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Antenna subtraction at NNLO for heavy quark pair production at hadron colliders: the non-diagonal channels

T0 review · 0 major / 5 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read The paper finishes NNLO antenna subtraction for the qq, qq' and qg channels of heavy-quark pair production, adding the missing massive soft factors and integrated massive antenna convolutions in full colour.

desk verdict Solid completion of the non-diagonal NNLO antenna pieces for top-pair, with new massive soft factors and convolutions that check out both analytically and against Top++. read the letter →

arxiv 2607.11741 v1 pith:ZKLHPYKL submitted 2026-07-13 hep-ph

Aude Gehrmann-De Ridder , João Pires This is my paper
classification hep-ph
keywords antennasubtractionNNLOQCDheavy-quarkpairproductionmassivesoftfactorsquark-gluonchannelinfraredpoleshadroncolliders
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Precision LHC measurements of top-pair production need next-to-next-to-leading-order QCD predictions that remain fully differential. This paper supplies the last missing pieces of the antenna-subtraction method for the three flavour-off-diagonal partonic channels (identical-quark, non-identical-quark and quark-gluon). It derives the integrated subtraction terms that cancel infrared poles at the real-virtual and double-virtual levels, introduces new massive soft factors that must be integrated over massive initial-final phase space, and evaluates the first convolutions of integrated massive antennae with mass-factorisation kernels. After analytic cancellation of every infrared pole, the numerical NNLO coefficients agree with independent inclusive codes at the per-mille level. The work therefore completes the NNLO description of these channels inside a parton-level generator, opening the way to arbitrary fiducial cuts and fully differential distributions for heavy-quark pairs.

What carries the argument

Massive soft factors (eikonal factors with one or two massive radiators) integrated over the initial-final massive antenna phase space, together with the first convolution products of integrated massive three-parton antennae and mass-factorisation kernels; these building blocks close the subtraction at real-virtual and double-virtual level.

What would settle it

Recompute the same NNLO coefficients with an independent subtraction method (or with a different Monte-Carlo integrator) and check whether the numbers still agree with the inclusive reference to the claimed sub-percent precision for every scale choice.

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Extended reading notes

Core claim

The NNLO antenna-subtraction terms for the qq, qq' and qg channels of heavy-quark pair production are now complete in full colour. Newly derived massive soft factors and convolutions of integrated massive antennae cancel all explicit infrared poles analytically; the resulting numerical NNLO coefficients match independent inclusive predictions to better than 0.4 percent.

Load-bearing premise

Logarithmic enhancements that appear when a heavy quark becomes collinear with a massless parton are neglected, on the grounds that they stay small when the top mass is comparable to the partonic centre-of-mass energy.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

0 major / 5 minor

Summary. The manuscript constructs the full-colour NNLO antenna-subtraction terms for the non-diagonal partonic channels (qq, qq', qg and charge conjugates) of heavy-quark pair production at hadron colliders, and implements them in NNLOJET. Building on earlier double-real results for the purely fermionic channels, the authors derive the integrated real-virtual and double-virtual subtraction contributions for qq/qq' and present the complete double-real, real-virtual and double-virtual subtraction for the qg channel for the first time. New analytic ingredients are the massive and massless soft factors integrated over the initial-final massive antenna phase space (Sec. 4) and the convolutions of integrated massive three-parton antennae with massless antennae and mass-factorisation kernels. Validation consists of analytic cancellation of all explicit infrared poles, a dedicated numerical soft-factor test (Sec. 4.3) in which RR and RV contributions cancel to 0.01 % within Monte-Carlo error, and inclusive NNLO coefficients that agree with Top++ to better than 0.4 % (Tables 3–4).

Significance. The work supplies the missing non-diagonal channels for a fully differential NNLO description of top-pair production inside the antenna-subtraction formalism and extends the integrated antenna library with ingredients (massive soft factors, massive–massless convolutions) that will be reusable for other processes with massive fermions. The analytic IR-pole cancellation, the compact dipole-operator organisation of the U-type terms (Eqs. 3.20, 3.31), the independent soft-factor consistency check of Sec. 4.3, and the sub-percent numerical agreement with the independent Top++ code constitute strong, falsifiable evidence that the construction is correct. The remaining gg and q¯q channels are left for future work, but the present results already enable precision phenomenology with arbitrary fiducial cuts for the channels treated here.

