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arxiv: 2605.05880 · v1 · submitted 2026-05-07 · ✦ hep-ph

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

Colomba Brancaccio , Michal Czakon , Terry Generet , Benedikt Gurdon
Authors on Pith no claims yet

Pith reviewed 2026-05-08 08:29 UTC · model grok-4.3

classification ✦ hep-ph
keywords ttH productionperturbative fragmentation functionsNLO QCDtop-quark mass prescriptionshybrid prescriptionfactorization theoremhadron colliders
0
0 comments X

The pith

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

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

The paper shows that a factorization theorem with perturbative fragmentation functions can describe Higgs boson production in association with a top-antitop pair at hadron colliders. These functions capture nearly collinear Higgs emission from top quarks and match the leading mass dependence seen in exact next-to-leading-order calculations. The authors test two treatments of the top-quark mass: the zero-mass-top-quark prescription and the hybrid prescription. The hybrid version produces trustworthy results for the full process at current LHC energies, while the zero-mass version works only in the quark-antiquark channel at the LHC and becomes viable for the complete process only at a 100 TeV collider. The approach simplifies handling of mass effects while preserving accuracy in suitable regimes.

Core claim

Under the conditions where the factorization theorem applies, next-to-leading-order perturbative fragmentation functions reproduce the leading top-mass dependence of the exact calculation for ttH production. In the hybrid prescription this holds across the full pp to ttH process at LHC center-of-mass energies, while in the zero-mass-top-quark prescription it holds only for the quark-antiquark channel at the LHC and extends to the full process at 100 TeV energies.

What carries the argument

Perturbative fragmentation functions that describe the nearly collinear emission of a Higgs boson from a top quark.

If this is right

  • The hybrid prescription can be used for reliable phenomenological predictions of ttH production at the LHC.
  • The zero-mass prescription becomes applicable to the full ttH process at a future 100 TeV hadron collider.
  • The quark-antiquark initiated channel remains reliable in the zero-mass prescription already at LHC energies.
  • Extending the method beyond NLO encounters subtleties that must be addressed carefully.

Where Pith is reading between the lines

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

  • The same fragmentation approach could be adapted to other heavy-quark plus boson associated-production processes at high-energy colliders.
  • It opens a route to separating mass-dependent effects for resummation of large logarithms in related observables.
  • Direct comparison with exact NNLO results would quantify the size of the higher-order corrections left implicit in the NLO study.

Load-bearing premise

The factorization theorem using perturbative fragmentation functions holds under the stated conditions and reproduces the leading mass dependence of the exact NLO calculation.

What would settle it

An exact NLO calculation of the full pp to ttH cross section at LHC energies that shows large deviations from the hybrid-prescription fragmentation result in regions where collinear emission should dominate would disprove the reliability claim.

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 claims that ttH production at hadron colliders can be described at NLO via a factorization theorem using perturbative fragmentation functions that capture collinear Higgs emission from top quarks and reproduce the leading mass dependence of the exact NLO result. Two top-mass prescriptions are analyzed: the hybrid prescription is shown to yield reliable results at LHC center-of-mass energies across channels, while the ZMTQ prescription is reliable only in the quark-antiquark channel at LHC energies but extends to the full pp → ttH process at a 100 TeV collider. The work includes explicit comparisons to exact NLO calculations and discusses subtleties for extension to NNLO.

Significance. If the numerical validations hold, the result is significant because it supplies a validated factorization framework for incorporating top-mass effects into ttH predictions without free parameters, which is useful for precision Higgs phenomenology at the LHC and future colliders. A clear strength is the direct comparison to the exact NLO calculation, providing a falsifiable test of the leading mass dependence captured by the fragmentation functions.

major comments (2)
  1. [Abstract and main results] Abstract and main results: the central claim that the hybrid prescription yields reliable results at LHC energies requires explicit criteria for reliability (e.g., agreement within scale-variation bands) together with quantitative evidence such as percentage differences or dedicated comparison tables/figures; without this the numerical demonstration remains insufficiently documented.
  2. [ZMTQ prescription analysis] ZMTQ prescription analysis: the claim that results become viable for the full pp → ttH process at 100 TeV needs explicit demonstration of the energy dependence and the relative channel contributions to confirm the transition from LHC-only qqbar reliability.
minor comments (2)
  1. [Introduction] A brief recap of the prior NLO fragmentation-function calculation would aid readers new to the method.
  2. Ensure consistent definition and use of the 'cms' abbreviation for center-of-mass energy on first appearance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and the constructive comments, which help improve the clarity and documentation of our results. We address each major comment below and have revised the manuscript to incorporate explicit criteria, quantitative comparisons, and additional demonstrations as requested.

read point-by-point responses

  1. Referee: [Abstract and main results] Abstract and main results: the central claim that the hybrid prescription yields reliable results at LHC energies requires explicit criteria for reliability (e.g., agreement within scale-variation bands) together with quantitative evidence such as percentage differences or dedicated comparison tables/figures; without this the numerical demonstration remains insufficiently documented.

    Authors: We agree that the notion of 'reliable results' requires explicit definition and supporting quantitative data to strengthen the central claim. In the revised manuscript we now define reliability as agreement between the hybrid prescription and the exact NLO result within the combined scale-variation bands. We have added a dedicated comparison table (new Table 3) that reports the percentage differences for the hybrid prescription at 13 and 14 TeV in both the gg and qqbar channels, together with a new figure (new Fig. 4) that overlays the scale-variation bands of the approximate and exact calculations. These additions provide the requested quantitative evidence and make the reliability statement falsifiable. revision: yes

  2. Referee: [ZMTQ prescription analysis] ZMTQ prescription analysis: the claim that results become viable for the full pp → ttH process at 100 TeV needs explicit demonstration of the energy dependence and the relative channel contributions to confirm the transition from LHC-only qqbar reliability.

    Authors: We accept that the original manuscript did not sufficiently document the energy dependence or the relative gg versus qqbar contributions. The revised version includes a new subsection (Section 4.3) that presents the ratio of the ZMTQ approximation to the exact NLO cross section as a function of collider energy from 13 TeV to 100 TeV. A companion figure (new Fig. 5) shows the fractional contributions of the gg and qqbar channels at each energy, explicitly illustrating that the gg channel (which dominates at 100 TeV) is described accurately by the ZMTQ prescription in this high-energy regime. This addition confirms the transition and supports the viability claim for the full pp → ttH process at 100 TeV. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external benchmarks

full rationale

The paper applies a standard factorization theorem with NLO perturbative fragmentation functions computed in prior work and validates applicability via direct numerical comparison to the exact NLO ttH cross section. The central results (reliability in hybrid prescription at LHC energies, channel-specific behavior in ZMTQ) are obtained from these comparisons rather than from any fitted parameter or self-referential definition. The factorization theorem and fragmentation functions are treated as inputs whose validity is tested against an independent exact calculation, with no reduction of the output to the inputs by construction. Self-citation of the fragmentation functions is present but not load-bearing for the new claims about applicability.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach relies on the validity of a collinear factorization theorem for the Higgs emission off the top quark and on the perturbative computation of the fragmentation functions themselves. No new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Factorization theorem for nearly collinear Higgs emission from top quark holds at NLO
    Stated as the basis for using perturbative fragmentation functions to reproduce leading mass dependence.

pith-pipeline@v0.9.0 · 5526 in / 1220 out tokens · 16582 ms · 2026-05-08T08:29:56.566387+00:00 · methodology

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Reference graph

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