Bottomonium suppression with a machine-learning-informed Debye mass

Ajaharul Islam; Fu-Peng Li; Guang-You Qin; Long-Gang Pang; Shibo Chen

REVIEW

Bottomonium suppression with a machine-learning-informed Debye mass

Ajaharul Islam, Shibo Chen, Fu-Peng Li, Long-Gang Pang, Guang-You Qin

High Energy Physics - Phenomenology · Submitted 8 Sep 2026

Pith's verdict: A clean, useful extension of the KSU/QTraj framework with a lattice-informed ML Debye mass, but the ad hoc rescaling in Eq. (4.18) and missing uncertainty bands leave the source of the improvement not fully pinned down.

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arXiv ID2609.09047 (version 2)

Pith IDAQKJ2NHW, Pith's permanent record of this paper and its review

CitationAjaharul Islam, Fu-Peng Li, Guang-You Qin, Long-Gang Pang, Shibo Chen. "Bottomonium suppression with a machine-learning-informed Debye mass." arXiv:2609.09047 (2026). https://pith.science/paper/AQKJ2NHW

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Editor's note

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The genuinely new thing here is that DLQPM quasi-particle masses, trained on lattice QCD thermodynamics rather than on quarkonium, are fed into the imaginary part of the KSU potential, and the resulting QTraj evolution gives a better visual match to bottomonium suppression data at 5.02 TeV. That is a real extension of the earlier DLQPM and QTraj work, not a paradigm shift. There is no circularity: bottomonium data enter only in the comparison, never in the training. The paper is also honest about its limits, noting that the 3S/2S ratio shows little or no improvement and that the ML modification is confined to the imaginary part.

What I like: the setup uses established machinery, the lattice input is independent of the predicted observable, feed-down is handled through a PDG branching matrix, and the numerics are solid (split-step pseudospectral QTraj with a million trajectories). If I worked on quarkonium phenomenology, I would want this as a reference point.

Now the soft spots. The stress-test note about Eq. (4.18) mostly lands. The ML Debye mass is not used directly; it is rescaled by sqrt(alpha_s(2pi T)/alpha_s^ML(T)), motivated by the HTL relation m_D ~ sqrt(alpha_s) T. Given that the imaginary potential prefactor already uses alpha_s(2pi T), some scale-matching is defensible, but the rescaling is asserted rather than derived, and it mixes a perturbative coupling at 2pi T with non-perturbative masses and couplings determined near scale T. So the reader cannot cleanly separate what the ML input contributes from what this rescaling does. That is the main weakness, and it is a real one.

Minor but related: the predictions are single lines. The model's own ML uncertainty, shown for alpha_s in Fig. 2, is not propagated to R_AA. With that band, and with a sensitivity study around Eq. (4.18), the central claim would be much easier to judge. As written, "improved agreement" is largely a visual statement; there is no chi-squared or other quantitative comparison.

The central idea is not broken. This paper deserves a serious referee, and the referees should push for uncertainty propagation and a direct test of whether the rescaling, rather than the lattice-constrained input, drives the improved excited-state survival. It is worth citing, and I would bring it to the reading group if the discussion is about how to put lattice constraints into quarkonium evolution.

Referee report

Significance

If the central claim holds, the paper is a useful demonstration of how lattice-constrained, ML-derived medium information can be transferred into real-time quarkonium evolution, and it has the important virtue of being non-circular: the ML input is obtained from the QCD equation of state, while bottomonium data are used only for comparison. The calculation has genuine strengths: it uses the established open-source QTraj solver, a nine-state feed-down matrix, a hydrodynamic background calibrated to LHC data, and one million sampled trajectories, and it reports no free parameters tuned to the bottomonium observables. However, the significance of the claimed improvement is currently limited by two addressable issues: the ad hoc rescaling that defines the effective ML Debye mass, and the absence of propagated uncertainty bands in the final predictions. Both issues are fixable within the scope of the manuscript, so the contribution is promising but needs further work before the headline conclusion is fully supported.

Major objections (3)

