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arxiv: 2604.11847 · v2 · submitted 2026-04-12 · ✦ hep-ph · hep-ex

Spin-Momentum Decoupling in Quarkonium Hadronization: Polarization Quenching via Environment-Induced Decoherence in Jets

Yi Yang This is my paper

Pith reviewed 2026-05-10 14:58 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords quarkonium polarizationjet fragmentationopen quantum systemsLindblad dissipationdecoherenceheavy quarksQCD hadronizationpolarization quenching
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The pith

Heavy quark spin decouples from jet momentum, quenching quarkonium polarization via environmental decoherence.

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

The paper proposes that suppressed polarization in high-p_T heavy quarkonia arises because the quark spin state decouples from its momentum during hadronization in jets. It retains NRQCD perturbative calculations for the initial production but models the jet's stochastic chromo-electric background as a decohering environment whose effective temperature rises as the fragmentation fraction z falls. This temperature enters a Lindblad framework that drives the spin density matrix toward a maximally mixed state, quenching all polarization anisotropies simultaneously. The approach accounts for CMS observations of soft Υ fragmentation by weighting toward small z, and it identifies z as the variable that controls the strength of the effect in fixed p_T bins.

Core claim

By treating the fragmenting jet as an open quantum system whose chromo-electric fluctuations are parametrized by a horizon-inspired effective temperature T_eff(z) ∝ √ln(1/z), the heavy-quark spin evolves under Lindblad dissipation while the momentum spectrum remains power-law preserved by high-p_T kinematic inertia, resulting in simultaneous suppression of the polar and azimuthal polarization parameters λ_θ, λ_φ, and λ̃ toward zero.

What carries the argument

Lindblad master equation for the quarkonium spin density matrix, driven by an effective temperature T_eff(z) ∝ √ln(1/z) set by the multiplicity of soft accompanying partons.

Load-bearing premise

The intense stochastic chromo-electric background inside the jet functions as a decoherence environment whose strength is captured by the specific scaling T_eff(z) proportional to the square root of the logarithm of one over z.

What would settle it

Observation that the polarization parameters λ_θ, λ_φ, or λ̃ remain large or fail to decrease with falling z in fixed quarkonium and jet p_T bins would contradict the predicted quenching.

Figures

Figures reproduced from arXiv: 2604.11847 by Yi Yang.

Figure 1
Figure 1. Figure 1: FIG. 1. Theoretical prediction of the concurrent quenching [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
read the original abstract

The suppression of heavy quarkonium polarization at high transverse momentum ($p_T$) remains a persistent puzzle in quantum chromodynamics (QCD). We propose an effective open-quantum-system paradigm demonstrating that the heavy quark spin state and its macroscopic momentum effectively decouple during hadronization. By retaining the short-distance non-relativistic QCD (NRQCD) perturbative calculations as a kinematic baseline, we argue that the immense kinematic inertia at high $p_T$ parametrically preserves the power-law momentum spectrum. Concurrently, the intense, stochastic chromo-electric background within a fragmenting jet acts as a dynamic decoherence environment. Using a horizon-inspired picture as a physically motivated parametrization, we derive an effective temperature $T_{\text{eff}}(z) \propto \sqrt{\ln(1/z)}$ driven by the multiplicity of soft accompanying partons. By incorporating this effective temperature into a Lindblad dissipation framework, we predict a simultaneous quenching of the polar and azimuthal anisotropies towards a maximally mixed state. Crucially, the recently observed ``soft'' fragmentation of $\Upsilon(nS)$ by the CMS Collaboration provides a highly consistent phase-space weighting required in our framework to explain the historical inclusive unpolarized anomaly. Identifying the fragmentation fraction $z=p_T^{\mathcal{Q}}/p_T^{\text{jet}}$ as the critical control variable, we propose that a key testable prediction is the simultaneous $z$-dependent suppression of $\lambda_\theta$, $\lambda_\phi$, and $\tilde{\lambda}$ in fixed quarkonium and jet $p_T$ bins.

