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.