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arxiv: 2604.11646 · v1 · submitted 2026-04-13 · ✦ hep-ph · hep-ex· hep-th· nucl-ex· nucl-th

Recognition: unknown

All-charm tetraquarks at hadron colliders: A high-precision fragmentation perspective

Francesco Giovanni Celiberto
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:10 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-thnucl-exnucl-th
keywords all-charm tetraquarksfragmentation functionsall-heavy exoticshadron collidersNRQCD factorizationDGLAP evolutionuncertainty quantificationjet observables
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0 comments X

The pith

This paper supplies the TQ4Q2.0 fragmentation functions for all-heavy tetraquarks in high-energy hadronic collisions.

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

The authors construct a new set of fragmentation functions for fully heavy tetraquarks carrying scalar, axial-vector, or tensor quantum numbers. These functions describe how gluons and heavy quarks split into these exotic particles during high-energy collisions. The update adds channels from non-constituent quarks and a replica method to estimate uncertainties from scale choices. The functions are evolved from low scales with a specialized threshold-aware scheme and released publicly in a standard format. This setup supports detailed calculations of production rates and associated jet observables at hadron colliders.

Core claim

We present the TQ4Q2.0 fragmentation functions for the production of all-heavy S-wave tetraquarks with scalar, axial-vector, and tensor quantum numbers in high-energy hadronic collisions. This work extends the previous framework by incorporating nonconstituent heavy-quark contributions and introducing a replica-based uncertainty-quantification strategy derived from multi-scale variations. The construction follows a nonrelativistic QCD factorization approach combining gluon- and heavy-quark-initiated fragmentation channels at leading power, with initial-scale inputs modeled through updated potential-inspired wave functions and subsequent DGLAP evolution performed via the threshold-aware HF-NR

What carries the argument

The TQ4Q2.0 fragmentation functions that give the probability for a gluon or heavy quark to fragment into an all-heavy tetraquark state, starting from low-scale wave-function inputs and evolved to collider energies.

If this is right

  • Precise predictions for all-charm tetraquark production cross sections become available for high-energy hadron colliders.
  • Systematic uncertainties arising from long-distance matrix elements and multiscale perturbative inputs are quantified for reliable use in phenomenology.
  • The publicly released grids enable studies of jet-associated observables involving these tetraquarks within existing simulation frameworks.
  • A complete baseline is established for future collider analyses of all-heavy multiquark states.

Where Pith is reading between the lines

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

  • The functions could be applied directly to reinterpret existing LHC data searches for fully heavy tetraquarks.
  • The replica-based uncertainty method may transfer to fragmentation calculations for other exotic heavy states or mixed-flavor tetraquarks.
  • This completes a resummation-driven program that could guide extensions to higher-order corrections or different collision energies.

Load-bearing premise

The initial values at the low starting energy scale are taken from wave functions inspired by quark potential models, and the factorization into short-distance and long-distance parts holds at the leading level for these tetraquark states.

What would settle it

A measurement of all-charm tetraquark production rates in proton-proton collisions at the LHC that deviates substantially from the cross sections predicted by convoluting the TQ4Q2.0 functions with parton distributions would falsify the leading-power description.

Figures

Figures reproduced from arXiv: 2604.11646 by Francesco Giovanni Celiberto.

Figure 1
Figure 1. Figure 1: FIG. 1: Leading-order diagrams for the collinear fragmentation of a gluon (left), a heavy quark (center), and a [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Two-stage evolution pipeline for [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Replica-like sampling of perturbative F-MHOUs in the two-dimensional scale space. [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Momentum dependence of the [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Momentum dependence of the [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Momentum dependence of the [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Energy dependence of the [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Distributions in rapidity for scalar [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Distributions in rapidity for scalar [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Distributions in rapidity for scalar [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Momentum dependence of the [PITH_FULL_IMAGE:figures/full_fig_p036_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Momentum dependence of the [PITH_FULL_IMAGE:figures/full_fig_p037_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Momentum dependence of the [PITH_FULL_IMAGE:figures/full_fig_p038_13.png] view at source ↗
read the original abstract

We present the TQ4Q2.0 fragmentation functions for the production of all-heavy (fully heavy) $S$-wave tetraquarks ($T_{4Q}$) with scalar ($0^{++}$), axial-vector ($1^{+-}$), and tensor ($2^{++}$) quantum numbers in high-energy hadronic collisions. This work extends the previous TQ4Q1.1 framework by incorporating nonconstituent heavy-quark contributions and introducing a replica-based uncertainty-quantification strategy derived from multi-scale variations (MHOUs). The construction follows a nonrelativistic QCD factorization approach, combining gluon- and heavy-quark-initiated fragmentation channels at leading power. Initial-scale inputs are modeled through updated potential-inspired wave functions, while the subsequent DGLAP evolution is performed via the threshold-aware HF-NRevo scheme. A comprehensive systematic analysis of uncertainties is carried out, with contributions from color-composite long-distance matrix elements (LDMEs) and perturbative multiscale inputs. The resulting TQ4Q2.0 grids, publicly released in LHAPDF6 format, provide the first complete phenomenological set for all-heavy exotics, enabling precise studies of all-charm tetraquark production and jet-associated observables within the JETHAD environment. This article completes the high-energy resummation-driven generation of the TQ4Q program and establishes a definitive baseline for future collider-oriented analyses of all-heavy multiquark dynamics.

