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arXiv · 2610.29499

Multi-Energy Analysis of Baryon Stopping: Extracting Non-Equilibrium Dynamics via Stochastic Rapidity Diffusion

Dhananjaya Thakur
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Abstract

We present a comprehensive extraction of baryon stopping transport properties derived from net-proton transverse momentum ($p_T$) spectra across a broad energy range, from $E_{\mathrm{lab}} = 2.0\,A\text{ GeV}$ ($\sqrt{s_{\mathrm{NN}}} = 2.70\text{ GeV}$) to $\sqrt{s_{\mathrm{NN}}} = 62.4\text{ GeV}$ in central heavy-ion collisions ($\le 10\%$ centrality). By performing a systematic, multi-rapidity blast-wave analysis of experimental invariant yields, we extract the continuous rapidity density profile $ρ_{\mathrm{net}}(y)$ and the transverse momentum broadening profile $\langle p_T^2 \rangle_{\mathrm{net}}(y)$. Utilizing a stochastic diffusion framework governed by relativistic Fokker-Planck dynamics, we analytically derive the longitudinal friction coefficient $α_{\mathrm{bw}}$, the rapidity diffusion coefficient $D_y$, the longitudinal relaxation time $τ_{\mathrm{relax}}$, and the associated longitudinal Reynolds number $\mathrm{Re}_L$. Our extracted central stopping fractions demonstrate qualitative consistency with the previous published two source thermal calculations. Crucially, the excitation function of $\mathrm{Re}_L$ reveals a drop by a factor of $\sim 163$, from $\mathrm{Re}_L \approx 4.88$ at $\sqrt{s_{\mathrm{NN}}} = 2.70\text{ GeV}$ to $\mathrm{Re}_L \approx 0.03$ at $62.4\text{ GeV}$. This provides a clear macroscopic baseline for the crossover from inertial, advection-dominated baryon stopping to thermal, diffusion-dominated nuclear transparency, establishing a solid data-driven baseline for the topological baryon junction dynamics and high-$μ_B$ matter anticipated at upcoming facilities, including FAIR, NICA, and the CEE.

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BibTeXRIS

Dhananjaya Thakur. 2026-10-21. Multi-Energy Analysis of Baryon Stopping: Extracting Non-Equilibrium Dynamics via Stochastic Rapidity Diffusion. https://arxiv.org/abs/2610.29499

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