minor comments (5)
  1. Introduction (paragraph after Eq. (1.3)): the decision to neglect quasi-collinear logarithmic enhancements is standard and already used by the reference calculations, but a short quantitative remark on the expected size of the neglected logs for the kinematics of Tables 3–4 would help non-specialist readers.
  2. Eqs. (3.13)–(3.15) and (3.26): only the leading-colour subtraction terms are written explicitly. A brief statement that the sub-leading colour pieces follow by the same building blocks (and are fully included in the numerical results) is already present; adding a pointer to the colour-stripped partial amplitudes that generate them would improve reproducibility.
  3. Sec. 4.1–4.2: the Laurent expansions of the integrated soft factors are lengthy. Depositing the unexpanded hypergeometric/Appell expressions (or a short Mathematica notebook) as ancillary material would facilitate reuse by other groups.
  4. Tables 3–4: the Top++ reference values carry no quoted uncertainty. A one-sentence remark on the Precision=3 setting and the absence of a returned error estimate would clarify the comparison.
  5. Notation: the distinction between calligraphic (integrated) and ordinary (unintegrated) antennae is standard but could be restated once in Sec. 2 for readers less familiar with the NNLOJET conventions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; subtraction terms are constructed from colour-ordered amplitudes and antennae, with new soft-factor integrals derived and validated independently.

full rationale

The paper constructs the NNLO antenna subtraction terms for the qq, qq' and qg channels by colour-decomposing the relevant tree and one-loop amplitudes, enumerating all soft and collinear unresolved limits, and writing local counterterms from known three- and four-parton antennae together with newly derived massive soft factors. The soft factors themselves (Sec. 4) are obtained by direct analytic integration of the eikonal factors over the initial-final massive antenna phase space; their Laurent expansions are checked by an auxiliary finite test contribution (Sec. 4.3) whose double-real and real-virtual pieces cancel to better than 0.01 % within Monte-Carlo error. Explicit infrared poles cancel analytically against mass-factorisation kernels, and the resulting inclusive NNLO coefficients agree with the independent Top++ code to <0.4 % (Tables 3–4). No parameters are fitted, no uniqueness theorem is imported from prior self-citations as a load-bearing premise, and the numerical agreement constitutes an external cross-check rather than a tautology. Prior self-citations supply only established antenna building blocks that are independently documented and do not reduce the present derivation to its inputs by construction.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The work rests on the established antenna-subtraction formalism, standard QCD colour and infrared factorisation, and the kinematic assumption that quasi-collinear logs can be dropped. No free parameters are fitted; the only new analytic objects are derived integrals, not postulated entities.

assumptions (3)
  • domain assumption Antenna subtraction correctly captures all soft and collinear singularities of QCD amplitudes involving massive fermions once the appropriate massive antennae and soft factors are used.
    Invoked throughout Sections 2–3; the entire construction inherits the validity of the massive-antenna programme of Refs. [16–22].
  • domain assumption Quasi-collinear logarithmic enhancements involving the heavy-quark mass are numerically negligible when mt is of order the partonic centre-of-mass energy.
    Stated explicitly after Eq. (1.3) and used to justify omitting quasi-collinear subtraction terms.
  • standard math Standard QCD colour decomposition, eikonal soft factors, and mass-factorisation kernels (Γ(1), Γ(2)) hold in dimensional regularisation.
    Used to construct colour-ordered matrix elements and integrated dipoles throughout.

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Cite this review

Pith. "Pith review of Antenna subtraction at NNLO for heavy quark pair production at hadron colliders: the non-diagonal channels." pith.science (2026). https://pith.science/paper/ZKLHPYKL

@misc{pith2026260711741,
  author       = {Pith},
  title        = {Pith review of: Antenna subtraction at NNLO for heavy quark pair production at hadron colliders: the non-diagonal channels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZKLHPYKL}},
  note         = {Machine review of arXiv:2607.11741}
}
abstract

We present the calculation involving the $qq$, $qq'$ and $qg$ partonic channels contributing to heavy-quark pair production at hadron colliders through next-to-next-to-leading order in QCD using the antenna subtraction formalism. The calculation is performed in full colour and implemented within the NNLOJET framework. Building upon previously available results, we complete the NNLO treatment of the $qq$ and $qq'$ channels by deriving the integrated subtraction contributions required at the real virtual and double-virtual levels. We further present for the first time the NNLO antenna subtraction terms related to the $qg$-channel in full colour. The calculation requires several new ingredients, including massive soft factors and convolutions involving integrated massive antennae thereby extending the integrated antenna library to cope with processes with massive fermions. We validate the calculation through analytic infrared pole cancellation and numerical comparisons with existing results. These results complete the NNLO description of the $qq$, $qq'$, and $qg$ channels and constitute an important step towards a fully differential NNLO treatment of heavy-quark pair production within the antenna subtraction formalism.

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