[§4.5, Eq. (4.18)] The effective ML Debye mass is defined by rescaling m_D^{ML}(T) by sqrt(alpha_s(2pi T)/alpha_s^{ML}(T)), but no independent derivation or validation of this hybrid object is provided. Since m_D^{ML}(T) already contains a factor sqrt(alpha_s^{ML}(T)) through Eq. (4.17), the rescaling effectively replaces the ML coupling by the perturbative coupling at the scale 2pi T and leaves the ML information only in the quasiparticle masses entering the kinetic-theory integral. The paper therefore does not establish that the quantity entering the imaginary potential is the Debye mass actually obtained from the ML framework, and the improved agreement in Figs. 5-8 cannot be cleanly attributed to the lattice-constrained ML input. Please either provide a derivation or explicit HTL justification for Eq. (4.18), or repeat the analysis using m_D^{ML}(T) directly from Eq. (4.17) and with alternative scale choices, so that the source of the improvement can be identified.
[§7, Figs. 5-8] All final predictions are presented as single curves without uncertainty bands, even though Fig. 2 shows a training-variance band for alpha_s^{ML}(T) and the text states that the band reflects multiple neural-network trainings. Because the central claim is a quantitative improvement in agreement with data, the absence of propagated uncertainty makes it impossible to judge whether the difference between the ML-CCNU and isotropic KSU curves is significant relative to the ML extraction variance. Please propagate the ensemble or training variance through the QTraj calculation, or alternatively demonstrate explicitly that the final observables are insensitive to this variance.
[§4.1, §4.4, Eqs. (4.10), (4.17)] The DLQPM in §4.1 predicts three mass functions (gluons, light quarks, strange quarks), but Eq. (4.10) uses only m_g and m_u/d, and Eq. (4.17) writes the quark contribution as a single 2N_f integral with one distribution f_q. It is therefore unclear whether the strange-quark mass enters the Debye mass at all, and if it does not, the 2+1-flavor lattice input is not fully used in the central quantity of the paper. Please clarify the value of N_f used in Eq. (4.17), state explicitly how the strange-quark mass is treated in the kinetic-theory integral, and quantify the sensitivity of m_D^{ML}(T) to that treatment.

Minor objections (5)

[Notation] N_F is used in Eqs. (3.3), (3.4), and (3.8) while N_f is used in Eqs. (4.8)-(4.17); the notation should be unified and its numerical value stated once.
[§7] The narrative for each figure repeats the same 'ML-CCNU is closer to data' statement; a compact summary table with the plotted observables and, ideally, a simple discrepancy metric would make the comparison easier to assess.
[Figs. 2-4] Several axis labels appear garbled in the rendered text (for example, the y-axis of Fig. 2 is typeset as 'ML_s(T)' twice); the figures should be regenerated with clean mathematical labels.
[References] Reference [74] is cited as a CERN technical report; if a journal publication exists, it should be cited in its published form.
[§6] The text says 'We solve the 3+1D Schrödinger equation' but the calculation is a spherically symmetric radial evolution on a 3+1D medium background; the wording should be clarified to avoid implying a full 3+1D quantum evolution.

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The paper

The paper claims

This paper incorporates a machine-learning-derived Debye screening mass, inferred from lattice QCD thermodynamics, into the imaginary part of the heavy-quark potential and shows that it significantly improves agreement with measured…

The reading

The authors aim to show that a data-driven, machine-learning-informed Debye mass, extracted from lattice QCD equation-of-state data via a deep-learning quasi-parton gas model, improves the theoretical description of bottomonium suppression in heavy-ion collisions. They replace the conventional perturbative Debye mass in the imaginary part of the KSU heavy-quark potential with their ML-derived effective Debye mass, then evolve bottomonium wave packets through a hydrodynamic background using the quantum trajectories framework. The resulting nuclear modification factors and double ratios for the Υ(1S), Υ(2S), and Υ(3S) states in Pb-Pb collisions at 5.02 TeV agree markedly better with ALICE, ATLAS, and CMS data than the standard isotropic KSU model, particularly for the more weakly bound excited states. This suggests that machine-learning-extracted medium parameters can capture non-perturbative QGP physics that is missed by perturbative estimates, offering a systematic path to incorporate lattice-constrained thermodynamics into phenomenological quarkonium models.

What carries the argument

The key machinery is the effective machine-learning Debye mass, $m_D^{{ML,eff}}$(T), defined as a rescaled version of the Debye mass computed from the DLQPM via the kinetic-theory formula (Eq. 4.13), with the rescaling factor $\sqrt$(α_s(2πT)/$α_s^{{ML}}$(T)) that aligns the coupling scale with the one used in the KSU potential's imaginary part. The DLQPM itself is a deep neural network that takes temperature as input and outputs quasi-parton masses (gluon, up/down, strange) that reproduce lattice QCD entropy density and trace anomaly. From these masses, the running coupling $α_s^{{ML}}$(T) is extracted via leading-order thermal mass relations (Eqs. 4.8–4.9), and then the Debye mass is obtained by integrating the momentum-space derivative of the quasi-particle distribution functions. This machine-learning-derived Debye mass is inserted into the leading-order perturbative expression for the imaginary part of the heavy-quark potential (Eq. 3.6), while the real part is kept unchanged from the conventional KMS potential.

Extended reading notes

Core claim

The central discovery is that replacing the conventional perturbative Debye mass in the imaginary part of the heavy-quark potential with a machine-learning-derived Debye mass (obtained from a deep-learning quasi-parton gas model constrained by lattice QCD thermodynamics) yields a quantitatively improved description of bottomonium suppression in heavy-ion collisions. The ML-informed potential predicts larger survival probabilities for Υ(2S) and Υ(3S) states than the standard isotropic KSU model, bringing the computed nuclear modification factors and double ratios into noticeably closer agreement with experimental data from ALICE, ATLAS, and CMS across centrality and transverse momentum. The improvement is most pronounced for the most weakly bound states, which are most sensitive to the in-medium decay width controlled by the imaginary part of the potential.

