A Coupled Source Description of Pseudorapidity Distributions from RHIC to LHC: Emergent $1/\mu_B$ Scaling and Limiting Fragmentation

Abstract

One of the most remarkable observations in heavy-ion collisions is the systematic regularity exhibited by pseudorapidity distributions of charged particles across collision energies. While single-source models fail at higher energies and independent multi-source approaches do not reproduce the central dip observed at LHC energies, a unified description across the full RHIC-LHC energy range remains elusive. These distributions from Au+Au collisions at RHIC ($\sqrt{s_{NN}}$ = 19.6--200 GeV) and Pb+Pb collisions at LHC ($\sqrt{s_{NN}}$ = 2.76--5.36 TeV) are analyzed using a novel parametrization based on coupled Gaussian sources where the interaction strength is quantified by parameter $\lambda$. This coupled two-source model captures the interaction between forward and backward sources through the medium formed in the collision. Remarkably, $\lambda$ exhibits empirical scaling behavior resembling $1/\mu_B$, suggesting sensitivity to baryon stopping and the strongly-interacting medium. All fitting parameters follow systematic energy trends, with the peak-to-peak distance and chemical freeze-out temperature exhibiting identical exponential saturation patterns, indicating that geometric expansion and thermal evolution share a common underlying dynamics governed by QCD phase structure. Furthermore, the approach naturally preserves limiting fragmentation behavior across all energies, in contrast to independent source models that suggest its violation at LHC energies. Although the theoretical basis requires further investigation, these empirical correlations successfully unify charged particle production across nearly two orders of magnitude in collision energy, revealing fundamental connections to underlying collision dynamics.