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 constructs and publicly releases the TQ4Q2.0 fragmentation functions for all-charm S-wave tetraquarks (T_{4Q}) with 0^{++}, 1^{+-}, and 2^{++} quantum numbers. It extends the prior TQ4Q1.1 framework by adding nonconstituent heavy-quark contributions, employs NRQCD factorization at leading power for gluon- and heavy-quark-initiated channels, models initial-scale inputs via updated potential-inspired wave functions, performs DGLAP evolution with the threshold-aware HF-NRevo scheme, and quantifies uncertainties through a replica-based multi-scale variation (MHOU) strategy on color-composite LDMEs and perturbative inputs. The grids are provided in LHAPDF6 format for use in the JETHAD environment.

Significance. If the leading-power NRQCD assumption holds, this supplies the first complete phenomenological fragmentation-function set for all-heavy tetraquarks together with systematic uncertainty bands, directly enabling collider studies of all-charm exotic production and jet-associated observables. The public grid release and the incorporation of a threshold-aware evolution scheme are concrete strengths that lower the barrier for phenomenological applications.

major comments (2)
  1. [Abstract and the NRQCD factorization framework section] The central claim rests on the applicability of leading-power NRQCD factorization to all-heavy tetraquarks, yet the manuscript provides no explicit power-counting argument or numerical estimate showing that higher-power operators (involving two heavy-quark pairs or additional color-octet transitions) remain suppressed at the relevant fragmentation scales; this assumption is load-bearing for the entire TQ4Q2.0 construction.
  2. [Section describing initial-scale modeling and LDME determination] Initial-scale inputs are obtained from potential-inspired wave functions whose parameters are fitted rather than derived; while the replica strategy quantifies variation among these inputs, it does not remove the model dependence that enters the LDMEs and therefore propagates directly into the quoted fragmentation functions.
minor comments (2)
  1. [Abstract] The abstract states that the work 'completes the high-energy resummation-driven generation of the TQ4Q program'; a brief explicit statement of what remains for future work would improve clarity.
  2. [Introduction or notation section] Notation for the three quantum-number channels (0^{++}, 1^{+-}, 2^{++}) is introduced without a compact table summarizing the corresponding color and spin structures; adding such a table would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and the NRQCD factorization framework section] The central claim rests on the applicability of leading-power NRQCD factorization to all-heavy tetraquarks, yet the manuscript provides no explicit power-counting argument or numerical estimate showing that higher-power operators (involving two heavy-quark pairs or additional color-octet transitions) remain suppressed at the relevant fragmentation scales; this assumption is load-bearing for the entire TQ4Q2.0 construction.

    Authors: We acknowledge that the manuscript does not contain an explicit power-counting argument or numerical estimate for the suppression of higher-power operators. The leading-power NRQCD factorization is adopted following the standard velocity scaling rules established for heavy quarkonia, where higher-power contributions are suppressed by powers of the relative velocity v^2 (with v^2 approximately 0.1-0.3 for charm systems, inferred from binding energies). Analogous scaling is expected to hold for all-heavy tetraquarks. We will add a concise discussion of this velocity power counting to the NRQCD factorization framework section, including references to the relevant literature. A quantitative numerical estimate of higher-power effects would require dedicated non-perturbative calculations of additional LDMEs that lie outside the present scope. revision: partial

  2. Referee: [Section describing initial-scale modeling and LDME determination] Initial-scale inputs are obtained from potential-inspired wave functions whose parameters are fitted rather than derived; while the replica strategy quantifies variation among these inputs, it does not remove the model dependence that enters the LDMEs and therefore propagates directly into the quoted fragmentation functions.

    Authors: We agree that the initial-scale inputs are obtained from potential-inspired wave functions with fitted parameters and that the replica strategy quantifies variations within this framework without eliminating the underlying model dependence. This dependence is inherent to the current phenomenological determination of the color-composite LDMEs, as first-principles calculations are not yet available. The replica approach provides a practical estimate of the associated uncertainties through multi-scale variations. We will revise the initial-scale modeling section to explicitly note this model dependence and its propagation into the fragmentation functions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model construction is explicit

full rationale

The paper explicitly states that it constructs the TQ4Q2.0 fragmentation functions by applying standard NRQCD factorization at leading power, with initial-scale inputs modeled via potential-inspired wave functions and DGLAP evolution via HF-NRevo. It acknowledges the inputs as modeled rather than derived from first principles and extends a prior framework without claiming the central result reduces to unverified self-citation or fitted parameters renamed as predictions. No load-bearing step equates the output FFs to the inputs by construction; the work is a transparent phenomenological model release, self-contained against external benchmarks like standard NRQCD applications in quarkonium studies.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard NRQCD assumptions and the use of modeled or fitted parameters for wave functions and LDMEs, with no new postulated particles or forces.

free parameters (2)
  • LDMEs
    Color-composite long-distance matrix elements whose contributions are analyzed for uncertainty
  • initial-scale wave-function parameters
    Updated potential-inspired inputs at the starting scale
axioms (2)
  • domain assumption NRQCD factorization at leading power
    Assumes nonrelativistic QCD applies to combine gluon- and heavy-quark-initiated channels for tetraquark fragmentation
  • domain assumption Validity of DGLAP evolution with HF-NRevo scheme
    Threshold-aware evolution from initial to collider scales is taken as reliable

pith-pipeline@v0.9.0 · 5559 in / 1467 out tokens · 75705 ms · 2026-05-10T15:10:13.559454+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Multimodal Fragmentation of All-Heavy Pentaquarks: Uncertainty-Aware Predictions for Hadron Colliders

    hep-ph 2026-05 unverdicted novelty 3.0

    Develops uncertainty-aware fragmentation functions PQ5Q1.1 for all-charm pentaquarks using multimodal perturbative and nonperturbative modeling for collider predictions.

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