Causal-Horizon Scaling of Quarkonium Suppression in Strong QCD Fields

Yi Yang

arxiv: 2603.24623 · v3 · pith:5EOZEHKFnew · submitted 2026-03-24 · ✦ hep-ph · hep-ex· nucl-ex· nucl-th

Causal-Horizon Scaling of Quarkonium Suppression in Strong QCD Fields

Yi Yang This is my paper

Pith reviewed 2026-05-15 00:02 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-exnucl-th

keywords quarkonium suppressionbottomoniumpre-equilibrium color fieldsUnruh causal horizonheavy-ion collisionssequential suppressionCGC scaling

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The pith

Strong pre-equilibrium color fields define a causal horizon that sets the survival probability for bottomonium states.

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

The paper proposes that the observed pattern of sequential suppression for the Υ(1S), Υ(2S), and Υ(3S) states arises from an early-time geometric mechanism. Strong color fields present before hydrodynamic expansion create local proper accelerations whose associated Unruh scale forms a causal horizon. The survival probability of each state is then given by a WKB-motivated exponential that depends on the ratio of the quarkonium radius to this horizon. When this factor is combined with CGC-inspired scaling in centrality and energy, the model reproduces the measured suppression across different collision centralities. Because the effect occurs locally before flow develops, it automatically produces little additional azimuthal anisotropy in the quarkonia.

Core claim

The survival probability of a quarkonium state is given by an exponential controlled by the ratio of its radius to the Unruh causal horizon induced by local proper acceleration in the strong pre-equilibrium color field; combined with CGC-inspired centrality and energy scaling, this yields a compact description of the Υ(1S, 2S, 3S) suppression pattern together with a definite prediction for its RHIC-to-LHC energy dependence.

What carries the argument

The Unruh causal horizon scale, set by the local proper acceleration in the pre-equilibrium color field, which determines the geometric survival factor through a WKB-motivated exponential of the radius-to-horizon ratio.

If this is right

The mechanism simultaneously accounts for strong sequential suppression and small azimuthal anisotropy of bottomonium states.
It supplies a definite prediction for how the suppression pattern evolves with collision energy from RHIC to LHC.
The suppression enters as a local scalar factor before hydrodynamic response begins.
The same radius-to-horizon ratio governs the ordering of survival probabilities for the different Υ states.

Where Pith is reading between the lines

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

The same early-time geometric factor could be applied to other heavy-quark bound states such as charmonium if their radii are inserted into the same ratio.
Centrality dependence arising from the CGC scaling could be tested directly in smaller collision systems where the pre-equilibrium field strength varies.
If the Unruh scale is indeed the controlling length, the suppression should weaken in collisions at lower energies where the color-field strength drops.

Load-bearing premise

The strong pre-equilibrium color field produces a local proper acceleration that defines an Unruh causal scale whose ratio to the quarkonium radius controls survival via a WKB exponential.

What would settle it

A measurement showing either no clear RHIC-to-LHC change in the Υ suppression pattern or a sizable additional quarkonium azimuthal anisotropy beyond what hydrodynamic flow alone would produce.

Figures

Figures reproduced from arXiv: 2603.24623 by Yi Yang.

**Figure 3.** Figure 3: FIG. 3. Resolving the Flow Paradox. While transport mod [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. (a) Υ [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

read the original abstract

The simultaneous observation of strong sequential suppression and small azimuthal anisotropy for bottomonium states provides a stringent constraint on the time scale and geometry of the suppression mechanism. We propose an early-time geometric survival mechanism in which the strong pre-equilibrium color field induces a local proper acceleration and an associated Unruh causal scale. The survival probability is modeled by a WKB-motivated exponential controlled by the ratio of the quarkonium radius to the causal horizon. Combined with CGC-inspired centrality and energy scaling, the framework gives a compact description of the $\Upsilon(1S, 2S, 3S)$ suppression pattern and predicts a definite RHIC/LHC energy dependence. Because the suppression acts as a local scalar factor before hydrodynamic response develops, it naturally produces little additional quarkonium momentum anisotropy.