Load-bearing premise

The Debye mass entering the imaginary potential is computed from the DLQPM quasi-particle masses and coupling via a leading-order kinetic-theory formula (Eq. 4.13) and then rescaled by $\sqrt$(α_s(2πT)/$α_s^{{ML}}$(T)) (Eq. 4.18), which assumes the perturbative HTL structure for the screening mass remains valid even when the quasi-particle masses and coupling are determined non-perturbatively from lattice thermodynamics, and that the rescaling is the correct way to match the scale 2πT used in the potential.

Editorial extensions

If this is right

The ML-CCNU model provides a systematic way to incorporate non-perturbative lattice QCD information into phenomenological quarkonium suppression calculations, reducing reliance on purely perturbative estimates of medium properties.
The same framework can be extended to charmonium states, where regeneration effects are larger, to test whether ML-derived medium parameters improve agreement with J/ψ and ψ(2S) data.
Because the imaginary part of the potential is the key control knob for the dissociation of weakly bound states, the improvement seen in excited bottomonia suggests that the ML Debye mass captures genuine non-perturbative physics of the QGP, which could be further tested with other observables like elliptic flow.
The approach can be generalized to anisotropic plasmas by incorporating the ML Debye mass into anisotropic potential models, potentially improving predictions for momentum-dependent observables.
The methodology can be adapted to extract other medium properties (e.g., transport coefficients, heavy-quark diffusion constant) from lattice QCD using similar deep-learning frameworks constrained by thermodynamic or spectral data.

Reading between the lines

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

The improvement for excited states implies that the imaginary part of the potential is more temperature-dependent and receives larger non-perturbative corrections than the real part, which is left unchanged; this could guide future effective field theory developments.
If the ML Debye mass is systematically smaller than the perturbative HTL value across the QGP temperature range (as shown in Fig. 4), this suggests that non-perturbative effects reduce screening, leading to longer-lived excited states; this picture could be tested by lattice QCD direct measurements of the Debye mass (e.g., from color-electric correlators).
The rescaled effective Debye mass (Eq. 4.18) is a pragmatic compromise; a more self-consistent approach would derive both real and imaginary parts of the potential from the same ML-extracted quasi-particle spectral functions, which could be attempted in future work.
The centrality and pT dependence of the double ratios [Υ(2S)/Υ(1S)] and [Υ(3S)/Υ(1S)] are quite well captured by the ML-CCNU model; the fact that [Υ(3S)/Υ(2S)] shows less sensitivity suggests that the relative survival probability of excited states is dominated by the overall magnitude of the imaginary potential rather than its detailed functional form.

Original abstract

Motivated by recent progress in data-driven approaches, we introduce a machine-learning (ML)-informed Debye mass, extracted from lattice-informed inputs, exclusively in the complex-valued heavy-quark Kent State University (KSU) potential. The resulting complex potential is used to solve the real-time Schr\"odinger equation within the quantum trajectories (QTraj) framework for the evolution of bottomonium in the quark-gluon plasma. We then compute the nuclear modification factors and double ratios for bottomonium $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ states in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. We compare our ML-induced results with those from the original KSU model and with experimental measurements from ALICE, ATLAS, and CMS collaborations. We find that the machine-learned Debye mass leads to improved agreement with data, particularly for excited states, highlighting the utility of machine learning in modeling in-medium QCD effects.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,473 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.87 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Motivated by recent progress in data-driven approaches, we introduce a machine-learning (ML)-informed Debye mass, extracted from lattice-informed inputs, exclusively in the complex-valued heavy-quark Kent State University (KSU) potential. The resulting complex potential is used to solve the real-time Schr\"odinger equation within the quantum trajectories (QTraj) framework for the evolution of bottomonium in the quark-gluon plasma. We then compute the nuclear modification factors and double ratios for bottomonium $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ states in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. We compare our ML-induced results with those from the original KSU model and with experimental measurements from ALICE, ATLAS, and CMS collaborations. We find that the machine-learned Debye mass leads to improved agreement with data, particularly for excited states, highlighting the utility of machine learning in modeling in-medium QCD effects.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Motivated by recent progress in data-driven approaches, we introduce a machine-learning (ML)-informed Debye mass, extracted from lattice-informed inputs, exclusively in the complex-valued heavy-quark Kent State University (KSU) potential.	contribution 0.85	0.94	0.04	asserted 0.99
s1	The resulting complex potential is used to solve the real-time Schr\"odinger equation within the quantum trajectories (QTraj) framework for the evolution of bottomonium in the quark-gluon plasma.	method 0.99	0.87	0.03	asserted 0.99
s2	We then compute the nuclear modification factors and double ratios for bottomonium $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ states in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV.	method 0.71	0.95	0.03	asserted 0.98
s3	We compare our ML-induced results with those from the original KSU model and with experimental measurements from ALICE, ATLAS, and CMS collaborations.	method 0.84	0.83	0.04	asserted 0.89
s4	We find that the machine-learned Debye mass leads to improved agreement with data, particularly for excited states, highlighting the utility of machine learning in modeling in-medium QCD effects.	result 0.67	0.97	0.94	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.65 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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