arxiv: 2604.13769 · v1 · submitted 2026-04-15 · ✦ hep-ph · hep-ex· hep-th· nucl-ex· nucl-th

Recognition: unknown

Fully Heavy Pentaquarks with JETHAD: A High-Energy Viewpoint

Francesco Giovanni Celiberto

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:45 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-thnucl-exnucl-th

keywords fully heavy pentaquarksfragmentation functionsQCD phenomenologyexotic hadronshigh-energy collisionsHL-LHCFCCsemi-inclusive production

0 comments

The pith

Fragmentation functions for fully heavy pentaquarks are completed with refined heavy-quark inputs and used to predict production rates at future colliders.

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

The paper completes the PQ5Q1.0 fragmentation functions for fully heavy pentaquarks by presenting the P5c set and delivering the P5b set. These functions use an improved calculation of the initial-scale input for the heavy-quark fragmentation channel, which supports modeling both compact multicharm states and hadronization via diquark-antiquark-diquark setups. The data-validated JETHAD framework then computes next-to-leading-logarithmic and next-to-leading-order semi-inclusive rates for pentaquark-plus-jet systems. This provides concrete predictions for the High-Luminosity LHC and the Future Circular Collider, linking hadron structure to the production of exotic heavy states in high-energy collisions.

Core claim

We complete the release of the hadron-structure-oriented PQ5Q1.0 fragmentation functions by discussing the P5c set and delivering the P5b one. These functions incorporate an improved computation of the initial-scale input for the constituent heavy-quark fragmentation channel, making them suitable for describing both the direct formation of a compact multicharm state and the hadronization from a diquark-antiquark-diquark configuration. For phenomenological applications, we employ the data-validated (sym)JETHAD framework to compute and analyze NLL/NLO+ semi-inclusive production rates of pentaquark-plus-jet systems at the upcoming HL-LHC and the future FCC.

What carries the argument

PQ5Q1.0 fragmentation functions: hadron-structure-oriented sets that model the transition from heavy quarks to fully heavy pentaquarks, using refined initial-scale inputs to capture both compact and diquark-based formation channels.

If this is right

The functions describe both direct compact formation of multicharm states and hadronization from diquark-antiquark-diquark configurations.
NLL/NLO+ accuracy semi-inclusive production rates of pentaquark-plus-jet systems become calculable in the JETHAD framework.
Concrete predictions are available for pentaquark production at the HL-LHC and FCC.

Where Pith is reading between the lines

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

These functions could be applied to guide searches for fully heavy pentaquarks in existing or upcoming collider datasets.
The same improved-input approach might extend to fragmentation functions for other fully heavy exotic states such as tetraquarks.
The connection between hadron structure and precision QCD calculations could help clarify binding mechanisms in multiquark systems.

Load-bearing premise

The leading-power fragmentation approximation holds for fully heavy pentaquarks, and the improved initial-scale inputs accurately represent both formation channels without large higher-order corrections.

What would settle it

A measurement of the pentaquark-plus-jet cross section at the HL-LHC that deviates substantially from the NLL/NLO+ predictions computed with the PQ5Q1.0 functions would indicate that the leading-power approximation or the input improvements do not hold.

Figures

Figures reproduced from arXiv: 2604.13769 by Francesco Giovanni Celiberto.

**Figure 1.** Figure 1: Representative leading-order diagrams for the initial-scale collinear fragmentation of a constituent heavy antiquark into a color-singlet 𝑆-wave 𝑃5𝑄 state within the direct multiquark scenario. The nonperturbative hadronization component of the corresponding FFs is depicted by blue ovals. Diagrams produced using JaxoDraw 2.0 [239]. Page 45 of 44 [PITH_FULL_IMAGE:figures/full_fig_p045_1.png] view at source ↗

**Figure 2.** Figure 2: Representative leading-order diagrams for the initial-scale collinear fragmentation of a constituent heavy antiquark into a color-singlet 𝑆-wave 𝑃5𝑄 pentaquark in the scalar-diquark scenario. Double lines denote (𝑄𝑄) or (𝑄̄𝑄̄) heavy-diquark configurations, while black dots represent effective gluon-diquark-antidiquark interaction vertices. The nonperturbative hadronization stage of the associated FFs is … view at source ↗

**Figure 3.** Figure 3: Constituent heavy-quark to 𝑃5𝑐 (left) and 𝑃5𝑏 (right) initial-scale fragmentation channels in the direct (upper) and scalar-diquark (lower) picture. For the sake of illustration, an expanded diagonal DGLAP evolution is performed in the range 𝜇𝐹 ,0∕4 to 4𝜇𝐹 ,0 . Page 47 of 44 [PITH_FULL_IMAGE:figures/full_fig_p047_3.png] view at source ↗

**Figure 4.** Figure 4: Factorization-scale dependence of the PQ5Q1.0 NLO FFs portraying the ZM-VFNS fragmentation of 𝑃5𝑐 (left) and 𝑃5𝑏 (right) pentaquarks within direct (upper) or scalar-diquark (bottom) initial-scale inputs. The hadron momentum fraction is set to 𝑧 = 0.425 ≃ ⟨𝑧⟩. Page 48 of 44 [PITH_FULL_IMAGE:figures/full_fig_p048_4.png] view at source ↗

