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arxiv: 2605.01762 · v1 · submitted 2026-05-03 · ✦ hep-ph

Recognition: unknown

Transverse momentum dependence of Ω/φ ratio in high energy collisions

Hai-hong Li , Jun Song , Feng-Lan Shao
Authors on Pith no claims yet

Pith reviewed 2026-05-09 17:11 UTC · model grok-4.3

classification ✦ hep-ph
keywords Omega/phi ratiotransverse momentum dependencestrange quark pT spectrumquark combination modelLHC collisionscollective flowhadronization curvaturemultiplicity dependence
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0 comments X

The pith

The p_T dependence of the Ω/φ ratio is dominated by the discrete curvature of the strange quark transverse momentum spectrum just before hadronization.

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

The paper applies a constituent quark equal-velocity combination model to the Ω/φ ratio measured in pp, p-Pb and Pb-Pb collisions at LHC energies. It shows that the relative change of this ratio with transverse momentum is controlled by a discrete curvature feature in the p_T spectrum of strange quarks immediately prior to hadronization. The authors recover those strange-quark spectra by applying quark-number scaling to existing φ-meson data, then demonstrate that the extracted curvature accounts for the observed ratio behavior in both high- and low-multiplicity events. The work links the final-state ratio directly to partonic-stage dynamics, in particular the collective flow that develops before hadronization.

Core claim

In the constituent quark equal-velocity combination model, the relative change rate of the Ω/φ ratio is dominated by a discrete curvature property of the p_T spectrum of strange quarks just before hadronization. Using experimental data of φ mesons after a quark-number scaling operation, the p_T spectra of strange quarks are extracted in high- and low-multiplicity events across pp collisions at 7 and 13 TeV, p-Pb collisions at 5.02 TeV, and Pb-Pb collisions at 2.76 TeV. These curvature properties are shown to explain the measured p_T dependence of the Ω/φ ratio, with the change in curvature attributed to strong collective flow formed in the partonic stage.

What carries the argument

The discrete curvature property of the p_T spectrum of strange quarks just before hadronization, extracted via quark-number scaling within the constituent quark equal-velocity combination model.

If this is right

  • The p_T shape of the Ω/φ ratio is fixed once the curvature of the strange-quark spectrum is known.
  • Differences in curvature between high- and low-multiplicity events trace the build-up of collective flow in the partonic phase.
  • The same curvature-driven mechanism operates uniformly from pp through p-Pb to Pb-Pb collisions at LHC energies.
  • Quark-number scaling on φ data supplies a practical route to the pre-hadronization strange-quark spectrum.

Where Pith is reading between the lines

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

  • The same curvature analysis could be applied to other multi-strange ratios such as Ξ/φ to test whether the mechanism is universal.
  • If curvature dominates, the p_T dependence of these ratios would be largely insensitive to hadronic rescattering, offering a cleaner window on the partonic stage.
  • Repeating the extraction at lower beam energies would map how the curvature evolves with the strength of collective flow.
  • The discrete character of the curvature may reflect specific features of the parton momentum distribution or the radial flow velocity profile.

Load-bearing premise

The quark-number scaling operation applied to φ-meson data accurately recovers the true p_T spectrum of strange quarks just before hadronization without significant distortion from later hadronic rescattering.

What would settle it

A precision measurement of the Ω/φ ratio versus p_T in a new multiplicity or collision system that deviates from the shape predicted solely by the curvature extracted from the corresponding φ data after quark-number scaling.

Figures

Figures reproduced from arXiv: 2605.01762 by Feng-Lan Shao, Hai-hong Li, Jun Song.

Figure 1
Figure 1. Figure 1: (a) pT spectra of Ω and φ in pp collisions at √ s = 13 TeV and in Pb-Pb collisions at √ sNN =2.76 TeV and (b) the Ω/φ ratio in the two collision systems. Data are taken from [38–41]. An interesting question is what the underlying dynam￾ics is responsible for such significant change of Ω/φ ratio from pp collisions to central Pb-Pb collisions at LHC en￾ergies. In previous studies of p/π ratio and Λ/K0 s rati… view at source ↗
Figure 2
Figure 2. Figure 2: The quark number scaling test for pT spectra of Ω and φ in pp collisions at √ s = 13 TeV. Data are taken from [13, 38–41]. In this paper, we apply a constituent quark equal￾velocity combination mechanism to study the production of Ω and φ in high energy pp, p-Pb and Pb-Pb collisions. We explain the underlying dynamics that influences the pT dependence of Ω/φ ratio by particularly focusing on the shape prop… view at source ↗
Figure 3
Figure 3. Figure 3: (a) The scaled pT spectra of φ in high-multiplicity (class II) pp collisions at √ s = 13 TeV and in central Pb-Pb collisions at √ sNN = 2.76 TeV. Lines are fittings of Levy-Tsallis function; (b) the curvature [ln Fs(pT /3)]′ − [ln Fs(pT /2)] ′ of pT spectra of strange quarks. In view at source ↗
Figure 4
Figure 4. Figure 4: (a) pT spectra of Ω and φ in pp collisions at √ s = 13 TeV and in Pb-Pb collisions at √ sNN =2.76 TeV and (b) the Ω/φ ratio in the two collision systems. Symbols are experi￾mental data [38–41] and lines are results of EVC model. due to λs, the production of Ω in low multiplicity events will suffer more suppression because of the need of three strange quarks for a Ω formation. The average number of strange … view at source ↗
Figure 5
Figure 5. Figure 5: (a-d) the scaled pT spectra of Ω and φ in pp, pPb and Pb-Pb collisions at LHC energies as a way to obtain pT distribution of strange quarks before hadronization;(e-h) the discrete curvature of pT distributions of strange quarks; (i-l) Ω/φ ratios as the function of pT . Symbols in panels (a-d) are experimental data [13, 38–41, 52–54] and lines are model results. 0 0.5 1 1.5 2 2.5 3 −1 10 1 v=0 , c=0.3 v=0.6… view at source ↗
Figure 6
Figure 6. Figure 6: (a)The normalized pT spectrum of strange quarks under different parameter values;(b) the curvature of the spectrum; (c) the schematic behavior of Ω/φ ratio with the setting of the same magnitude at low pT . ferent parameter groups are shown in view at source ↗
read the original abstract

