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

TL;DR

This work addresses the challenge of unifying charged-particle pseudorapidity distributions across RHIC–LHC energies, where single-source models fail at high energies and independent multi-source fits miss the central midrapidity dip. It introduces a coupled two-source Gaussian parametrization with an error-function modulation, where the coupling strength λ encodes forward–backward interactions through the medium and scales with collision energy. The analysis reveals that 1/λ scales linearly with the baryon chemical potential μ_B, while the peak-to-peak separation d_p2p and the chemical freeze-out temperature T_ch follow identical exponential saturation, linking geometric expansion to QCD thermodynamics; importantly, limiting fragmentation is preserved across all energies. The framework demonstrates predictive capability for incomplete data at 5.02 and 5.36 TeV and provides a compact, physically motivated description of particle production across nearly two orders of magnitude in energy, suggesting deep connections between source coupling, baryon stopping, and the QCD phase boundary.

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 $λ$. This coupled two-source model captures the interaction between forward and backward sources through the medium formed in the collision. Remarkably, $λ$ exhibits empirical scaling behavior resembling $1/μ_B$, 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.

Figures (10)

• Figure 1: (color online) Limitations of traditional parametrizations. Left: Single-Gaussian fits to PHOBOS data at $\sqrt{s_{NN}} = 19.6$ and $200$ GeV, illustrating the inability of a single source component to describe the broad midrapidity plateau at higher energies. Right: Double-Gaussian fits to PHOBOS ($200$ GeV) and ALICE ($2.76$ TeV) data, showing that even two independent sources fail to reproduce the characteristic central dip observed at LHC energies.
• Figure 2: (color online)(Left) Schematic illustration of the two-source picture with error function modulation for Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV. The blue and green hatched areas represent contributions from forward and backward sources; the pink overlap region visualizes source interaction near midrapidity. (Right) Pseudorapidity distributions of charged particles in central (0-5%) Au+Au collisions at RHIC and Pb+Pb collisions at LHC. Points represent experimental data, dashed curves show fits using Eq. (\ref{['eq:parametrization']}).
• Figure 3: (color online) Energy dependence of the fitted amplitude parameters $A_1$ (left) and $A_2$ (right). The dashed red curves correspond to fits using the functional form $a(\log\sqrt{s_{NN}})^{\,b} + c$, demonstrating a systematic increase of both amplitudes with collision energy. The dark red circles indicate the extrapolated values at $\sqrt{s_{NN}} = 5.02$ and $5.36$ TeV.
• Figure 4: (color online) Energy dependence of the fitted width parameters $\sigma_1$ (left) and $\sigma_2$ (right). The dashed red curves correspond to fits using the functional form $a(\log\sqrt{s_{NN}})^{\,b} + c$, indicating a systematic broadening of both source components with increasing collision energy. The dark red circles show the extrapolated values at $\sqrt{s_{NN}} = 5.02$ and $5.36$ TeV.
• Figure 5: (color online) Energy dependence of the fitted modulation parameters $\lambda_1$ (left) and $\lambda_2$ (right). The dashed red curves correspond to fits of the form $a + b\sqrt{s_{NN}}$, showing the rapid rise of both parameters at high collision energies. The dark red circles denote the extrapolated values at $\sqrt{s_{NN}} = 5.02$ and $5.36$ TeV.