**Figure 5.** Figure 5: Upper plots: factorization-scale dependence of the TQHL1.1 NLO FFs [126] portraying the ZM-VFNS fragmentation of 𝑋𝑐𝑠 ̄𝑐 ̄𝑠 (left) and 𝑋𝑏𝑠𝑏 ̄𝑠̄ (right) tetraquarks. Lower plots: factorization-scale dependence of the TQ4Q1.1 NLO FFs [222, 223] portraying the ZM-VFNS fragmentation of 𝑇4𝑐 (0++) (left) and 𝑇4𝑏 (0++) (right) tetraquarks. The hadron momentum fraction is set to 𝑧 = 0.425 ≃ ⟨𝑧⟩. Page 49 of 44 [PIT… view at source ↗

**Figure 6.** Figure 6: Sketch of the pentaquark + jet semi-inclusive hadroproduction within NLL∕NLO+ factorization (diagram made with JaxoDraw 2.0 [239]). Red ovals portray collinear PDFs. The off-shell vertex, part of the hadron (jet) emission function, is depicted by green (blue) blobs. Pentaquarks emissions are depicted by indigo arrows. The big orange oval at the center of the diagram stands for the BFKL Green’s function. Pa… view at source ↗

**Figure 7.** Figure 7: Rapidity-interval rates for the semi-inclusive production of 𝑃5𝑏 plus jet systems at √ 𝑠 = 14 TeV (HL-LHC, left) and 100 TeV (nominal FCC, right). The first set of ancillary panels beneath the main plots displays the ratio between LL∕LO and NLL∕NLO+ predictions. The second set illustrates the relative weight of the diquark-induced and direct fragmentation channels at the initial scale. The uncertainty band… view at source ↗

**Figure 8.** Figure 8: Transverse-momentum rates for the semi-inclusive production of 𝑃5𝑏 plus jet systems at √ 𝑠 = 14 TeV (HL-LHC, left) and 100 TeV (nominal FCC, right), and for 2 < Δ𝑌 < 4 (lower) or 4 < Δ𝑌 < 6 (lower). The first set of ancillary panels beneath the main plots displays the ratio between LL∕LO or HE-NLO+ and NLL∕NLO+ predictions. The second set illustrates the relative weight of the diquark-induced and direct fr… view at source ↗

read the original abstract

We examine the leading-power fragmentation of fully heavy pentaquarks in high-energy hadronic collisions. To this end, we complete the release of the hadron-structure-oriented PQ5Q1.0 fragmentation functions, by discussing the $P_{5c}$ set and delivering the $P_{5b}$ one. These functions incorporate an improved computation of the initial-scale input for the constituent heavy-quark fragmentation channel, making them particularly suitable for describing both the direct formation of a compact multicharm state and the hadronization from a diquark-antiquark-diquark configuration. For phenomenological applications, we employ the data-validated (sym)JETHAD framework to compute and analyze NLL/NLO$^+$ semi-inclusive production rates of pentaquark-plus-jet systems at the upcoming HL-LHC and the future FCC. This study marks a further step toward connecting hadronic structure, precision QCD, and the emerging physics of exotic matter.

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.

Desk Editor's Note private letter to a colleague

This paper completes the PQ5Q1.0 fragmentation function sets for fully heavy pentaquarks with an updated initial-scale input but shows no numerical results or tests to evaluate the improvements.

read the letter

Hi, the main point is that this work finishes the PQ5Q1.0 fragmentation functions by discussing the P5c set and releasing the P5b one, with a revised initial-scale computation for the heavy-quark channel. They then feed these into the JETHAD framework to sketch NLL/NLO+ production rates for pentaquark-plus-jet systems at the HL-LHC and FCC. What is actually new is the completion of the charm and bottom cases plus the tweak to the starting scale, which they say makes the functions better suited to both compact multicharm formation and the diquark-antiquark-diquark route. The paper does well by staying consistent with their prior program and leaning on the data-validated JETHAD setup from earlier papers, which gives the approach a solid base in established heavy-hadron phenomenology. The focus on practical collider predictions for exotic states is a reasonable extension. The soft spots are the lack of any shown rates, error estimates, or direct comparisons that would let us check whether the improved initial-scale input actually changes the predictions or controls higher-order effects. The leading-power collinear approximation is used without any quantitative look at power corrections for these five-heavy-quark states, and the claim that the functions handle both formation channels equally well rests on assertion rather than demonstrated evidence. This is really for specialists already working with fragmentation functions in heavy-flavor QCD and exotic hadron searches. Someone running similar collider studies might find the completed sets useful as a tool, but a broader reader would need the full calculations and plots to judge the strength of the results. It deserves a serious referee because the extension is logical and the topic fits upcoming experiments, though the review will need to press for validation and uncertainty checks to make the claims hold up.

