Exploring QGP-like phenomena with Charmonia in $p+p$ collisions at $\sqrt{s} = 13$ TeV

Captain R. Singh; Jan-e Alam; Partha Bagchi; Raghunath Sahoo

REVIEW 5 major objections 6 minor 1 cited by

Exploring QGP-like phenomena with Charmonia in $p+p$ collisions at $\sqrt{s} = 13$ TeV

T0 review · 5 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper predicts that combined nonadiabatic evolution and in-medium dissociation/regeneration of charmonia produce a distinctive, multiplicity-dependent yield pattern—up to 50% J/ψ suppression, up to 80% χc(1P) suppression, and…

desk verdict A coherent model calculation that predicts ψ(2S) enhancement in high-multiplicity pp, but the prediction conflicts with the CMS data the authors cite and never compare to, so the 'robust probe' claim is not credible as written. read the letter →

arxiv 2501.00753 v2 pith:M67RKN63 submitted 2025-01-01 hep-ph hep-exnucl-exnucl-th

Captain R. Singh , Partha Bagchi , Raghunath Sahoo , Jan-e Alam This is my paper · ORCID

classification hep-phhep-exnucl-exnucl-th

keywords charmoniumsuppressionquark-gluonplasmasmallcollisionsystemsnonadiabaticevolutionproton-protoncollisionsJ/psipsi(2S)Gubserflow

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the very short, hot fireball formed in high-multiplicity proton-proton collisions at $\sqrt{s}=13$ TeV may be hot enough to form a quark-gluon plasma, and that charmonium states (bound charm-anticharm mesons such as $J/\psi$) can detect it. Because the fireball cools so quickly, the usual adiabatic assumption fails, so the paper solves a time-dependent Schrodinger equation for the evolving charmonium wavefunction while also including collisional damping, gluonic dissociation, and regeneration. Its central prediction is a distinctive, multiplicity- and $p_{\rm T}$-dependent pattern: up to 50% suppression of $J/\psi$, up to 80% suppression of $\chi_c(1P)$, and a 130% to 200% enhancement of $\psi(2S)$ relative to $J/\psi$ at high multiplicity. If observed, this pattern would be evidence that a thermalized QCD medium forms in small collision systems. The calculation combines a pre-equilibrium temperature profile from bottom-up thermalization, a Gubser-type transverse expansion for the thermalized medium, and a transport equation for the charmonium yields.

What carries the argument

The central object is the time-dependent Hamiltonian of a charmonium state, which starts as the zero-temperature Cornell potential and becomes the finite-temperature complex potential once the medium thermalizes. Its real part drives nonadiabatic transitions: solving the time-dependent Schrodinger equation by the Crank-Nicolson finite-difference scheme gives survival probabilities as overlaps of the evolved wavefunction with the initial $J/\psi$, $\chi_c(1P)$, and $\psi(2S)$ states. The imaginary part gives collisional damping, while gluonic dissociation adds a thermal decay width and regeneration is fixed by detailed balance from the dissociation cross section. Temperature evolution is supplied by a pre-equilibrium pseudo-temperature scaling followed by a Gubser-type flow with third-order viscous corrections, and the moving charmonium feels a Doppler-shifted effective temperature. The net yield is governed by the transport equation $dN/d\tau = \Gamma_F N_c N_{\bar c}/V(\tau) - \Gamma_D N$, whose solution is multiplied by the nonadiabatic survival probabilities and feed-down corrections to produce the reported patterns.

What would settle it

Measure the $\psi(2S)/J/\psi$ double ratio as a function of charged-particle multiplicity and $p_{\rm T}$ in 13 TeV proton-proton collisions. The model predicts the ratio rises to 1.3–2.0 at low $p_{\rm T}$ in the highest-multiplicity class; data showing no rise above unity, or a decline, would falsify the central claim. A second check is to recompute the model with the pre-equilibrium parameter $\alpha$ varied over its plausible range; if the enhancement disappears for some allowed value, the predicted signature is not a stable probe.

