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arxiv: 2606.31286 · v1 · pith:A2LXOGGQnew · submitted 2026-06-30 · ✦ hep-ph

Boosted Higgs-strahlung off a W boson at next-to-next-to-next-to-leading order in QCD

Aude Gehrmann-De Ridder , Alexander Huss , Matteo Marcoli , Pier Francesco Monni , Emanuele Re , Luca Rottoli , Federico Silvetti , Paolo Torrielli This is my paper

Pith reviewed 2026-07-01 05:08 UTC · model grok-4.3

classification ✦ hep-ph
keywords Higgs productionN3LO QCDboosted regimeWH associated productionperturbative correctionshadron collidersdifferential cross section
5
0 comments X

The pith

The first fully differential N³LO QCD calculation for boosted Higgs plus W production finds corrections of about +2% that sit at or beyond the NNLO scale-variation band.

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

The paper delivers the first fully differential computation of Higgs-strahlung off a W boson at next-to-next-to-next-to-leading order in QCD. In the boosted regime the N³LO corrections reach approximately +2% and typically lie at the edge of or outside the uncertainty band obtained from scale variation at the preceding order. At the same time the residual dependence on perturbative scales falls below the percent level. This combination tightens the theoretical prediction for a channel that dominates Higgs production at large transverse momentum and supplies direct sensitivity to Higgs couplings and possible new physics.

Core claim

We present the first fully differential calculation of boosted Higgs-strahlung off a W boson at N³LO in perturbative QCD. The N³LO corrections amount to approximately +2% in the boosted regime and generally lie at the edge of or outside the standard scale variation band of the previous perturbative order, while the residual dependence of the N³LO prediction on perturbative scales is reduced to below the percent level.

What carries the argument

The fully differential N³LO QCD computation of the pp → WH cross section, incorporating all virtual and real-emission contributions through third order in the strong coupling.

Load-bearing premise

That the conventional scale-variation procedure performed at NNLO supplies a reliable estimate of the size of the missing higher-order corrections.

What would settle it

A high-precision measurement of the boosted WH cross section whose central value lies well inside the NNLO scale band but outside the N³LO prediction band.

Figures

Figures reproduced from arXiv: 2606.31286 by Alexander Huss, Aude Gehrmann-De Ridder, Emanuele Re, Federico Silvetti, Luca Rottoli, Matteo Marcoli, Paolo Torrielli, Pier Francesco Monni.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Born-level Feynman diagram for the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: N [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Fiducial [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: , we show the N3LO correction to the inclusive cross section as a function of q cut T , decomposed into initial￾state flavor channels and compared with the numerical results of n3loxs. We find excellent agreement across the full range 3 GeV ≤ q cut T ≤ 10 GeV, with residual variations well within the Monte Carlo integration uncertainty of the N3LO correction. The latter reaches at most ±30% in the qq¯ chan… view at source ↗
read the original abstract

The production of a boosted Higgs boson in association with a charged weak ($W$) boson is a key process to scrutinize the electroweak symmetry breaking mechanism at hadron colliders. This reaction constitutes the dominant Higgs production channel at large transverse momentum, providing unique sensitivity to Higgs-boson interactions with other Standard Model particles as well as to physics beyond the Standard Model. In this Letter, we present the first fully differential calculation of this important scattering process at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative Quantum Chromodynamics (QCD). We find that the N$^3$LO corrections, amounting to approximately $+2\%$ in the boosted regime, generally lie at the edge of or outside the standard scale variation band of the previous perturbative order. The residual dependence of the N$^3$LO prediction on perturbative scales is reduced to below the percent level, marking a milestone for the Higgs precision program.

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 / 1 minor

Summary. The manuscript presents the first fully differential N³LO QCD calculation of Higgs-strahlung off a W boson (WH production) in the boosted Higgs regime at hadron colliders. The central numerical result is that N³LO corrections amount to approximately +2% and generally lie at the edge of or outside the NNLO scale-variation band, while reducing residual perturbative scale dependence to below the percent level.

Significance. If the result holds, this constitutes a milestone for precision Higgs phenomenology, as boosted WH is the dominant production mode at high pT and provides direct sensitivity to Higgs couplings and potential BSM effects. Achieving sub-percent residual scale uncertainty supplies more robust theoretical inputs for LHC analyses than previous orders.

major comments (1)
  1. [Abstract] Abstract: The statement that the N³LO corrections 'generally lie at the edge of or outside the standard scale variation band of the previous perturbative order' rests on the assumption that the conventional 7-point scale variation performed at NNLO furnishes a faithful envelope for the size of the uncalculated N³LO terms. The manuscript provides no independent cross-check of this assumption (e.g., via an alternative uncertainty prescription, comparison against a known N³LO process, or explicit demonstration in a solvable limit). This directly affects the strength of the claim that the N³LO shift lies outside the previous uncertainty estimate.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the collider energy and the precise kinematic definition of the 'boosted regime' used for the quoted +2% correction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive overall assessment. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The statement that the N³LO corrections 'generally lie at the edge of or outside the standard scale variation band of the previous perturbative order' rests on the assumption that the conventional 7-point scale variation performed at NNLO furnishes a faithful envelope for the size of the uncalculated N³LO terms. The manuscript provides no independent cross-check of this assumption (e.g., via an alternative uncertainty prescription, comparison against a known N³LO process, or explicit demonstration in a solvable limit). This directly affects the strength of the claim that the N³LO shift lies outside the previous uncertainty estimate.

    Authors: We agree that conventional 7-point scale variation provides an estimate of higher-order effects rather than a rigorous bound, and that the manuscript does not include an independent cross-check such as an alternative prescription or comparison to a different N³LO process. Our statement is an empirical observation based on the explicit computation: the N³LO correction size is compared directly to the NNLO 7-point band obtained with the same scale choices. This follows the standard practice used in all prior N³LO QCD calculations. In the revised manuscript we have added a clarifying sentence after the abstract claim noting that the observation relies on the conventional scale-variation prescription and does not constitute a general proof. We have also softened the wording slightly to 'lie at or beyond the edge of the NNLO scale-variation band obtained with the standard 7-point prescription.' We believe this addresses the concern without altering the numerical results or the main conclusions. revision: partial

Circularity Check

0 steps flagged

No circularity: direct N³LO perturbative computation

full rationale

The paper reports an explicit higher-order QCD calculation of differential distributions for WH production at N³LO. All results follow from standard matrix-element evaluation, infrared subtraction, and phase-space integration; no quantity is obtained by fitting a parameter to a subset of the same data and then relabeling it a prediction, nor does any central claim reduce to a self-citation chain or imported ansatz. Scale variation is used only as a conventional uncertainty estimate after the calculation is complete and does not enter the derivation itself.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The calculation rests on standard perturbative QCD assumptions; no new entities or data-fitted parameters are introduced beyond conventional scale choices.

free parameters (1)
  • renormalization and factorization scales
    Standard choices in pQCD; varied to estimate uncertainty but not fitted to data.
axioms (1)
  • domain assumption Perturbative QCD expansion remains valid and convergent at N³LO for this process
    Invoked throughout the abstract to justify the calculation and uncertainty reduction.

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discussion (0)

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