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arxiv: 2606.07744 · v1 · pith:VH5U5KI6new · submitted 2026-06-05 · ✦ hep-ph · nucl-th

Open quantum system approach to the transverse momentum broadening of a colour dipole

Fran\c{c}ois Arleo , Pietro Benzoni , Paul Caucal , Pol Bernard Gossiaux This is my paper

Pith reviewed 2026-06-27 21:33 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords open quantum systemsLindblad equationcolour dipoletransverse momentum broadeningQCD plasmaWigner distributioncolour decoherencequarkonium
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The pith

In the correlation limit a quark-antiquark pair's Wigner distribution in a QCD plasma quasi-factorises into a hard splitting factor and a medium-induced q_perp distribution, modified by a colour decoherence factor controlled by theta_qqbar

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

The paper applies the open quantum systems formalism to derive a Lindblad equation governing the density matrix of a boosted quark-antiquark colour dipole traversing a QCD plasma of length L with transport coefficient qhat. In the regime where the relative transverse momentum p_perp greatly exceeds both the imbalance q_perp and the medium scale Q_s = sqrt(qhat L), the resulting Wigner distribution separates into a hard factor for the initial splitting and a q_perp distribution for medium broadening. This separation holds only up to a multiplicative colour decoherence factor whose theta_qqbar dependence is set by the ratio of the dipole opening angle to a critical angle theta_c approximately (qhat L^3)^{-1/2}. The same critical time t_c that governs the onset of this factor also marks the suppression of off-diagonal colour elements and the singlet-to-octet transition, with colour decoherence appearing before complete decoherence of the full density matrix.

Core claim

In the correlation limit p_perp >> q_perp, Q_s and the boosted regime theta_qqbar << 1, the Wigner distribution obtained from the Lindblad evolution displays quasi-factorisation between the hard splitting factor and the q_perp-broadening distribution; the factorisation is violated by a colour decoherence factor that encodes the theta_qqbar dependence through the ratio theta_qqbar/theta_c with theta_c ~ (qhat L^3)^{-1/2}. The open quantum systems treatment shows that the associated critical time t_c controls both the decay of off-diagonal colour matrix elements and the singlet-octet mixing, yet colour decoherence precedes the full decoherence of the density matrix, signalling the start of cla

What carries the argument

The Lindblad evolution equation for the colour dipole density matrix, whose solution in the correlation limit yields a Wigner distribution containing the quasi-factorised hard factor multiplied by the q_perp distribution and the colour decoherence factor.

If this is right

  • The transverse momentum imbalance distribution acquires an explicit dependence on the dipole opening angle through the ratio theta_qqbar/theta_c.
  • The critical time t_c simultaneously suppresses off-diagonal colour elements and drives the transition between singlet and octet states.
  • Colour decoherence appears before the density matrix reaches full decoherence, indicating the onset of classical behaviour.
  • Quantum diffusion corrections in the relative momentum p_perp produce only mild deviations from the quasi-factorised form.

Where Pith is reading between the lines

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

  • The same Lindblad framework could be applied to other colour-singlet or octet systems whose evolution is governed by a similar medium-induced decoherence scale.
  • The separation between colour decoherence and full kinematic decoherence suggests that classical transport approximations may become valid at earlier times than previously assumed for jet substructure observables.
  • Extending the calculation beyond the correlation limit would require retaining the full p_perp diffusion term and could quantify the size of non-factorising corrections at moderate p_perp.

Load-bearing premise

The analysis requires that the quark-antiquark relative momentum p_perp remain much larger than both the imbalance q_perp and the medium scale Q_s while the dipole opening angle stays small.

What would settle it

A measurement of the q_perp spectrum of back-to-back quark pairs produced in heavy-ion collisions that shows a theta_qqbar dependence matching the predicted colour decoherence factor for varying dipole opening angles would support the claim; absence of that angular dependence at fixed p_perp would falsify the quasi-factorisation picture.