Watch

Extended reading notes

Core claim

The paper claims that in proton-proton collisions at $\sqrt{s}=13$ TeV, the combined action of nonadiabatic evolution and in-medium dissociation/regeneration produces a calculable, testable modification of charmonium yields. In the highest-multiplicity events, the $J/\psi$ survival probability falls to roughly 50% after feed-down from higher resonances, $\chi_c(1P)$ is suppressed by up to 80%, and $\psi(2S)$ is enhanced by 130% to 200% relative to $J/\psi$ at low $p_{\rm T}$. The authors contend that this pattern is a probe for the existence of a thermalized QCD medium in a small system, because the only medium effects present in $p+p$ are hot-partonic ones and the adiabatic approximation fails when the QGP lifetime is shorter than the charmonium transition timescale.

Load-bearing premise

The predictions depend on the rate at which the pre-equilibrium fireball heats up, which is controlled by a parameter $\alpha$ in the temperature profile that the paper never assigns a numerical value; a different thermalization history could change or remove the nonadiabatic transitions, including the $\psi(2S)$ enhancement.

Editorial extensions

If this is right

At high multiplicity (0–1%) and low $p_{\rm T}$, the $J/\psi$ suppression reaches about 40–50% once feed-down is included, so high-multiplicity $p+p$ data should show a clear multiplicity-dependent suppression.
The $\psi(2S)/J/\psi$ double ratio should rise with multiplicity to 1.3–2.0 at low $p_{\rm T}$, opposite to the $\psi(2S)$ suppression seen in heavy-ion collisions; this is the paper's sharpest signature.
The $\chi_c(1P)/J/\psi$ ratio should fall by 30–70% with increasing multiplicity, a prediction that could be tested once $\chi_c(1P)$ reconstruction in $p+p$ becomes practical.
At $p_{\rm T}\gtrsim 30$ GeV the nonadiabatic contribution dies out and the remaining suppression is mostly collisional damping, so the $p_{\rm T}$ dependence separates the two mechanism classes.
If confirmed, $p+p$ collisions can no longer be treated as a purely baseline system for quarkonia; the baseline itself would carry a QGP-like medium effect.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the pre-equilibrium parameter $\alpha$ is left free, a natural extension is to scan it over its plausible range to map how much of the $\psi(2S)$ enhancement is genuine and how much is an artifact of the chosen thermalization history.
The same nonadiabatic treatment should apply to peripheral and ultraperipheral heavy-ion collisions, where rapid cooling could produce a $\psi(2S)$ enhancement that would complicate the standard sequential-suppression interpretation.
The paper multiplies nonadiabatic survival probabilities with transport-equation survival probabilities, treating the two as independent; a coupled calculation in which the evolving wavefunction and the decay widths feed back on each other could either strengthen or weaken the predicted pattern.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This paper is a serious phenomenological calculation with a headline prediction that I think is already dead on arrival against data the authors themselves cite. They predict a 130–200% enhancement of ψ(2S) relative to J/ψ in high-multiplicity pp at 13 TeV, driven by nonadiabatic evolution. CMS (PRL 120, 142301 (2018)), which they cite as [16], reports that the ψ(2S)-to-J/ψ ratio actually decreases with multiplicity in pp at that same energy. The paper never compares with that measurement. If the CMS result is right, the central claim that these mechanisms are a “robust probe” of a thermalized medium in pp has the wrong sign.

What is new here: the specific combination of pre-equilibrium bottom-up thermalization, Gubser flow, nonadiabatic evolution via the Crank-Nicolson solver, plus the usual collisional damping/gluonic dissociation/regeneration machinery applied to J/ψ, χc, and ψ(2S) in pp. The idea that rapid cooling can cause transitions into ψ(2S) is an interesting mechanism, and the calculation is internally coherent. The authors also include feed-down corrections and give pT- and multiplicity-dependent predictions, which is the right level of detail for a model paper.

The soft spots are real. Eq. (1) contains an unassigned exponent α, so the pre-equilibrium temperature profile is not fully specified and the figures are not reproducible as written. The initial charmonium numbers come from the authors' own earlier fit, so the predictions inherit that calibration. More importantly, the paper's assertion that any yield modification in pp must come from a hot partonic medium glosses over other small-system effects. But the biggest issue is empirical: a model whose defining signature is the opposite of the existing measurement cannot be called a robust probe.

