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arxiv: 2605.05880 · v2 · pith:AGC3OI2Tnew · submitted 2026-05-07 · ✦ hep-ph

Top-associated Higgs-boson production using perturbative fragmentation functions at next-to-leading-order

Colomba Brancaccio , Michal Czakon , Terry Generet , Benedikt Gurdon This is my paper

Pith reviewed 2026-05-19 17:06 UTC · model grok-4.3

classification ✦ hep-ph
keywords Higgs boson productiontop quark pairperturbative fragmentation functionsNLO QCDhadron collidersfactorisation theoremmass effectsttH process
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The pith

Perturbative fragmentation functions reliably approximate top-associated Higgs production at NLO using the hybrid prescription at LHC energies.

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

The paper shows how a factorisation theorem with perturbative fragmentation functions can describe Higgs boson production together with a top-antitop pair at hadron colliders. These functions model the nearly collinear emission of the Higgs from a top quark and match the leading mass dependence in the exact next-to-leading-order calculation. The authors compare two ways of treating the top-quark mass and demonstrate that the hybrid prescription produces reliable results across the full process at current LHC center-of-mass energies. The zero-mass prescription works only in the quark-antiquark channel at the LHC but becomes viable for the complete process at a future 100 TeV collider. The analysis also flags complications that appear when the same approach is pushed to next-to-next-to-leading order.

Core claim

Under certain conditions the production of a Higgs boson in association with a top-antitop pair can be described via a factorisation theorem that employs perturbative fragmentation functions. The functions reproduce the leading mass dependence of the exact next-to-leading-order calculation. The method yields reliable results at LHC center-of-mass energies in the hybrid prescription, while the zero-mass-top-quark prescription remains reliable only in the quark-antiquark channel at the LHC and becomes applicable to the full process at 100 TeV.

What carries the argument

Perturbative fragmentation functions for the nearly collinear emission of a Higgs boson from a top quark, used inside a factorisation theorem at next-to-leading order.

If this is right

  • The hybrid prescription supplies accurate approximations for the full pp to ttH process at present LHC energies.
  • The zero-mass-top-quark prescription is limited to the quark-antiquark channel at the LHC but extends to the complete process at 100 TeV colliders.
  • Extensions of the method to next-to-next-to-leading order encounter additional subtleties that must be resolved.
  • The factorisation approach isolates the dominant mass-dependent effects without computing the full massive matrix elements.

Where Pith is reading between the lines

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

  • The same fragmentation functions could reduce the computational burden when simulating other heavy-quark associated processes at hadron colliders.
  • Combining the method with resummation of large mass logarithms might improve precision at high transverse momenta.
  • Validation against exact higher-order calculations at future collider energies would clarify the range of applicability.
  • The approach may integrate naturally into parton-shower Monte Carlo programs for more efficient event generation.

Load-bearing premise

The perturbative fragmentation functions reproduce the leading mass dependence of the exact next-to-leading-order calculation under the kinematic conditions and prescriptions examined.

What would settle it

A direct numerical comparison of the fragmentation-function approximation against the full next-to-leading-order calculation for differential distributions in ttH production at LHC energies would test whether the agreement holds beyond the leading mass terms.

read the original abstract

Under certain conditions, the production of a Higgs boson in association with a top-anti-top pair at hadron colliders can be described via a factorisation theorem using perturbative fragmentation functions. The latter describe the nearly collinear emission of a Higgs boson from a top-quark and reproduce the leading mass dependence of the exact next-to-leading-order (NLO) calculation. Although the NLO fragmentation functions have been calculated a few years ago, it has not been possible up to now to demonstrate the applicability of the approximation in a realistic setup. At NLO, we analyse two different ways of treating the top-quark mass, called the zero-mass-top-quark (ZMTQ) and the hybrid prescription. We show that the method yields reliable results at LHC center-of-mass (cms) energies in the hybrid prescription. In the ZMTQ prescription, the results at LHC cms energies are only reliable in the quark-anti-quark channel, but become viable for the full $pp \rightarrow t\bar{t}H$ process at a 100 TeV hadron collider. In addition, we discuss some subtleties and complications arising when extending the formalism to next-to-next-to-leading-order (NNLO) and beyond.

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

2 major / 2 minor

Summary. The manuscript develops a factorization approach to ttH production at hadron colliders using NLO perturbative fragmentation functions that capture the leading top-mass dependence of collinear Higgs emission from top quarks. It examines two top-mass treatments—the zero-mass-top-quark (ZMTQ) prescription and a hybrid prescription—and concludes that the hybrid scheme produces reliable results for the full pp → t tbar H process at LHC energies, while ZMTQ is reliable only in the q qbar channel at the LHC but becomes viable for the complete process at 100 TeV. The paper also outlines subtleties that arise when extending the formalism to NNLO.

