SM

full rationale

The paper computes LO O(α^6) and NLO O(α^7), O(α_s α^6) corrections to pp → ℓ⁺ν_ℓ + 4j via direct evaluation of Feynman diagrams in the Standard Model for two fiducial regions. No load-bearing step reduces to a fitted parameter, self-definition, or self-citation chain; the central results are obtained from explicit diagrammatic evaluation rather than by construction from inputs. The assumption that NLO truncation is reliable inside the regions is an external validity claim, not a circular reduction of the reported numbers. This is the normal case of a self-contained perturbative calculation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on the Standard Model perturbative expansion and standard choices for scales and parton distributions; no new entities or ad-hoc assumptions beyond those common to NLO phenomenology are introduced.

free parameters (1)
  • renormalization and factorization scales
    Standard choice in NLO calculations to estimate missing higher orders; values not specified in abstract.
axioms (1)
  • standard math Standard Model Feynman rules and perturbative expansion
    The calculation is performed within the SM at fixed orders in α and α_s.

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discussion (0)

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Reference graph

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