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 / 2 minor

Summary. The manuscript proposes an effective open-quantum-system paradigm to resolve the suppression of heavy quarkonium polarization at high p_T. Retaining NRQCD short-distance coefficients as a kinematic baseline, it models the jet's stochastic chromo-electric background as a decoherence environment whose effective temperature is parametrized as T_eff(z) ∝ √ln(1/z) from a horizon-inspired picture driven by soft-parton multiplicity. This is inserted into a Lindblad master equation to predict simultaneous quenching of the polarization parameters λ_θ, λ_φ, and λ̃ toward a maximally mixed state. The CMS observation of soft Υ(nS) fragmentation is adopted as the phase-space weighting that simultaneously accounts for the historical inclusive unpolarized anomaly, with z = p_T^Q / p_T^jet identified as the control variable for testable predictions in fixed-p_T bins.

Significance. If the central claims hold, the work would supply a mechanism that unifies the polarization puzzle with the unpolarized cross-section anomaly by treating hadronization as an open-system process while preserving the power-law p_T spectrum. The emphasis on a concrete, z-dependent experimental signature distinguishes it from purely perturbative or feed-down explanations and could motivate dedicated measurements. The retention of NRQCD baselines is a positive feature, but the parametrized character of T_eff and the Lindblad implementation limit the result's immediate theoretical impact.

major comments (3)
  1. [Effective temperature and Lindblad framework] The functional form T_eff(z) ∝ √ln(1/z) is introduced by horizon analogy without an explicit mapping from NRQCD short-distance operators, the multiplicity of soft partons, or the jet's chromo-electric fluctuations to the Lindblad jump operators and rates. Because this z-dependence is load-bearing for the predicted simultaneous suppression of λ_θ, λ_φ, and λ̃, the absence of a derivation or error estimate renders the quenching result an input rather than an output of the framework.
  2. [Consistency with CMS data and phase-space weighting] The framework adopts the CMS-observed soft fragmentation phase-space weighting to reproduce the inclusive unpolarized anomaly. The manuscript must demonstrate that the z-dependent quenching prediction is not circularly shaped by the same data used as input; otherwise the claim that the model explains the anomaly reduces to a consistency check rather than an independent test.
  3. [Abstract and proposed predictions] No quantitative validation, fit results, or exclusion of alternative mechanisms (e.g., color-octet NRQCD transitions or feed-down) is supplied for the asserted consistency with CMS data or for the Lindblad quenching rates. The central claim that the power-law momentum spectrum remains parametrically intact while polarization is quenched therefore lacks the numerical control required to assess its robustness.
minor comments (2)
  1. [Notation] The precise definition and relation of the tilde-lambda parameter to the standard polarization observables should be stated explicitly when first introduced.
  2. [Introduction] Additional references to prior applications of Lindblad or open-system methods in jet or heavy-quark contexts would help situate the present effective-temperature parametrization.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments identify key areas where the effective framework requires further clarification and strengthening. We address each major comment below and have revised the manuscript to incorporate additional derivations, explicit distinctions between inputs and predictions, and expanded discussion of alternatives.

read point-by-point responses

  1. Referee: The functional form T_eff(z) ∝ √ln(1/z) is introduced by horizon analogy without an explicit mapping from NRQCD short-distance operators, the multiplicity of soft partons, or the jet's chromo-electric fluctuations to the Lindblad jump operators and rates. Because this z-dependence is load-bearing for the predicted simultaneous suppression of λ_θ, λ_φ, and λ̃, the absence of a derivation or error estimate renders the quenching result an input rather than an output of the framework.

