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arxiv: 2606.25928 · v1 · pith:I3GERQIDnew · submitted 2026-06-24 · ✦ hep-ph · hep-th

Electroweak corrections to Higgs boson pair production: The quark channel

Marco Bonetti , Gudrun Heinrich , Philipp Rendler , William J. Torres Bobadilla This is my paper

Pith reviewed 2026-06-25 20:05 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords Higgs boson pair productionmixed QCD-electroweak correctionsquark-antiquark channeldifferential equationslarge mass expansionPOWHEG-BOXinvariant mass distribution
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The pith

The quark-antiquark channel for Higgs pair production receives mixed QCD-electroweak corrections that reach +10 percent near threshold.

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

This paper computes the mixed QCD-electroweak corrections to Higgs boson pair production in the quark-antiquark annihilation channel at next-to-leading order. The virtual amplitudes are obtained analytically through the method of differential equations, with integration constants fixed by matching to the large-mass expansion limit. The results are implemented in the POWHEG-BOX Monte Carlo framework. These corrections modify the shapes of differential cross sections, with the largest effects of order +10 percent appearing in the Higgs-pair invariant mass distribution close to the production threshold. A reader would care because this channel had not been included in prior electroweak correction calculations for the process.

Core claim

The mixed QCD-electroweak corrections to Higgs boson pair production in the quark-antiquark channel are computed fully analytically. The virtual amplitudes are obtained using the method of differential equations, with integration constants fixed by matching to the large mass expansion. When implemented in the POWHEG-BOX, these corrections impact the shapes of differential cross sections, reaching up to +10% for the invariant mass distribution of the Higgs boson pair near the production threshold.

What carries the argument

Analytic evaluation of the virtual amplitudes via the method of differential equations, with integration constants fixed through matching to the large-mass expansion limit of the canonical integrals.

If this is right

  • The quark-antiquark channel must now be included to obtain complete next-to-leading-order electroweak predictions for Higgs pair production.
  • The Higgs-pair invariant mass distribution receives shape distortions of up to ten percent near threshold.
  • Phenomenological predictions generated with POWHEG-BOX incorporate these corrections for collider observables.
  • This supplies the previously missing quark-initiated contribution at the present perturbative order.

Where Pith is reading between the lines

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

  • These corrections could shift the extracted value of the Higgs trilinear coupling when pair-production data are interpreted.
  • The same differential-equation technique may be reusable for other mixed-correction calculations involving top-quark loops.
  • Threshold enhancements suggest that soft-gluon resummation could further improve accuracy in that region.
  • Omitting the channel in uncertainty estimates would leave an unquantified theoretical error in Higgs pair production rates.

Load-bearing premise

The integration constants obtained by matching to the large mass expansion correctly determine the amplitudes throughout the relevant kinematic regions.

What would settle it

An independent numerical evaluation of the virtual amplitudes near the Higgs-pair production threshold that differs from the analytic expressions beyond the stated precision.

Figures

Figures reproduced from arXiv: 2606.25928 by Gudrun Heinrich, Marco Bonetti, Philipp Rendler, William J. Torres Bobadilla.

Figure 1
Figure 1. Figure 1: Top sectors of the virtual NLO. Straight lines indicate massless particles, curved lines EW bosons with mass 𝑚𝑊/𝑍 and dashed lines Higgs bosons with mass 𝑚𝐻 . −𝑡/𝑚 2 𝐻 𝑠/𝑚 2 𝐻 𝑠 = 4𝑚 2 𝐻 physical region (𝑠0, 𝑡0) (𝑠, 𝑡) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic illustration of the integration path used to evaluate the independent functions. Expressing the amplitude in terms of independent functions removes all artificial poles. The remaining UV poles are treated by renormalising the strong coupling constant 𝛼𝑠 in the 𝑀𝑆 scheme, and the IR poles are removed using the Catani subtraction scheme [56]. To evaluate the independent functions numerically in the… view at source ↗
Figure 3
Figure 3. Figure 3: Invariant mass distribution of the Higgs boson pair (a) and transverse momentum distribution of a single Higgs boson (b). The error bands represent the scale uncertainty, while the error bars show the statistical error from the Monte Carlo simulation. The amplitude can be evaluated in this way with a precision of 16 significant digits in approxi￾mately O (1 ′ ) per phase space point. As this is not suffici… view at source ↗
read the original abstract

We present the mixed QCD-electroweak corrections to Higgs boson pair production in the quark-antiquark channel. The virtual amplitudes are computed fully analytically using the method of differential equations. We determine the integration constants by matching our expressions to the large mass expansion limit of the canonical integrals. We implement the results in the POWHEG-BOX framework for phenomenological studies. The corrections are found to have a significant impact on the shapes of differential cross sections, reaching up to +10% for the invariant mass distribution of the Higgs boson pair near the production threshold. This channel has not been considered before in calculations of the next-to-leading order electroweak corrections to Higgs boson pair production.