The paper deserves serious peer review, not a desk rejection. The conflict with CMS data is important, and the α dependence should be explored. I would send it to a referee with instructions to check the sign mismatch and the sensitivity to α. If the authors confront the data, either the model changes or we learn something about what the nonadiabatic mechanism cannot do. I would not cite it as established, but I would mention it in a review as a cautionary example.

Yours,

Referee Report

5 major / 6 minor

Summary. The paper proposes a model for charmonium yield modification in high-multiplicity proton-proton collisions at sqrt(s) = 13 TeV, combining a Gubser-flow medium expansion with a bottom-up pre-equilibrium temperature profile, collisional damping, gluonic dissociation, regeneration, and nonadiabatic time-dependent Schroedinger evolution. It claims that the combined effects of these mechanisms can serve as a robust probe of a thermalized QCD medium in small systems, predicting up to about 50% suppression of J/psi, up to about 80% suppression of chi_c(1P), and a 130% to 200% enhancement of psi(2S) relative to J/psi at high multiplicity.

Significance. The topic is timely, and the attempt to include nonadiabatic evolution together with conventional suppression and regeneration mechanisms in a small-system charmonium calculation is a useful exploratory step. The transport equations and complex-potential formalism are standard, and the paper provides explicit expressions for the survival probabilities and feed-down corrections. However, the paper's headline prediction is not compared with existing high-multiplicity pp data, and the pre-equilibrium temperature profile contains an unspecified parameter, so the quantitative conclusions are neither validated nor reproducible as presented. The central claim that the proposed mechanisms constitute a robust probe of a thermalized QCD medium is therefore not currently supported.

major comments (5)

[Section V / Fig. 5] The abstract and Section V claim that the combined mechanisms can serve as a robust probe of a thermalized QCD medium, with Fig. 5 predicting a 130% to 200% enhancement of psi(2S) relative to J/psi at high multiplicity. The paper cites the CMS high-multiplicity pp measurement [16] as evidence of QGP-like phenomena but never compares its predictions with the measured multiplicity dependence of the psi(2S)-to-J/psi ratio reported in that reference. That measurement shows the ratio decreasing with multiplicity, which is the opposite sign of the model's defining signature. As stated, the central conclusion is therefore contradicted by the existing data, and the paper does not address this conflict.
[Sec. II A, Eq. (1)] The pre-equilibrium pseudo-temperature profile in Eq. (1) contains an exponent parameter alpha that is never assigned a numerical value in the text. The nonadiabatic Hamiltonian evolution between tau = 0 and tau_Hydro, and hence the transition probabilities that produce the psi(2S) enhancement, depend directly on this profile. Without a stated value for alpha, the figures are not reproducible and the sensitivity of the predictions to this parameter is unknown. This is a load-bearing modeling choice, not a cosmetic detail.
[Sec. III E, Eq. (30)] The net survival probability is written as the product of the CGR survival probability and the nonadiabatic survival probability, assuming the two sets of mechanisms are statistically independent. Both mechanisms are driven by the same temperature history and the same charmonium wave functions, so the factorization in Eq. (30) needs a dynamical justification. Without such a justification, the 'Net' curves cannot be regarded as a consistent combination of the two mechanisms, and the combined predictions may double-count or miss correlations.
[Sec. II B / Sec. III C] The thermalization time is set to tau_0 = 0.1 fm for pp collisions in Sec. II B, while the Gubser-flow demonstration quoted from Ref. [27] uses tau_Hydro = 0.3 fm for the initial conditions. The value actually used in the yield calculations is not stated explicitly. The results are likely sensitive to this timescale because it sets the duration of the pre-equilibrium nonadiabatic evolution, so the missing specification is an obstacle to reproducibility.
[Sec. III E, Eq. (26)] The initial charmonium numbers N_i and N_{car c} are taken from Ref. [8], a model by the same authors fitted to pp charmonium yield data. The quantitative predictions therefore inherit the calibration of that model, and the paper does not discuss how the results change if these inputs are varied. This does not by itself invalidate the approach, but it limits the strength of the numerical claims and should be discussed explicitly.

minor comments (6)