Significance. If the hybrid prescription is shown to reproduce the leading m_t dependence of the exact NLO calculation across the relevant phase space, the work supplies a practical tool for incorporating finite top-mass effects into ttH phenomenology without performing a fully massive calculation. This could ease higher-order computations and improve efficiency for LHC analyses. The explicit discussion of NNLO complications is a constructive contribution.

major comments (2)
  1. [§4] §4 (numerical results for LHC energies): The central claim that the hybrid prescription yields reliable results at LHC cms energies rests on the assertion that the NLO fragmentation functions reproduce the leading mass dependence of the exact NLO ttH calculation, particularly in gluon-initiated channels. However, no explicit quantitative comparisons (e.g., ratios of the approximate to exact cross sections, differences in m_t logarithms, or validation plots) are presented to demonstrate the accuracy of this reproduction for gg → ttH diagrams.
  2. [§3.2] §3.2 (hybrid prescription definition): The hybrid scheme is stated to regulate collinear singularities and absorb mass logarithms appropriately, yet the manuscript does not show how residual non-fragmentation contributions are controlled in the gluon channel at LHC kinematics; this control is load-bearing for the reliability statement in the abstract.
minor comments (2)
  1. A summary table comparing the ZMTQ and hybrid prescriptions (including their treatment of collinear singularities and mass logarithms) would improve readability.
  2. [§5] The discussion of NNLO subtleties in the final section would benefit from a short list of the specific technical obstacles that must be overcome.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comments point by point below. Where the concerns identify areas for improved clarity or support, we will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§4] §4 (numerical results for LHC energies): The central claim that the hybrid prescription yields reliable results at LHC cms energies rests on the assertion that the NLO fragmentation functions reproduce the leading mass dependence of the exact NLO ttH calculation, particularly in gluon-initiated channels. However, no explicit quantitative comparisons (e.g., ratios of the approximate to exact cross sections, differences in m_t logarithms, or validation plots) are presented to demonstrate the accuracy of this reproduction for gg → ttH diagrams.

    Authors: We thank the referee for this observation. The manuscript grounds the reliability claim in the factorization theorem and the known properties of the NLO fragmentation functions, which are constructed to capture the leading collinear mass logarithms. However, we acknowledge that direct numerical ratios or validation plots comparing the hybrid approximation to the exact massive NLO result specifically for the gg-initiated subprocess are not presented in the current version. To address this, we will add new figures and accompanying text in §4 displaying the ratio of the hybrid cross section to the full NLO result, the residual m_t logarithmic dependence, and comparisons across phase-space regions at LHC energies. This will provide the quantitative evidence requested and strengthen the central claim. revision: yes

  2. Referee: [§3.2] §3.2 (hybrid prescription definition): The hybrid scheme is stated to regulate collinear singularities and absorb mass logarithms appropriately, yet the manuscript does not show how residual non-fragmentation contributions are controlled in the gluon channel at LHC kinematics; this control is load-bearing for the reliability statement in the abstract.

    Authors: We agree that an explicit demonstration of the control over residual non-fragmentation terms would improve the presentation. In the hybrid prescription, the zero-mass calculation is supplemented by mass-dependent counterterms that absorb the collinear logarithms, with power-suppressed corrections remaining. We will revise §3.2 to include a more detailed discussion, including the relevant subtraction terms and their suppression in the gluon channel at typical LHC kinematics. These clarifications will be cross-referenced to the new numerical comparisons added in the revised §4, thereby supporting the reliability statement in the abstract. revision: yes

Circularity Check

0 steps flagged

Minor self-citation of prior fragmentation functions; central reliability claim remains independently verifiable

full rationale

The paper applies NLO perturbative fragmentation functions (calculated in prior work) within standard QCD factorization to the ttH process, comparing ZMTQ and hybrid top-mass prescriptions. The claim that the hybrid prescription yields reliable results at LHC energies rests on numerical demonstration that the approximation reproduces leading mass dependence of the exact NLO calculation. This is an application and validation step, not a re-derivation or fit defined inside the present manuscript. Any citation to the earlier fragmentation-function calculation is not load-bearing for the new applicability result, which is presented as externally checkable against the full NLO benchmark. No step reduces by construction to a parameter fitted or defined within this paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the standard QCD factorization theorem for collinear emissions and on NLO fragmentation functions computed in prior literature; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Factorization theorem holds for nearly collinear Higgs emission from top quarks at NLO.
    Invoked to justify the use of perturbative fragmentation functions in the ttH process.

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Reference graph

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