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 computes the mixed QCD-electroweak corrections to Higgs boson pair production in the quark-antiquark channel. Virtual amplitudes are obtained analytically via the differential-equation method for master integrals; integration constants are fixed exclusively by matching the canonical integrals to their large-mass expansion. The results are implemented in POWHEG-BOX and used for phenomenological studies, which report corrections that distort differential distributions by up to +10 % near the HH production threshold. The calculation is presented as the first NLO EW treatment of this channel.

Significance. If the amplitudes are correct, the work supplies the previously missing NLO EW piece for the qqbar channel, which is relevant for precision LHC predictions of Higgs-pair production and the extraction of the trilinear coupling. The analytic differential-equation approach and public Monte-Carlo implementation are positive features. The reported 10 % shape effect near threshold would be phenomenologically important if confirmed.

major comments (1)
  1. [Computation of virtual amplitudes (differential equations and matching)] The integration constants of the differential-equation solution are determined solely by matching to the large-mass expansion of the canonical integrals. The phenomenological results, however, are evaluated near the HH threshold (m_HH ≈ 2 m_H), a regime whose mass hierarchy is distinct from the large-mass limit used for the boundary condition. It is not shown whether this single matching point captures all independent constants or whether analytic continuation across branch cuts introduces additional terms. Because the quoted +10 % correction to the invariant-mass distribution rests directly on these amplitudes, an independent verification (numerical evaluation at a benchmark point or matching to a second kinematic limit) is required.
minor comments (1)
  1. A short comparison of the new qqbar corrections with existing results for the gluon-fusion channel would help place the size of the reported effect in context.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We address the major point regarding the determination of integration constants below.

read point-by-point responses

  1. Referee: [Computation of virtual amplitudes (differential equations and matching)] The integration constants of the differential-equation solution are determined solely by matching to the large-mass expansion of the canonical integrals. The phenomenological results, however, are evaluated near the HH threshold (m_HH ≈ 2 m_H), a regime whose mass hierarchy is distinct from the large-mass limit used for the boundary condition. It is not shown whether this single matching point captures all independent constants or whether analytic continuation across branch cuts introduces additional terms. Because the quoted +10 % correction to the invariant-mass distribution rests directly on these amplitudes, an independent verification (numerical evaluation at a benchmark point or matching to a second kinematic limit) is required.

    Authors: We thank the referee for highlighting this important aspect of the calculation. In the differential-equation approach, the canonical basis yields a system whose solution depends on a finite number of integration constants equal to the number of master integrals. These constants are fixed by matching the full analytic solution to the independently computed large-mass expansion, which supplies a sufficient number of independent conditions through its series coefficients. The resulting expression is then valid throughout the kinematic plane; the differential equations themselves govern the analytic continuation, with branch cuts properly incorporated via the imaginary parts of the iterated integrals. We have confirmed that the solution satisfies the original differential equations at sample points in the threshold region. To address the concern explicitly, we will add a short explanatory paragraph in the revised manuscript detailing the number of master integrals and the matching procedure, together with a statement confirming the validity of the continuation to the threshold kinematics. revision: partial

Circularity Check

0 steps flagged

No circularity: standard DE solution with external large-mass matching

full rationale

The derivation solves differential equations for canonical integrals and fixes constants via matching to the independent large-mass expansion limit. This boundary condition is external to the target kinematics and does not reduce any result to a self-defined quantity, fitted subset, or self-citation chain. No load-bearing self-citations, uniqueness theorems, or ansatze imported from prior author work appear in the abstract or described method. The computation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no free parameters, axioms, or invented entities are identifiable. The work relies on standard methods in quantum field theory such as differential equations for Feynman integrals and large-mass expansions.

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discussion (0)

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Reference graph

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