[Eq. (1)] The exponent in Eq. (1) is garbled in the text; the authors should provide the correct LaTeX expression and clearly define the allowed range of alpha.
[Figs. 3-12] The captions and legends use the abbreviations CGR, NAb, and Net without defining them; these should be defined in each caption or once in the text.
[Sec. IV A] The statement that the pT-integrated yield is obtained using a charmonium distribution function 1/E_T^4 is not defined; the explicit formula should be provided.
[Sec. III C] The estimate tau_ev approximately 0.3 fm for the evolution timescale is quoted without specifying the temperature profile used; this estimate should be derived from the actual Gubser-flow profile used in the calculations.
[Sec. II A / Sec. II B] The notation alternates between 'pseudo temperature', 'pseudotemperature', and 'effective temperature'; these terms should be defined consistently and used uniformly.
[Sec. IV A] There are several typographical errors, including 'depeicts' in the discussion of Fig. 5, and the symbol 'gd' in Eq. (12) is not defined in the text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: predictions are computed from the stated transport and Schrödinger dynamics; self-cited inputs are not the predicted observables.

full rationale

The derivation chain is not circular. The headline predictions are survival probabilities SP = Nf/Ni (Eq. 29) and double ratios formed from these, normalized by the initial charmonium number Ni taken from the authors' earlier UMQS paper [8]. Ni and Ncbar enter only through the regeneration gain term in Eq. (26) and largely cancel in the ratio observables; the dominant new effects—the up-to-50% J/psi suppression, 80% chi_c(1P) suppression, and 130-200% psi(2S)/J/psi enhancement—are produced by the decay widths Gamma_D (Eqs. 8-13) and by the explicitly solved time-dependent Schrödinger equation (Eqs. 16-21), neither of which is fitted to the target observables. The paper recomputes the nonadiabatic survival overlaps with its own Crank-Nicolson evolution rather than importing them from Ref. [49], and it gives its own tau_ev ~ 0.3 fm versus tau_tr ~ 4.0 fm estimate for abandoning adiabaticity, so the self-citations [4,6,8,27,40,49] function as model inputs and motivation, not as forced conclusions. No uniqueness claim is imported from prior work. The genuine problems are non-circular: Eq. (1) contains an exponent parameter alpha that is never assigned a numerical value, making the temperature ramp and hence the figures non-reproducible; and the predicted psi(2S) enhancement is in qualitative tension with the CMS high-multiplicity pp measurement cited as Ref. [16], which reports psi(2S)/J/psi decreasing with multiplicity. That is a falsification/correctness risk for the 'robust probe' claim, not a circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper relies on a chain of modeling assumptions inherited from the authors' earlier work, with at least one free parameter (α) not specified and initial yields taken from a self-cited fitted model. No new particles or forces are introduced.

free parameters (5)

α (pre-equilibrium temperature exponent parameter)
Controls the rise of the pseudo-temperature in Eq. (1); no value is given in the text, so the pre-equilibrium Hamiltonian evolution is underdetermined.
τ0 (thermalization time) = 0.1 fm
Assumed from the scaling τ0 ∝ 1/sqrt(s); not fitted to charmonium data in this paper.
THydro (initial temperature for Gubser flow) = T0 from Eq. (2), not explicitly tabulated
Set from charged-particle multiplicity data via Eq. (2); the paper references 350 MeV from an earlier work by the same group for some cases.
η/s (specific shear viscosity) = not stated, c = 5 η/s
Input controlling the relaxation time in Gubser flow; inherited from Ref. [36].
Initial charmonium number Ni and Ncbar = from Ref. [8]
Inputs for the transport equation; taken from a model by the same authors that was fitted to p+p charmonium data.

assumptions (4)

domain assumption A thermalized QCD medium exists in high-multiplicity p+p collisions and follows Gubser flow with viscous corrections.
The entire calculation presumes this; it is the hypothesis to be probed, not independently established.
domain assumption Charmonia form during the very initial stage of the collision and evolve coherently under a zero-temperature Hamiltonian until the medium thermalizes.
Sec. III C; required for the nonadiabatic transition calculation, but no formation-time argument is given.
ad hoc to paper Nonadiabatic evolution is statistically independent of the collisional damping, gluonic dissociation, and regeneration mechanisms, so the survival probabilities factorize (Eq. 30).
Sec. III E; stated as an assumption without justification or quantitative check.
domain assumption The angle-averaged effective temperature from Eq. (7) is the correct temperature to use in all thermal decay widths.
Borrowed from Refs. [6,40]; no derivation given in this paper.

