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arxiv: 2606.30959 · v1 · pith:ZVYVK46Cnew · submitted 2026-06-29 · ✦ hep-ph

A multi-differential constraint map for quarkonium suppression mechanisms in high-multiplicity pp and pPb collisions

Renato Campanini This is my paper

Pith reviewed 2026-07-01 01:04 UTC · model grok-4.3

classification ✦ hep-ph
keywords quarkonium suppressionhigh-multiplicity collisionspp and pPb collisionsdifferential constraintsmultiplicity dependenceUpsilon statestopology-sensitive suppressionpre-hadronic environment
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The pith

Six differential constraints disfavour local track density and total multiplicity as sole controllers of quarkonium suppression in high-multiplicity pp and pPb collisions.

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

The paper examines how the suppression of excited upsilon states depends on event multiplicity in proton-proton and proton-lead collisions using existing LHC data. It applies six different ways of slicing the data—such as isolating particles in cones or checking azimuthal sectors—to test possible suppression mechanisms. These slices together point away from explanations based only on how many tracks are nearby or the overall number of particles produced. Instead they support a picture where suppression is set early and responds to the global shape of the collision. This matters because it narrows the range of models that could explain quarkonium behavior in dense but small collision systems and links the onset scale to a known change in soft-particle production.

Core claim

Taken together, the six complementary differential constraints disfavour mechanisms controlled solely by local track density or by total multiplicity, and are consistent with an early, globally correlated, topology-sensitive suppression pattern. The characteristic multiplicity scale at which suppression sets in is independently consistent with the onset of a qualitative change in soft-sector behaviour identified from inclusive charged-particle observables. The result is a data-driven constraint map consistent with an early, coloured pre-hadronic environment, possibly involving a deconfined stage.

What carries the argument

The multi-differential constraint map constructed from the six observables (cone isolation, azimuthal-sector equivalence, transverse sphericity, transverse-momentum ordering, forward-ET long-range correlation, and pPb/Pbp forward-backward asymmetry).

If this is right

  • Suppression is not explained by mechanisms that depend only on local track density.
  • Suppression is not explained by mechanisms that depend only on total multiplicity.
  • The pattern is consistent with an early, globally correlated suppression that is sensitive to event topology.
  • The multiplicity scale where suppression begins matches an earlier observed shift in soft-particle production.
  • The data support the possibility of an early coloured pre-hadronic environment that may include a deconfined stage.

Where Pith is reading between the lines

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

  • If the constraints hold, models of quarkonium suppression in small systems must incorporate global event topology at early times rather than purely local or integrated quantities.
  • The link to soft-sector changes suggests that the same underlying dynamics may affect both heavy and light particle production.
  • Further tests could involve applying the same differential slices to other quarkonium states or collision systems to check consistency.
  • The constraint map provides a benchmark that any microscopic model must satisfy before being considered viable.

Load-bearing premise

The six listed differential constraints are independent of each other and together sufficient to rule out local-density and total-multiplicity mechanisms without needing explicit model simulations to check for hidden degeneracies.

What would settle it

An explicit model calculation demonstrating that a local track density mechanism can simultaneously reproduce all six differential constraints in the observed data patterns.

Figures

Figures reproduced from arXiv: 2606.30959 by Renato Campanini.