    Authors: We agree that the T_eff(z) scaling is introduced via a horizon-inspired parametrization rather than a first-principles derivation from NRQCD operators. This is inherent to the effective open-system approach. In the revised manuscript we have added an appendix providing a scaling argument that connects the soft-parton multiplicity in the jet to the strength of chromo-electric fluctuations and thence to the Lindblad jump rates. We also include a rough uncertainty band on T_eff arising from multiplicity variations. These additions make the quenching rates explicit outputs of the model assumptions. revision: yes

  2. Referee: The framework adopts the CMS-observed soft fragmentation phase-space weighting to reproduce the inclusive unpolarized anomaly. The manuscript must demonstrate that the z-dependent quenching prediction is not circularly shaped by the same data used as input; otherwise the claim that the model explains the anomaly reduces to a consistency check rather than an independent test.

    Authors: The CMS soft-fragmentation distribution is used solely to fix the z-weighting that resolves the unpolarized cross-section anomaly. The polarization observables are then computed by propagating the spin density matrix through the Lindblad equation under this fixed weighting, with no additional free parameters. We have revised the text and added a new figure that displays the predicted λ_θ(z), λ_φ(z), and λ̃(z) in fixed-p_T bins; these curves constitute independent, testable predictions that are not constrained by the inclusive unpolarized data. revision: yes

  3. Referee: No quantitative validation, fit results, or exclusion of alternative mechanisms (e.g., color-octet NRQCD transitions or feed-down) is supplied for the asserted consistency with CMS data or for the Lindblad quenching rates. The central claim that the power-law momentum spectrum remains parametrically intact while polarization is quenched therefore lacks the numerical control required to assess its robustness.

    Authors: The manuscript presents a conceptual framework and identifies the distinctive z-dependent signature rather than performing a full numerical fit. We have revised the abstract and conclusions to state explicitly that the consistency with CMS data is at the level of the observed soft z-distribution, and we have added a discussion arguing that color-octet transitions and feed-down do not naturally produce the simultaneous quenching of all three λ parameters with the same z-dependence. The parametric preservation of the p_T spectrum follows directly from the NRQCD short-distance coefficients at high p_T. A dedicated numerical study with event generators is planned as follow-up work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained.

full rationale

The paper's chain begins with NRQCD short-distance coefficients as an independent kinematic baseline, posits high-p_T inertia to preserve the power-law spectrum, introduces a horizon-motivated parametrization T_eff(z) ∝ √ln(1/z) driven by soft-parton multiplicity, inserts this into a standard Lindblad master equation to obtain quenching of λ_θ, λ_φ and λ̃ toward a mixed state, and invokes CMS soft-fragmentation data only as a consistent phase-space weight that makes the inclusive unpolarized anomaly compatible with the model. The central claim—a new, differential z-dependent suppression in fixed-p_T bins—is a forward prediction whose functional form is not obtained by re-fitting or redefining the same inclusive data; the Lindblad evolution and the explicit T_eff(z) ansatz supply independent dynamical content. No self-definitional loop, fitted-input-as-prediction, or load-bearing self-citation reduces the result to its inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The claim depends on retaining NRQCD as an unchanged kinematic baseline, assuming the Lindblad framework applies to hadronization, and introducing a horizon-inspired temperature parametrization whose functional form is chosen to match multiplicity trends.

free parameters (1)
  • T_eff(z) proportionality constant
    The effective temperature is introduced as T_eff(z) ∝ √ln(1/z) without a first-principles derivation; its overall scale is implicitly adjusted to produce the observed quenching.
axioms (2)
  • domain assumption Short-distance NRQCD perturbative calculations remain valid as the kinematic baseline at high p_T
    Explicitly retained while the long-distance hadronization is replaced by the open-system treatment.
  • domain assumption The stochastic chromo-electric background inside the jet can be modeled as a Markovian environment amenable to Lindblad dissipation
    Invoked to derive the quenching toward a maximally mixed state.
invented entities (1)
  • horizon-inspired effective temperature T_eff(z) no independent evidence
    purpose: Parametrizes the decoherence strength driven by soft-parton multiplicity
    New functional form introduced without independent experimental handle outside the fit to fragmentation data.

pith-pipeline@v0.9.0 · 5582 in / 1715 out tokens · 82110 ms · 2026-05-10T14:58:13.033414+00:00 · methodology

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Reference graph

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