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Cite this review

Pith. "Pith review of Exploring QGP-like phenomena with Charmonia in $p+p$ collisions at $\sqrt{s} = 13$ TeV." pith.science (2026). https://pith.science/paper/M67RKN63

@misc{pith2026250100753,
  author       = {Pith},
  title        = {Pith review of: Exploring QGP-like phenomena with Charmonia in $p+p$ collisions at $\sqrts = 13$ TeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M67RKN63}},
  note         = {Machine review of arXiv:2501.00753}
}

abstract

In ultrarelativistic collisions of nuclei at the Large Hadron Collider, the created QCD environment rapidly changes, leading to a non-adiabatic evolution of the quantum states involved. Considering this, we first examine the pre-equilibrium state of QCD matter and its effect on the initially produced charmonium using a temperature-independent Hamiltonian. As the QCD matter reaches local thermal equilibrium, this Hamiltonian transforms to its finite temperature counterpart. To model the pre-equilibrium stage, we use the bottom-up thermalization approach to determine the effective temperature of the QCD matter, followed by a Gubser-type expansion for the thermalized medium. Additionally, we consider collisional damping, gluonic dissociation, and regeneration mechanisms, which specifically modify the charmonium yield in the thermalized medium. Mainly, the gluonic dissociation and collisional damping cause a reduction in the yield conversely, regeneration through gluonic deexcitation enhances the yield of charmonium. Further, we explore the combined effects of these mechanisms on the collective yield of charmonium states with transverse momentum ($p_{\rm T}$) and event multiplicity in the proton-proton collisions at $\sqrt{s} = 13$ TeV. Based on our findings, we contend that the combined effects of these mechanisms can serve as a robust probe for determining the possible existence of a thermalized QCD medium in such a small collision system.

Figures

Figures reproduced from arXiv: 2501.00753 by the authors.

**Figure 2.** FIG. 2. (Color online) The ratio between the decay widths [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3. (Color online) Survival probability [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4. (Color online) Survival probability [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: FIG. 5. (Color online) Double ratio as a function of multi [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: FIG. 6. (Color online) Particle number ratio as a function of [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 8.** Figure 8: FIG. 8. (Color online) Survival probability [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 10.** Figure 10: FIG. 10. (Color online) Survival probability [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

**Figure 11.** Figure 11: FIG. 11. (Color online) Double ratio as a function of [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

**Figure 12.** Figure 12: FIG. 12. (Color online) Particle number ratio as a function o [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]

Discussion (0). Continue with ORCID to comment.

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Reference graph

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In comparison, the ratio Γc,nl Γgd,nl ≈ 0.1, illustrates the marginal eﬀect of gluonic dissociation on J/ψ than the collisional damping

In this inset, the ratio of Γ c,nl to Γ D,nl indicates that collisional damping is the domi- nant dissociation mechanism, as the ratio varies around 0.9. In comparison, the ratio Γc,nl Γgd,nl ≈ 0.1, illustrates the marginal eﬀect of gluonic dissociation on J/ψ than the collisional damping. C. Time-dependent Schr ¨odinger equation: Nonadiabatic evolution o...

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and ( 4) with initial conditions T =THydro = 350 MeV and ˆπ = 4 3 ˆβπ ˆτπ at τ =τHydro = 0.3 fm for various system sizes ( rT ) was demonstrated in Ref. [ 27]. The results indicate that, as rT increases, the lifetime of the QGP increases. At suﬃciently large rT , the variation of temperature ( T ) 4 with proper time ( τ ) for Gubser ﬂow closely resembles ...

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Ad- ditionally, Fig

These results align with previous observations, indicating a notably higher pro- duction and relatively less suppression of J/ψ compared toχc(1P) and ψ(2S) during the transportation from ini- tial production to the QGP endpoint, i.e., T = T c. Ad- ditionally, Fig. 6 suggests that χc(1P) dissociation due to the CGR mechanism is relatively smaller in compar...

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