Figure 1
Figure 1. Figure 1: CMS pp data at √ s = 7 TeV: R21 and R31 as functions of Ntrack in inclusive and high-pT selections. The figure is reproduced from the public CMS/HEPData-based plot used for the present analysis. Both ratios decrease with multiplicity, with a stronger relative decrease for the more weakly bound Υ(3S) state. The transverse-momentum dependence provides an additional constraint. At fixed Ntrack, higher-pT quar… view at source ↗
Figure 2
Figure 2. Figure 2: CMS pT -sliced multiplicity dependence of R21 and R31 in pp collisions at √ s = 7 TeV. The suppression is strongest in low-pT slices and weakens at high pT , consistent with a finite-size escape effect. The mean transverse momentum of the surviving Υ population carries the same information in a complementary form. At high multiplicity, the surviving-state mean-pT hierarchy ⟨pT ⟩Υ(3S) > ⟨pT ⟩Υ(2S) > ⟨pT ⟩Υ(… view at source ↗
Figure 3
Figure 3. Figure 3: Mean transverse momentum of the three Υ states as a function of Ntrack in CMS pp data. The high-multiplicity hierarchy of the surviving population is consistent with preferential depletion of low-pT excited states. The multiplicity trend and the transverse-momentum ordering are not by themselves sufficient to discriminate among suppression scenarios. The discriminating information comes from the geometry, … view at source ↗
Figure 4
Figure 4. Figure 4: Cone-isolation test in CMS pp data at √ s = 7 TeV. Empty-cone and dense-cone selec￾tions give statistically compatible R21 and R31 values. This places direct pressure on mechanisms in which the suppression probability scales with the local density of hadrons around the quarko￾nium. The conclusion is not that every conceivable comover-type construction is excluded. Rather, the local-density interpretation o… view at source ↗
Figure 5
Figure 5. Figure 5: CMS azimuthal-sector test. The suppression trends obtained using forward, transverse and backward sector multiplicities are mutually compatible within uncertainties. The transverse sector, located around 90◦ relative to the Υ direction, is especially constraining because it is neither co-moving with nor recoiling against the quarkonium. The transverse sector is particularly informative. Tracks at roughly 9… view at source ↗
Figure 6
Figure 6. Figure 6: CMS sphericity test. Jet-like and isotropic events with comparable Ntrack show different suppression patterns. This demonstrates that the suppression is not a function of Ntrack alone and that event topology contains independent physical information. The observed topology dependence is the key discriminator. As reported by CMS [18], in jet-like events (ST < 0.55) the ratios are approximately independent of… view at source ↗
Figure 7
Figure 7. Figure 7: Normalised prompt (left panels) and non-prompt (right panels) ψ(2S)/J/ψ production ratio as a function of charged-particle multiplicity Ntrack/⟨Ntrack⟩MB in pp collisions at √ s = 13 TeV, shown in five pT intervals. Data extracted from LHCb HEPData [19]. The non-prompt ratio is consistent with a constant (dashed line) in every pT bin. The prompt ratio shows a suppression that weakens with increasing pT , c… view at source ↗
read the original abstract

The multiplicity-dependent suppression of $\Upsilon(nS)$ excited states in high-multiplicity $pp$ and $p$Pb collisions is analysed using publicly available CMS and LHCb data; preliminary CMS Physics Analysis Summary results in $p$Pb and light-ion collisions are used only as supporting cross-system evidence. Six complementary differential constraints are considered: cone isolation, azimuthal-sector equivalence, transverse sphericity, transverse-momentum ordering, forward-$E_T$ long-range correlation, and the pPb/Pbp forward-backward asymmetry. Taken together, these constraints disfavour mechanisms controlled solely by local track density or by total multiplicity, and are consistent with an early, globally correlated, topology-sensitive suppression pattern. The characteristic multiplicity scale at which suppression sets in is independently consistent with the onset of a qualitative change in soft-sector behaviour identified by Campanini and Ferri \cite{CampaniniFerri2011} from inclusive charged-particle observables. The result is a data-driven constraint map consistent with an early, coloured pre-hadronic environment, possibly involving a deconfined stage.

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 / 1 minor

Summary. The manuscript analyzes multiplicity-dependent suppression of Υ(nS) excited states in high-multiplicity pp and pPb collisions using publicly available CMS and LHCb data (with preliminary CMS results as supporting evidence). It defines six differential constraints—cone isolation, azimuthal-sector equivalence, transverse sphericity, transverse-momentum ordering, forward-ET long-range correlation, and pPb/Pbp forward-backward asymmetry—and interprets their combined pattern as disfavouring mechanisms controlled solely by local track density or total multiplicity. The constraints are instead taken to support an early, globally correlated, topology-sensitive suppression pattern. The multiplicity scale at onset is stated to be independently consistent with a qualitative change in soft-sector behaviour identified in Campanini and Ferri (2011). The result is presented as a data-driven constraint map consistent with an early coloured pre-hadronic environment.

Significance. If the central claim holds after quantitative validation, the work supplies a parameter-free, data-driven framework for constraining quarkonium suppression mechanisms in small systems by combining multiple differential observables. The approach leverages public data and avoids ad-hoc model tuning, offering a reproducible way to distinguish local-density from global, topology-sensitive effects. This could inform interpretations of possible deconfined stages in high-multiplicity collisions. The multi-differential strategy itself is a methodological strength that merits further development.

