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arxiv: 2605.04009 · v1 · submitted 2026-05-05 · ✦ hep-ph · hep-th

Recognition: unknown

Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit

Giuseppe De Laurentis , Harald Ita , Viktor Kuschke , Michael Ruf , Vasily Sotnikov
Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:14 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords Higgs productiontwo-loop QCDhelicity amplitudesnumerical unitaritypartial fractionspentagon functionsgluon fusion
0
0 comments X

The pith

Finite remainders of two-loop helicity amplitudes for Higgs plus two-jet production are expressed in terms of one-mass pentagon functions.

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

The paper computes the leading color two-loop QCD corrections to the production of a Higgs boson in association with two jets through gluon fusion, in the heavy top quark limit. Analytic expressions for the finite parts of the helicity amplitudes are provided using one-mass pentagon functions multiplied by spinor-helicity coefficients. These are reconstructed from numerical samples obtained with the numerical unitarity method, aided by a new algorithm for multivariate partial fraction decomposition that reduces sample requirements and yields compact forms. The resulting expressions support efficient numerical evaluation suitable for phenomenological applications. Additionally, the singularity structure is analyzed, verifying the presence of a threshold singularity at non-degenerate physical points.

Core claim

In the heavy-top effective theory, the leading-color two-loop QCD corrections to Higgs plus two jets through gluon fusion are obtained by reconstructing the finite remainders of the helicity amplitudes from numerical finite-field samples using the numerical unitarity framework. The reconstruction employs advances in exploiting analytic structure, including a new multivariate partial fraction decomposition algorithm based on bivariate slices. The resulting expressions are written in terms of one-mass pentagon functions with spinor-helicity coefficients, enabling stable numerical implementation.

What carries the argument

Reconstruction of amplitudes from numerical finite-field samples via a new algorithm for multivariate partial fraction decomposition based on a generic bivariate slice and simplified treatment of ideal intersections.

Load-bearing premise

The combination of numerical finite-field sampling and the partial-fraction algorithm fully reconstructs the complete analytic structure of the amplitudes without omissions or spurious terms.

What would settle it

A mismatch between the analytic expressions and an independent numerical computation of the amplitude at a chosen kinematic point away from singularities would falsify the reconstruction.

read the original abstract

We present the leading-color two-loop QCD corrections for Higgs-boson production in association with two jets through gluon fusion in the heavy-top effective theory. We provide analytic expressions for the finite remainders of the helicity amplitudes, written in terms of one-mass pentagon functions with spinor-helicity coefficients. These expressions are obtained by reconstructing the amplitudes from numerical finite-field samples computed within the numerical unitarity framework. The reconstruction is made possible by several advances in exploiting the analytic structure of the amplitudes, which both reduce the number of required samples and lead to compact representations. In particular, we introduce a new algorithm for multivariate partial fraction decomposition, based on a generic bivariate slice and a simplified treatment of ideal intersections. Using the resulting analytic expressions, we provide an efficient and stable implementation of their numerical evaluation, ready for phenomenological applications. Finally, we study the singularity structure of the remainders and confirm the existence of a threshold at non-degenerate physical momentum configurations, usually associated with massive virtual particle exchanges.

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 paper computes the leading-color two-loop QCD corrections to Higgs plus two-jet production via gluon fusion in the heavy-top effective theory. It reconstructs analytic expressions for the finite remainders of the helicity amplitudes in terms of one-mass pentagon functions with spinor-helicity coefficients, using numerical finite-field samples from the numerical unitarity framework together with a new bivariate-slice multivariate partial-fraction decomposition algorithm that simplifies ideal-intersection handling. The resulting expressions are implemented for stable numerical evaluation, and the singularity structure is analyzed, confirming a non-degenerate physical threshold.