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

The paper offers a geometric Unruh-horizon picture for early quarkonium suppression that organizes sequential patterns and low anisotropy under CGC scaling, but the survival exponential is posited without a derived link from field acceleration to the bound-state factor.

read the letter

The main takeaway is that this paper proposes using an Unruh causal horizon from pre-equilibrium color fields to set a geometric survival probability for quarkonia, which could neatly explain the observed sequential suppression of bottomonium states and their small azimuthal anisotropy. What stands out as new is the specific connection between the quarkonium radius and this causal scale in a WKB-style exponential, layered with CGC-inspired scaling for different centralities and energies. The paper shows how this early-time scalar factor naturally avoids adding much momentum anisotropy, since it acts before hydrodynamic flow develops. It also gives a definite prediction for how the suppression should vary with collision energy from RHIC to LHC. The framework does a reasonable job of organizing the Υ(1S, 2S, 3S) pattern under one compact description. If the assumptions hold, it supplies testable energy dependence without needing complex time evolution. The soft spot is the lack of a first-principles derivation for the key step. The model assumes that the strong color field produces a local proper acceleration whose Unruh scale controls the survival via that exponential ratio, but there is no explicit mapping shown from the CGC field strength to the acceleration or from the resulting temperature to the suppression factor. The functional form is introduced rather than derived from the underlying QCD dynamics. Without seeing numerical results or comparisons in the full text, it is hard to tell how much of the agreement comes from the physics versus the choice of parameters like the causal horizon scale. This work is for specialists in heavy-ion collisions and quarkonium phenomenology who are open to alternative geometric mechanisms. It could spark useful discussion even if the details need tightening. I think it deserves peer review. The idea is fresh and the predictions are concrete, so referees can check the derivation and any fits for robustness.

Referee Report

2 major / 2 minor

Summary. The paper proposes an early-time geometric survival mechanism for quarkonium suppression in which strong pre-equilibrium color fields induce a local proper acceleration and associated Unruh causal scale. Survival probability is modeled via a WKB-motivated exponential controlled by the ratio of the quarkonium radius to this causal horizon; combined with CGC-inspired centrality and energy scaling, the framework is claimed to compactly describe the sequential suppression pattern of Υ(1S, 2S, 3S) states, predict definite RHIC/LHC energy dependence, and naturally yield little additional azimuthal anisotropy because the suppression acts as a local scalar factor before hydrodynamics develops.

Significance. If the central modeling step can be placed on firmer footing, the approach would supply a compact, early-time explanation for observed bottomonium suppression patterns together with a built-in account of small momentum anisotropy and falsifiable energy dependence. The framework's emphasis on pre-equilibrium geometry rather than late-stage medium effects is a potentially useful alternative perspective, provided the posited functional form is justified.

major comments (2)

[Abstract] Abstract (and the proposed mechanism): the survival probability is modeled by a WKB-motivated exponential controlled by the ratio of the quarkonium radius to the causal horizon, yet no explicit mapping is supplied from CGC field strength to the local proper acceleration a, nor from the resulting Unruh temperature to the bound-state suppression factor; the functional form is posited rather than derived. This single step controls both the sequential Υ(1S/2S/3S) pattern and the predicted RHIC/LHC energy dependence and therefore requires a first-principles or at least quantitatively justified derivation.
[Abstract] The manuscript states that the suppression acts as a local scalar factor before hydrodynamic response develops and therefore produces little additional quarkonium momentum anisotropy, but no quantitative estimate or comparison to measured v2 values is provided to substantiate how small the induced anisotropy remains after folding with the hydrodynamic evolution.

minor comments (2)

[Abstract] The abstract refers to 'CGC-inspired centrality and energy scaling' without specifying the exact functional forms or parameter values used; these should be written explicitly (ideally with equations) in the main text.
Notation for the causal horizon scale and the Unruh temperature should be introduced with clear definitions and units at first appearance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on the proposed mechanism. We address each major point below, indicating where revisions have been made to strengthen the manuscript.

read point-by-point responses

Referee: The survival probability is modeled by a WKB-motivated exponential controlled by the ratio of the quarkonium radius to the causal horizon, yet no explicit mapping is supplied from CGC field strength to the local proper acceleration a, nor from the resulting Unruh temperature to the bound-state suppression factor; the functional form is posited rather than derived. This single step controls both the sequential Υ(1S/2S/3S) pattern and the predicted RHIC/LHC energy dependence and therefore requires a first-principles or at least quantitatively justified derivation.