read the original abstract

Using the open quantum systems formalism, we study the propagation of a quark-antiquark pair propagating through a dense QCD plasma of size $L$ and transverse momentum broadening transport coefficient $\hat q$, and we derive the Lindblad evolution equation for the density matrix of the system. We focus on the boosted regime where the opening angle $\theta_{q\bar q}$ of this effective colour dipole satisfies $\theta_{q\bar q}\ll 1$. In the correlation limit where the quark-antiquark relative transverse momentum $p_\perp$ is much larger than the imbalance $q_\perp$ as well as the medium typical transverse momentum scale $Q_s=\sqrt{\hat q L}$, we demonstrate that the resulting Wigner distribution displays quasi factorisation between a hard factor describing the hard splitting producing the $q\bar q$ pair and the transverse momentum imbalance $q_\perp$-distribution encoding the broadening induced by the medium. The factorisation is violated by a "colour decoherence" factor that controls the $\theta_{q\bar q}$ dependence of the $q_\perp$-distribution through the ratio $\theta_{q\bar q}/\theta_c$, with $\theta_c \sim (\hat q L^3)^{-1/2}$. The open quantum systems approach enables us to clarify the role of this critical angle $\theta_c$ and its associated critical time $t_c$ in the genuine quantum decoherence of the density matrix in colour and kinematic space: in particular, $t_c$ controls both the suppression of the off-diagonal elements of the density matrix in colour space and the transition between singlet and octet states. We find, however, that colour decoherence sets in earlier than the full decoherence of the density matrix, thereby marking the onset of classical behaviour in the system. Finally, we investigate the corrections beyond the quasi-factorised picture due to the quantum diffusion term in $p_\perp$ of the Lindblad equation and we find that these corrections are mild.

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

0 major / 3 minor

Summary. The manuscript applies the open quantum systems formalism to derive the Lindblad evolution equation for the density matrix of a boosted quark-antiquark color dipole propagating through a QCD plasma of length L with transport coefficient ĥq. In the correlation limit p_⊥ ≫ q_⊥, Q_s = √(ĥq L) together with heta_qqbar ≪ 1, the resulting Wigner distribution is shown to exhibit quasi-factorization between a hard splitting factor and the medium-induced q_⊥ broadening distribution; factorization is violated by a color decoherence factor controlled by the ratio heta_qqbar/ heta_c where heta_c ~ (ĥq L^3)^(-1/2). The work identifies the critical time t_c as governing both suppression of off-diagonal color-space matrix elements and the singlet-octet transition, notes that color decoherence precedes full kinematic decoherence, and reports that corrections from the quantum diffusion term in p_⊥ remain mild.

Significance. If the derivation and limit analysis hold, the paper supplies a controlled quantum-mechanical framework for transverse-momentum broadening and color decoherence of dipoles in dense media. Explicit connection of heta_c and t_c to the Lindblad dynamics, together with the demonstration that color decoherence sets in earlier than full decoherence, offers a concrete bridge between quantum and classical regimes relevant to jet quenching. The quasi-factorization result, when the stated kinematic limits are satisfied, provides a falsifiable prediction for the heta_qqbar dependence of the q_⊥ distribution.

minor comments (3)
  1. The abstract states the quasi-factorization result but does not display the explicit form of the Lindblad operator or the Wigner distribution; adding the key equations (or their section references) would improve readability for readers who do not consult the full text immediately.
  2. The definition of the critical angle heta_c ~ (ĥq L^3)^(-1/2) and its relation to the decoherence time t_c should be stated once with an explicit equation number in the main text to avoid repeated verbal descriptions.
  3. Figure captions (if present) should explicitly label the curves corresponding to the quasi-factorized limit versus the full Lindblad evolution so that the mildness of the quantum-diffusion corrections can be assessed visually.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No major comments were listed in the report, so we have no specific points requiring rebuttal or clarification at this stage. We will prepare the revised manuscript accordingly once any additional minor suggestions are provided.

Circularity Check

0 steps flagged

Derivation self-contained from Lindblad equation

full rationale

The paper starts from the open quantum systems formalism to derive the Lindblad evolution equation for the density matrix of the quark-antiquark pair, then analyzes it in the boosted regime and correlation limit p_perp >> q_perp, Q_s to obtain the quasi-factorised Wigner distribution with the colour decoherence factor. No step reduces a claimed prediction or first-principles result to a fitted input, self-definition, or self-citation chain; the critical angle theta_c and decoherence time t_c emerge from the dynamics rather than being presupposed. The derivation remains independent of any external fitted parameters or prior author-specific uniqueness theorems.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The derivation rests on the applicability of the open-quantum-systems Lindblad master equation to a color dipole in a QCD medium and on the validity of the stated kinematic limits; no new entities are postulated.

free parameters (2)
  • hat q
    Medium transport coefficient that sets the transverse momentum broadening scale; treated as an external input characterizing the plasma.
  • L
    Longitudinal size of the plasma; external input that enters the critical angle and time scales.
axioms (2)
  • domain assumption The evolution of the quark-antiquark density matrix in the QCD plasma obeys a Lindblad master equation.
    Invoked at the outset to obtain the evolution equation for the system.
  • domain assumption The boosted regime theta_qqbar << 1 and the correlation limit p_perp >> q_perp, Q_s are physically realized and permit the quasi-factorisation.
    Stated as the regime in which the main result holds.

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