major comments (3)
  1. [Abstract] Abstract: the claim that the six constraints 'taken together' disfavour mechanisms controlled solely by local track density or total multiplicity rests on an interpretive summary; no quantitative demonstration (e.g., joint likelihood, degeneracy checks, or explicit comparison to tuned local-density models) is supplied showing that such models cannot reproduce all six patterns simultaneously. This is load-bearing for the central exclusion result.
  2. [Abstract] Abstract / multiplicity-scale paragraph: the characteristic multiplicity scale is described as independently consistent with the onset identified in Campanini and Ferri (2011), yet the current differential constraints are not shown to provide an independent test beyond the inclusive charged-particle observables of that earlier work; the independence of the consistency therefore requires explicit justification.
  3. [Abstract] Abstract: the central conclusion is presented without accompanying quantitative results, error bars, statistical significance measures, or explicit data-selection criteria, leaving the exclusion of local-density and total-multiplicity mechanisms resting on qualitative pattern interpretation rather than falsifiable metrics.
minor comments (1)
  1. The six constraints are listed without a dedicated table or figure summarizing their individual and joint implications; adding such a summary would improve clarity of the constraint map.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive report and the recognition of the multi-differential strategy as a methodological strength. We address each major comment below with the strongest honest defense of the manuscript while acknowledging where clarifications or additions are warranted. The core result remains the joint pattern of six independent constraints derived from public data.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the six constraints 'taken together' disfavour mechanisms controlled solely by local track density or total multiplicity rests on an interpretive summary; no quantitative demonstration (e.g., joint likelihood, degeneracy checks, or explicit comparison to tuned local-density models) is supplied showing that such models cannot reproduce all six patterns simultaneously. This is load-bearing for the central exclusion result.

    Authors: The exclusion rests on the logical incompatibility of a purely local-density or total-multiplicity mechanism with the full set of six constraints simultaneously: cone isolation and pT-ordering disfavour locality, while azimuthal equivalence, sphericity, forward-ET correlations and pPb asymmetry disfavour global multiplicity scaling without topology dependence. Because the constraints are constructed from orthogonal observables, a local model would require coordinated fine-tuning across all six to mimic the data pattern. We agree that an explicit discussion of possible degeneracies would strengthen the presentation and will add a dedicated paragraph in the revised manuscript. revision: partial

  2. Referee: [Abstract] Abstract / multiplicity-scale paragraph: the characteristic multiplicity scale is described as independently consistent with the onset identified in Campanini and Ferri (2011), yet the current differential constraints are not shown to provide an independent test beyond the inclusive charged-particle observables of that earlier work; the independence of the consistency therefore requires explicit justification.

    Authors: The multiplicity variable is the same, but the test is independent because the new constraints involve topology (sphericity, azimuthal sectors), long-range correlations (forward-ET), and system asymmetry (pPb/Pbp) that are absent from the inclusive charged-particle analysis of Campanini and Ferri. These observables probe whether the suppression onset coincides with a change in event structure rather than merely with multiplicity. We will revise the abstract and the relevant paragraph to state this distinction explicitly. revision: yes

  3. Referee: [Abstract] Abstract: the central conclusion is presented without accompanying quantitative results, error bars, statistical significance measures, or explicit data-selection criteria, leaving the exclusion of local-density and total-multiplicity mechanisms resting on qualitative pattern interpretation rather than falsifiable metrics.

    Authors: The data-selection criteria follow the published CMS and LHCb analyses (explicitly referenced); the patterns are taken directly from the public distributions. The result is falsifiable because any future measurement violating one or more of the six constraints would invalidate the map. While we do not perform new statistical fits (covariance matrices are not public), the multi-differential consistency itself supplies the metric. We will add a short table in the methods section summarising the data sources and selection criteria. revision: partial

Circularity Check

0 steps flagged

No significant circularity; main claim is data-driven from external observables

full rationale

The paper constructs its multi-differential constraint map directly from six listed observables (cone isolation, azimuthal-sector equivalence, transverse sphericity, pT ordering, forward-ET correlation, pPb/Pbp asymmetry) applied to publicly available CMS and LHCb Υ(nS) data. The disfavouring of local-density or total-multiplicity mechanisms is asserted from the observed patterns in these data. The single self-citation to CampaniniFerri2011 is invoked only for external consistency of the multiplicity scale and is not required for the derivation of the constraint map itself. No equations, fitted parameters, or self-referential definitions reduce the central result to its inputs by construction. The argument remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields limited visibility into free parameters or axioms; the analysis implicitly assumes standard heavy-quarkonium production and suppression frameworks without introducing new fitted constants or postulated entities beyond the interpretive suggestion of a possible deconfined stage.

axioms (1)
  • standard math Standard assumptions of perturbative QCD and heavy-quarkonium production models hold for the interpretation of Υ suppression.
    Invoked implicitly when mapping differential constraints onto suppression mechanisms.

pith-pipeline@v0.9.1-grok · 5717 in / 1417 out tokens · 53229 ms · 2026-07-01T01:04:45.380210+00:00 · methodology

discussion (0)

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