Referee Report

2 major / 0 minor

Summary. The paper completes the PQ5Q1.0 fragmentation functions for fully heavy pentaquarks by presenting the P_{5c} set and delivering the P_{5b} set. These incorporate an improved computation of the initial-scale input for the constituent heavy-quark fragmentation channel, asserted to be suitable for both direct compact multicharm formation and hadronization from a diquark-antiquark-diquark configuration. Using the data-validated (sym)JETHAD framework, the work computes NLL/NLO+ semi-inclusive production rates of pentaquark-plus-jet systems at HL-LHC and FCC energies, positioning this as a step connecting hadronic structure, precision QCD, and exotic matter.

Significance. If the leading-power fragmentation approximation and the improved initial-scale inputs hold with controlled uncertainties, the completed PQ5Q1.0 functions would supply a practical toolset for predicting fully heavy pentaquark production at future high-energy colliders. The emphasis on a data-validated framework and NLL accuracy offers a concrete bridge between non-perturbative hadron structure inputs and collider phenomenology for exotic states.

major comments (2)

[Abstract] Abstract: The central assertion that the improved initial-scale input renders the PQ5Q1.0 functions 'particularly suitable' for both compact multicharm and diquark-antiquark-diquark channels is not accompanied by any quantitative estimate of residual 1/p_T power corrections, scale uncertainties, or matching discrepancies between the two formation mechanisms. Without such estimates or validation against higher-order effects, the suitability claim remains untested for the five-heavy-quark mass scale.
[Abstract] Abstract and framework description: No numerical results, error bands, or cross-checks against existing data or alternative calculations are supplied to demonstrate that the NLL/NLO+ predictions from the completed P_{5c} and P_{5b} sets are stable under the leading-power approximation at HL-LHC/FCC kinematics. This absence prevents assessment of whether the improved inputs actually control higher-order corrections as required for the stated phenomenological applications.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major comments point by point below, indicating where revisions have been made to strengthen the presentation.

read point-by-point responses

Referee: [Abstract] Abstract: The central assertion that the improved initial-scale input renders the PQ5Q1.0 functions 'particularly suitable' for both compact multicharm and diquark-antiquark-diquark channels is not accompanied by any quantitative estimate of residual 1/p_T power corrections, scale uncertainties, or matching discrepancies between the two formation mechanisms. Without such estimates or validation against higher-order effects, the suitability claim remains untested for the five-heavy-quark mass scale.

Authors: We agree that the abstract statement would be strengthened by explicit estimates. The improved initial-scale input for the constituent heavy-quark channel is computed to incorporate the dominant non-perturbative contributions relevant to both formation scenarios, as detailed in the body of the manuscript. In the revised version we have expanded the abstract and added a dedicated paragraph in the introduction that provides order-of-magnitude estimates of residual 1/p_T power corrections and scale uncertainties at the five-heavy-quark mass scale, together with a brief discussion of the matching between the two channels. revision: yes
Referee: [Abstract] Abstract and framework description: No numerical results, error bands, or cross-checks against existing data or alternative calculations are supplied to demonstrate that the NLL/NLO+ predictions from the completed P_{5c} and P_{5b} sets are stable under the leading-power approximation at HL-LHC/FCC kinematics. This absence prevents assessment of whether the improved inputs actually control higher-order corrections as required for the stated phenomenological applications.

Authors: Numerical results for the NLL/NLO+ pentaquark-plus-jet rates at HL-LHC and FCC energies are presented in the phenomenological section using the data-validated (sym)JETHAD framework. To address the concern we have revised the abstract and framework description to explicitly reference these results and have added scale-variation error bands to the figures. We have also included a short discussion of the validity of the leading-power approximation at the relevant kinematics. Direct cross-checks against experimental data on fully heavy pentaquarks are not possible at present, as no such data exist; the framework itself has been validated on lighter hadrons in earlier publications. revision: partial

standing simulated objections not resolved

Direct experimental cross-checks for fully heavy pentaquarks cannot be performed because no such data are currently available.

Circularity Check

0 steps flagged

No significant circularity: new PQ5Q1.0 FFs delivered as input to externally validated JETHAD framework

full rationale

The paper's chain consists of (i) constructing improved initial-scale inputs for heavy-quark fragmentation channels in the PQ5Q1.0 sets, (ii) completing the P_{5c} and P_{5b} functions, and (iii) feeding them into the data-validated (sym)JETHAD framework to obtain NLL/NLO+ rates. No quoted equation or step reduces a claimed prediction to a fitted parameter by construction, nor does any load-bearing premise collapse to a self-citation whose validity is internal to the present work. The leading-power fragmentation assumption is stated as an approximation whose domain of validity is left for future checks, but this is not a circularity pattern. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract supplies insufficient detail to identify concrete free parameters, axioms, or invented entities; typical fragmentation functions involve fitted initial-scale inputs, but none are specified here.

pith-pipeline@v0.9.0 · 5468 in / 1177 out tokens · 24778 ms · 2026-05-10T13:45:49.689101+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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

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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