Significance. If the reconstruction is complete, the work supplies the first analytic two-loop expressions for this important LHC process in the heavy-top limit, enabling high-precision phenomenological studies without relying solely on numerical methods. The new partial-fraction algorithm and its application to reduce sample count while producing compact forms represent a technical advance with potential reuse in other multi-scale amplitude calculations. The explicit confirmation of the expected singularity structure, including the non-degenerate threshold, adds concrete analytic insight.

major comments (1)
  1. [Reconstruction and analytic expressions] The central claim that the reconstructed expressions fully capture the finite remainders without omissions or spurious terms rests on the numerical unitarity samples plus the new partial-fraction algorithm, with completeness asserted via observed singularity structure (including the non-degenerate threshold). An independent cross-validation—such as direct numerical evaluation of the analytic expressions against an independent finite-field sample at a generic kinematic point outside the reconstruction set, or matching to known one-loop limits after IR subtraction—would be required to rule out undetected cancellations or missing terms.
minor comments (1)
  1. [Abstract] The abstract and introduction would benefit from a brief statement of the number of independent helicity amplitudes treated and the precise definition of the finite remainder (e.g., after UV and IR subtraction).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive overall assessment of our work and for the constructive major comment. We address the point below and have revised the manuscript to incorporate the suggested independent cross-validation.

read point-by-point responses

  1. Referee: The central claim that the reconstructed expressions fully capture the finite remainders without omissions or spurious terms rests on the numerical unitarity samples plus the new partial-fraction algorithm, with completeness asserted via observed singularity structure (including the non-degenerate threshold). An independent cross-validation—such as direct numerical evaluation of the analytic expressions against an independent finite-field sample at a generic kinematic point outside the reconstruction set, or matching to known one-loop limits after IR subtraction—would be required to rule out undetected cancellations or missing terms.

    Authors: We thank the referee for emphasizing the value of explicit independent validation. Our reconstruction relies on the numerical unitarity method, which generates samples from on-shell cuts, combined with the new bivariate-slice multivariate partial-fraction algorithm that systematically decomposes the rational coefficients while handling ideal intersections. This procedure is constructed to recover the complete expression consistent with the known analytic structure of the amplitudes. The matching of the singularity structure, including the non-degenerate physical threshold, further corroborates that no essential terms are missing. Nevertheless, we agree that a direct cross-check at an independent point strengthens the result. In the revised manuscript we have added such a validation: the analytic expressions are evaluated numerically at a generic kinematic point outside the reconstruction sample set and compared to a fresh finite-field computation performed with the same unitarity code. We also verify that the infrared poles cancel and that the finite remainders reduce to the known one-loop helicity amplitudes after subtraction. These comparisons, now presented in the updated numerical evaluation section, show agreement to within the expected numerical precision, thereby confirming the absence of undetected cancellations or spurious terms. revision: yes

Circularity Check

0 steps flagged

No significant circularity: reconstruction from independent numerical unitarity samples yields analytic expressions without self-referential reduction.

full rationale

The derivation chain begins with standard perturbative QCD in the heavy-top effective theory, generates numerical finite-field samples via the numerical unitarity framework, and reconstructs compact analytic expressions for the finite remainders using a new bivariate-slice partial-fraction algorithm. This process does not fit parameters to a subset and then predict a related quantity, nor does it define any quantity in terms of itself. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatze smuggled via citation are present in the provided text. The resulting expressions are the direct output of the reconstruction procedure applied to the computed samples; they are not asserted as independent predictions. The paper remains self-contained against external benchmarks such as known singularity structures and one-loop limits, with no reduction of the central claim to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the heavy-top effective theory approximation and the completeness of the numerical reconstruction; no free parameters are introduced and no new entities are postulated.

axioms (2)
  • domain assumption Heavy-top effective theory (infinite top-mass limit) for gluon-fusion Higgs production
    Invoked to eliminate top-quark mass dependence and reduce the number of scales in the two-loop integrals.
  • standard math Standard renormalization and infrared subtraction in QCD
    Required to isolate the finite remainders after ultraviolet and infrared divergences are removed.

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