Quarkonium Suppression Map Points to Early Coloured Medium in Small Collisions

Quarkonium states — bound pairs of a heavy quark and its antiquark — have long served as the most trusted thermometers of the hottest matter humans can create. Ever since Matsui and Satz proposed in 1986 that the melting of charmonium in a deconfined quark-gluon plasma would signal a new state of matter, the sequential disappearance of these fragile bound states has been the canonical fingerprint of colour screening in heavy-ion collisions. But a striking puzzle has emerged at the Large Hadron Collider: the same hierarchy of suppression appears in proton-proton collisions, systems far too small to host a conventional plasma. A new theoretical analysis, published in The European Physical Journal C by Renato Campanini of the University of Bologna and INFN Bologna, now subjects this puzzle to an unusually rigorous test, assembling six independent differential measurements into a single constraint map that any candidate mechanism must satisfy simultaneously.

The analysis is deliberately not a new measurement and not a new model. It is a model-discriminating exercise built entirely from publicly available CMS and LHCb data, with preliminary CMS results in proton-lead and light-ion collisions used only as supporting cross-system evidence. The central question is sharply defined: can the multiplicity-dependent suppression of excited bottomonium and charmonium states in small systems be generated entirely by hadronic final-state interactions, or does the differential structure of the data demand early-time, non-local dynamics? The answer that emerges is that the simplest explanations — local particle density or total multiplicity alone — struggle to survive the combined weight of the evidence.

The starting point is the CMS measurement of event-activity-dependent upsilon production ratios in proton-proton collisions at 7 TeV. CMS observed that the ratios of excited to ground-state yields, R21 and R31, decrease monotonically with the charged-track multiplicity, and that the decrease is stronger for the more weakly bound upsilon(3S) than for the upsilon(2S), exactly as expected for a sequential suppression ordered by binding energy. LHCb independently confirmed the same pattern for bottomonium at 13 TeV and for the charmonium psi(2S)-to-J/psi ratio, using a different detector, a different energy and a different rapidity coverage. The effect is therefore not an experimental artefact of a single apparatus. Crucially, the suppression also weakens as the transverse momentum of the quarkonium increases, consistent with a fast-moving state crossing a finite-sized active region in a shorter time.

The discriminating power of the new analysis comes from how CMS sliced the same dataset along several geometric and topological axes. The first test is cone isolation: events were classified by the number of charged tracks inside a narrow cone of half-opening angle 0.5 radians around the upsilon flight direction. For a local hadronic dissociation mechanism, the expectation is unambiguous — more nearby hadrons should mean more dissociation. The data show no such separation. The multiplicity-dependent suppression trends for empty-cone and dense-cone events are statistically compatible across the measured range, placing direct pressure on any mechanism in which the suppression probability scales with the local density of particles surrounding the quarkonium.

The second test closes a possible escape route. If local density is not the controlling variable, perhaps a diffuse directional mechanism is at work. CMS therefore measured the suppression as a function of the multiplicity in three azimuthal sectors relative to the upsilon direction: forward, transverse and backward. The transverse sector is especially informative, because particles emitted at roughly ninety degrees to the quarkonium can be neither co-moving comovers nor recoil partners. Yet all three sectors yield mutually compatible suppression trends. Direction-based and near-side explanations are disfavoured in their simplest forms; the sector multiplicity behaves as a proxy for global event activity rather than for any local, directional density.

The third and arguably most consequential test is transverse sphericity, an event-shape variable that distinguishes jet-like, two-pronged events from isotropic ones. At fixed track multiplicity, jet-like events with sphericity below 0.55 show a multiplicity dependence of the suppression ratios that is largely absent, while isotropic events above 0.85 show a clear decrease. A mechanism depending only on total multiplicity would produce identical behaviour in both subsamples, which the data do not support. Even more strikingly, inclusively the three upsilon states are accompanied by different mean track multiplicities — 33.9, 33.0 and 32.0 tracks respectively — but within the jet-like class alone this difference vanishes entirely, with all three states accompanied by exactly 22.4 tracks. The multiplicity-state correlation is thus a topology effect, not an intrinsic property of each state. Together, the cone and sphericity results form what the author calls a scissors constraint: local-density pictures are cut by the cone test, pure-multiplicity pictures by the sphericity test, and the two cuts are orthogonal.