Authors: The mapping from CGC field strength to proper acceleration follows from the saturation scale Q_s setting the typical field E ~ Q_s^2/g, yielding a ~ Q_s^2/(m_Q) for the local acceleration experienced by the heavy quark pair. The WKB exponential is motivated by the tunneling probability across the Unruh horizon scale 1/a, giving P_surv ~ exp(-r_B a) as the leading suppression factor. While a complete non-perturbative QCD derivation lies beyond the present scope, the ansatz is quantitatively justified by its ability to reproduce the observed sequential suppression with a single parameter set fixed to LHC data. In the revision we have added an expanded derivation of the acceleration scale in Section 2 together with a sensitivity study showing robustness to variations in the field-to-acceleration relation. revision: partial
Referee: The manuscript states that the suppression acts as a local scalar factor before hydrodynamic response develops and therefore produces little additional quarkonium momentum anisotropy, but no quantitative estimate or comparison to measured v2 values is provided to substantiate how small the induced anisotropy remains after folding with the hydrodynamic evolution.

Authors: Because the suppression is applied at τ ≲ 0.3 fm/c as a position-dependent scalar multiplier on the initial production, it does not generate additional flow. We have added a quantitative estimate in the revised manuscript: the suppression factor is folded with a standard hydrodynamic evolution (using the same initial conditions as for light hadrons), resulting in an additional v2 contribution below 0.01 at p_T = 10 GeV for all three Υ states. This remains well below the measured bottomonium v2 values reported by CMS and ATLAS, confirming that the mechanism introduces negligible extra anisotropy. revision: yes

Circularity Check

0 steps flagged

No circularity: posited WKB-motivated survival form and CGC scaling remain independent modeling choices

full rationale

The paper introduces the survival probability as a modeled WKB-motivated exponential in the ratio of quarkonium radius to causal horizon, then combines it with CGC-inspired centrality and energy scaling to describe suppression patterns and predict RHIC/LHC dependence. No quoted equation or section shows this functional form reducing to the input data by construction, nor any self-citation chain that bears the central claim. The mechanism is presented as a proposal rather than a derivation forced by prior results or fits. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The proposal rests on applying the Unruh effect and WKB approximation to pre-equilibrium QCD without independent verification of the mapping; likely free parameters exist for the horizon scale and CGC centrality factors.

free parameters (2)

causal horizon scale
Controls the exponential suppression strength and is expected to be adjusted to data.
CGC centrality and energy scaling factors
Combined with the geometric factor to match observed patterns.

axioms (2)

domain assumption Unruh effect applies directly to strong pre-equilibrium color fields in QCD
Invoked to define the causal horizon scale.
standard math WKB approximation yields valid exponential survival probability
Used to model the ratio of radius to horizon.

invented entities (1)

Unruh causal horizon in strong QCD fields no independent evidence
purpose: Sets the geometric scale for quarkonium survival probability
Postulated new application without external falsifiable evidence provided in abstract.

pith-pipeline@v0.9.0 · 5425 in / 1471 out tokens · 54951 ms · 2026-05-15T00:02:13.557922+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The survival probability is modeled by a WKB-motivated exponential controlled by the ratio of the quarkonium radius to the causal horizon... R_AA = exp[−κ r_nS (N_part^{1/3} − N_pp^{1/3})]
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

dynamical Hawking-Unruh event horizon... r_H = 1/a
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

anchored to the QCD pseudo-critical temperature (T_c)

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