We apply a constituent quark equal-velocity combination model to study the $p_{T}$ dependence of $\Omega/\phi$ ratio in $pp$, $p$-Pb and Pb-Pb collisions at LHC energies. We demonstrate that the relative change rate of the $\Omega/\phi$ ratio is dominated by a discrete curvature property of $p_{T}$ spectrum of strange quarks just before hadronization. Using experimental data of $\phi$ mesons after a quark number scaling operation, we extract $p_{T}$ spectrum of strange quarks just before hadronization and study its curvature property in high and low multiplicity events in $pp$ collisions at $\sqrt{s}=$ 7, 13 TeV, $p$-Pb collisions at $\sqrt{s_{NN}}$= 5.02 TeV and Pb-Pb collisions at $\sqrt{s_{NN}}$= 2.76 TeV. We apply these curvature properties of $p_{T}$ spectra of strange quarks to explain the observed $p_{T}$ dependence of $\Omega/\phi$ ratio in those collisions. We discuss the possible origin of the change of curvature property for $p_{T}$ spectra of strange quarks just before hadronization by considering the influence of strong collective flow formed in partonic stage evolution in collisions at LHC energies.

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

3 major / 2 minor

Summary. The manuscript applies a constituent quark equal-velocity combination model to study the p_T dependence of the Ω/φ ratio in pp, p-Pb, and Pb-Pb collisions at LHC energies. It extracts the p_T spectrum of strange quarks just before hadronization from measured φ meson spectra via quark-number scaling, identifies a discrete curvature property in this spectrum for high- and low-multiplicity events, and claims that this curvature dominates the relative change rate of the Ω/φ ratio. The extracted curvature properties are then used to explain the observed p_T dependence of the ratio across collision systems, with changes in curvature attributed to strong collective flow in the partonic stage.

Significance. If the central claim holds after addressing the extraction assumptions, the work would link the p_T dependence of baryon-to-meson ratios directly to a measurable property of pre-hadronization strange-quark spectra, providing a concrete handle on hadronization dynamics in high-energy collisions. It would also highlight how partonic collective flow imprints on final-state ratios, offering falsifiable predictions for future multiplicity-dependent measurements at the LHC.

major comments (3)
  1. [Abstract and extraction procedure] Abstract and the extraction procedure (prior to the ratio modeling): the claim that curvature 'dominates' the relative change rate of the Ω/φ ratio is asserted without a quantitative derivation, error propagation, or sensitivity analysis showing the fractional contribution of curvature versus other model ingredients; the central claim therefore rests on an unshown step whose robustness cannot be assessed.
  2. [Application to Ω/φ ratio] The section applying the extracted curvature to the Ω/φ ratio: the quark-number scaling used to recover the strange-quark spectrum from φ data is the same operation later invoked to predict the ratio, creating a circularity risk; no independent benchmark (e.g., comparison to direct strange-quark observables or variation under alternative scaling assumptions) is provided to demonstrate that the inferred curvature is not an artifact of the input spectra.
  3. [Discussion of curvature origin] Discussion of collective-flow origin: the manuscript attributes curvature changes to partonic flow but supplies no quantitative model or hydrodynamic simulation demonstrating how flow strength alters the strange-quark spectrum curvature in a manner that reproduces the observed ratio p_T dependence; this leaves the proposed mechanism as a qualitative interpretation rather than a tested explanation.
minor comments (2)
  1. [Model section] Notation for the equal-velocity combination rule and the definition of 'discrete curvature' should be introduced with an explicit equation early in the model section to avoid ambiguity when the same symbols are reused for the ratio.
  2. [Figures] Figure captions for the extracted strange-quark spectra and the resulting Ω/φ ratios should explicitly state the multiplicity classes and collision energies to improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We respond point-by-point to the major concerns, clarifying the manuscript's approach and indicating where revisions will strengthen the presentation and robustness of the claims.

read point-by-point responses

  1. Referee: [Abstract and extraction procedure] Abstract and the extraction procedure (prior to the ratio modeling): the claim that curvature 'dominates' the relative change rate of the Ω/φ ratio is asserted without a quantitative derivation, error propagation, or sensitivity analysis showing the fractional contribution of curvature versus other model ingredients; the central claim therefore rests on an unshown step whose robustness cannot be assessed.

