Dynamical Causal Horizons and the Quarkonium Flow Paradox

Abstract

The sequential suppression of heavy quarkonia in ultra-relativistic $A+A$ collisions is conventionally interpreted as evidence of a thermalized Quark-Gluon Plasma. However, the simultaneous observation of vanishing elliptic flow ($v_2 \approx 0$) for bottomonium contradicts the path-length dependence inherent in macroscopic transport models. We propose a geometric resolution: quarkonium suppression is governed by the extreme spacetime geometry generated during initial fragmentation, rather than continuous late-stage partonic scattering. The intense color string tension induces extreme local deceleration, giving rise to a dynamical Hawking-Unruh causal horizon. By employing the bottomonium ($Υ$) family as pristine quantum rulers, we demonstrate that dissociation is a causal event determined at the earliest moments ($τ\lesssim 0.1$ fm/$c$). The dynamical horizon restricts the maximum causal range over which the evolving wave packet can maintain quantum coherence. When the intrinsic bound-state radius exceeds the local Unruh horizon ($r_{nS} > r_H$), the heavy quark pair is causally decoupled. This framework yields a single-scale analytical nuclear modification factor $R_{AA} = \exp[-κr_{nS} (N_{\text{part}}^{1/3} - N_{pp}^{1/3})]$, which naturally reproduces the suppression hierarchy observed in Pb+Pb collisions without state-by-state tuning. Crucially, because this instantaneous scalar decoupling preserves primordial momentum isotropy, kinematic independence and $v_2 \approx 0$ emerge as robust geometric expectations, providing a testable mechanism that bridges subatomic fragmentation and causal event horizons.

Figures (3)

• Figure 1: (a) Comparison between the analytical Horizon Model and CMS Pb+Pb 5.02 TeV data for $\Upsilon(nS)$$R_{AA}$ vs $N_{\text{part}}$. The single scale $\kappa = 0.63 \text{ fm}^{-1}$ is anchored to the QCD $T_c$. (b) Geometric dissociation threshold: bound states undergo continuous quantum tunneling suppression ($\mathcal{S} \propto e^{-r_{nS}/r_H}$). The indicated $r_H \approx 0.47$ fm corresponds to typical mid-central collisions, where the causal geometry actively severs larger excited states while partially suppressing the ground state.
• Figure 2: (a) $\Upsilon$$R_{AA}$ vs $p_T$ for Pb+Pb 5.02 TeV, demonstrating the kinematic independence of the causal limit. (b) The Double Ratio $\Upsilon(2S)/\Upsilon(1S)$ as a function of $N_{\text{part}}$, governed strictly by the radius difference $\Delta r$.
• Figure 3: Resolving the Flow Paradox. While transport models predict persistent flow due to path-length dependence, our Causal Horizon theory identifies a convergence to $v_2=0$ for both $J/\psi$ ($M_c$) and $\Upsilon$ ($M_b$) at high $p_T$. This figure illustrates the contrasting geometric expectations consistent with ATLAS and CMS data.