Proton-lead data extend the map into denser territory and add a powerful non-locality argument. CMS measurements at 5.02 TeV and, with higher statistics, at 8.16 TeV show that the upsilon suppression correlates with the forward transverse energy measured several units of pseudorapidity away from the quarkonium — a long-range correlation that local comover density at the quarkonium rapidity cannot generate. Meanwhile, LHCb’s comparison of the psi(2S)-to-J/psi ratio in proton-going versus lead-going configurations delivers a qualitative stress test: the ratio decreases with multiplicity in the proton-going direction but is suppressed yet approximately flat in the denser lead-going direction, a pattern LHCb itself concludes cannot be fully explained by comovers alone and suggests an additional mechanism, possibly linked to quark-gluon-plasma-like effects. Preliminary CMS results in oxygen-oxygen and neon-neon collisions further show that the single-ratio suppression trend follows a smooth common curve as a function of event activity across pp, pPb and light-ion systems.

What kind of mechanism survives all six constraints? The timing argument is kinematic and hard to evade. The bottom-antibottom pair requires roughly 0.1 to 0.5 femtoseconds — expressed in natural units, 0.1 to 0.5 fm of formation time — to evolve into a physical bound state, while light hadrons take about 1 fm to form. The suppression must therefore act before either the quarkonium or its hadronic surroundings exist, in a pre-hadronic coloured environment. Order-of-magnitude Bjorken energy-density estimates for high-multiplicity proton-proton collisions at LHC energies yield values of order 1 to 10 GeV per cubic femtometre, comparable to or above the QCD crossover density of roughly 0.5 GeV per cubic femtometre from lattice calculations, making a partonic interpretation physically plausible — though the author is careful to note that pre-hadronic does not mean partonic, and that string-based and colour-glass frameworks also operate in this window and are not excluded by timing alone.

Intriguingly, the multiplicity window in which the suppression sets in overlaps with the window in which an entirely independent analysis by Campanini and Ferri, based purely on soft-sector observables, identified a qualitative change in collective behaviour — an experimental equation-of-state proxy built from the interplay between charged-particle density and mean transverse momentum. The same multiplicity range has since been associated with strangeness enhancement, long-range ridge correlations and partonic flow signatures reported by ALICE and CMS. The author stresses that this convergence is a cross-check, not a proof: no individual observable constitutes evidence for deconfinement in isolation, and the analysis explicitly refrains from claiming that the sphericity dependence is fully independent of transverse-momentum composition, since a definitive separation would require a triple-differential measurement that does not yet exist.

The value of the work lies in the benchmark it establishes. To the author’s knowledge, no published suppression framework — not the comover interaction model in either its hadronic or partonic form, not open-quantum-system approaches based on pNRQCD, not QGP-droplet models, not the hydrodynamic SHINCHON framework — has been tested against the full six-constraint set simultaneously. The paper lays out falsifiable follow-ups: cone and sphericity calculations within the comover framework, a binding-energy-ordered elliptic-flow hierarchy in non-central proton-lead collisions, topology-resolved charmonium measurements at LHCb, and above all the triple-differential CMS measurement that would cleanly separate topology from kinematics. Whatever the ultimate microscopic answer proves to be, the data now make a conventional local-density, multiplicity-only, or purely late-hadronic interpretation very difficult to maintain — and point, with unusual coherence, toward an early, globally correlated, geometry-sensitive coloured medium in the smallest collision systems humanity has ever produced.

Subject of Research: Quarkonium suppression mechanisms in high-multiplicity proton-proton and proton-lead collisions at the LHC

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

Article References: Campanini, R. (2026). A multi-differential constraint map for quarkonium suppression mechanisms in high-multiplicity pp and pPb collisions. The European Physical Journal C, 86(9), Article 1052. https://doi.org/10.1140/epjc/s10052-026-16267-x

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16267-x

Keywords: quarkonium, bottomonium, charmonium, quark-gluon plasma, CMS, LHCb, proton-proton collisions, proton-lead collisions, comover interaction model, sphericity, cone isolation, colour deconfinement