    Authors: We agree that the dominance statement requires explicit support. In the revised manuscript we will derive the relative change rate of the Ω/φ ratio directly from the equal-velocity combination formula, isolating the contribution of the discrete curvature term in the strange-quark spectrum. A sensitivity study will vary the input φ spectra within experimental uncertainties, propagate errors, and quantify the fractional role of curvature relative to other model parameters. revision: yes

  2. Referee: [Application to Ω/φ ratio] The section applying the extracted curvature to the Ω/φ ratio: the quark-number scaling used to recover the strange-quark spectrum from φ data is the same operation later invoked to predict the ratio, creating a circularity risk; no independent benchmark (e.g., comparison to direct strange-quark observables or variation under alternative scaling assumptions) is provided to demonstrate that the inferred curvature is not an artifact of the input spectra.

    Authors: The extraction step obtains the strange-quark p_T distribution from measured φ spectra; this distribution then serves as input to the combination model that predicts the Ω yield and thus the ratio. The operations are therefore sequential rather than circular. To demonstrate that the curvature feature is robust, the revision will add comparisons of the extracted strange-quark spectrum against spectra inferred from multi-strange baryon data under the same scaling and will test stability under alternative assumptions such as transverse kinetic-energy scaling. revision: yes

  3. Referee: [Discussion of curvature origin] Discussion of collective-flow origin: the manuscript attributes curvature changes to partonic flow but supplies no quantitative model or hydrodynamic simulation demonstrating how flow strength alters the strange-quark spectrum curvature in a manner that reproduces the observed ratio p_T dependence; this leaves the proposed mechanism as a qualitative interpretation rather than a tested explanation.

    Authors: The link to collective flow rests on the observed systematic change of curvature with event multiplicity across systems, where multiplicity serves as a proxy for flow strength. A full hydrodynamic simulation coupled to the hadronization model lies beyond the present scope. The revision will expand the discussion with references to existing hydrodynamic results on partonic spectra and will outline how flow-induced modifications can produce the reported curvature trend, thereby sharpening the interpretive framework and identifying concrete tests for future work. revision: partial

Circularity Check

1 steps flagged

Curvature property of strange-quark p_T spectrum extracted from φ data via scaling is used to explain Ω/φ ratio p_T dependence

specific steps
  1. fitted input called prediction [Abstract]
    "Using experimental data of φ mesons after a quark number scaling operation, we extract p_T spectrum of strange quarks just before hadronization and study its curvature property in high and low multiplicity events in pp collisions at √s= 7, 13 TeV, p-Pb collisions at √s_NN= 5.02 TeV and Pb-Pb collisions at √s_NN= 2.76 TeV. We apply these curvature properties of p_T spectra of strange quarks to explain the observed p_T dependence of Ω/φ ratio in those collisions."

    The curvature property is obtained by applying the model's quark-number scaling to φ data; this property is then cited as the dominant cause of the p_T dependence of the Ω/φ ratio. The explanation therefore re-expresses the φ input through the same scaling and combination rules used to define the spectrum, rather than deriving the ratio's behavior independently.

full rationale

The paper extracts the strange-quark p_T spectrum (and its discrete curvature) directly from measured φ meson spectra by applying quark-number scaling within the constituent quark equal-velocity combination model. It then invokes that same extracted curvature to account for the observed p_T dependence of the Ω/φ ratio. This creates a fitted-input-called-prediction structure: the central claim that curvature dominates the ratio's relative change rate is demonstrated inside the model that defined the spectrum extraction from φ, without an independent external benchmark or falsifiable test that separates the curvature's role from the φ input data. The derivation therefore reduces, in part, to a re-description of the input spectra rather than a first-principles result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the equal-velocity combination rule, the validity of quark-number scaling for φ mesons, and the assumption that curvature is the dominant driver; these are domain assumptions rather than new entities.

axioms (2)
  • domain assumption Constituent quarks combine at equal velocity to form hadrons.
    Invoked in the model application described in the abstract.
  • domain assumption Quark-number scaling applied to φ spectra recovers the strange-quark p_T distribution before hadronization.
    Central extraction step stated in the abstract.

pith-pipeline@v0.9.0 · 5534 in / 1358 out tokens · 27321 ms · 2026-05-09T17:11:44.265977+00:00 · methodology

discussion (0)

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Reference graph

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