Investigation of the Spectator Effect on Light Nuclei Production in Nucleus-Nucleus Collisions at High Baryon Density Region

Technical Summary: Investigation of the Spectator Effect on Light Nuclei Production in Nucleus-Nucleus Collisions at High Baryon Density Region

Problem Statement
Light nuclei yields and their ratios (e.g., $N_p \times N_t / N_{2d}$) serve as sensitive probes for the QCD phase structure, particularly in the high baryon density region accessible at low-energy heavy-ion collisions (e.g., $\sqrt{s_{NN}} = 3$ GeV). A critical challenge in analyzing these yields arises from limited detector acceptance, which necessitates extrapolating measured transverse momentum ($p_T$) spectra to unmeasured low-$p_T$ regions using model-based fits (typically Blast-Wave functions). The authors posit that standard extrapolation procedures may systematically miss a significant low-$p_T$ component driven by spectator nucleons, leading to an underestimation of $p_T$-integrated light-nucleus yields, especially in peripheral collisions and at forward/backward rapidities.

Methodology
The study employs the AMPT-HC (A Multi-Phase Transport model with Hadronic Cascade), a pure hadron cascade version of AMPT designed for the few-GeV energy regime where partonic interactions are negligible. Key methodological features include:

• Initial Conditions: Nucleon positions are initialized using a Woods-Saxon density distribution, and momenta are initialized via a local Thomas-Fermi approximation to account for Fermi motion.
• Dynamics: The evolution of the system is simulated by solving Hamiltonian canonical equations in the presence of baryon mean-field potentials (controlled by an incompressibility parameter $k_0 = 380$ MeV), electromagnetic fields, and kaon potentials. Unlike high-energy models, nucleon-nucleon inelastic scattering is determined dynamically by tracking the initial and final states of collisions rather than relying solely on geometric criteria.
• Coalescence: An after-burner coalescence mechanism is applied post-kinetic freeze-out to form light nuclei (deuterons and tritons). The study utilizes a box coalescence approach with an elliptical window in phase space to account for short-range nucleon repulsion. Parameters ($r_{high}$, $p_{high}$, $r_{low}$) are optimized by minimizing the $\chi^2$ deviation against STAR experimental data in specific rapidity and centrality bins.
• Component Analysis: The model explicitly categorizes nucleons into participants (undergoing inelastic interactions), spectators (undergoing only elastic scattering or no collisions), and mixed components (nuclei formed from a combination of both).

Key Results

• Spectral Shapes: The AMPT-HC model successfully reproduces the total $p_T$ spectra of protons, deuterons, and tritons in Au+Au collisions at $\sqrt{s_{NN}} = 3$ GeV, matching STAR data qualitatively.
• Spectator Dominance at Low $p_T$: A significant enhancement of light nuclei production is observed in the low-$p_T$ region ($p_T < 0.4$ GeV/c for protons), particularly in peripheral collisions (40–80% centrality) and at backward rapidities. This enhancement is driven primarily by the spectator component, which retains the initial beam momentum and Fermi motion.
• Failure of Standard Extrapolation: When the simulated $p_T$ spectra are subjected to standard Blast-Wave fitting and extrapolation (mimicking experimental acceptance limits), the resulting integrated yields deviate significantly from the true total yields. Specifically, at backward rapidity, the Blast-Wave fit fails to capture the steep slope of the spectator-dominated low-$p_T$ region.
• Yield Underestimation: The study demonstrates that applying standard experimental extrapolation methods to the model data leads to a systematic underestimation of the total rapidity density ($dN/dy$) and total yields ($4\pi$). When the same acceptance cuts and fitting procedures are applied to the model data, the results align with the "experimental" data points, confirming that the discrepancy arises from the extrapolation method rather than the physics model itself.
• Centrality Dependence: The total yield exhibits a decreasing trend from central to peripheral collisions due to the increasing relative contribution of the spectator component, whereas mid-rapidity yields increase. This contrasts with the behavior of participant-only yields.

Significance and Claims
The paper claims that the spectator effect is a non-negligible factor in light nuclei production at high baryon densities. The primary contribution is the identification that standard extrapolation procedures, which assume a smooth $p_T$ distribution, systematically underestimate yields by missing the spectator-driven low-$p_T$ component. The authors conclude that incorporating spectator effects is essential for the precise determination of light nuclei yields in the high-baryon-density regime, which is critical for accurately probing the QCD phase structure and potential first-order phase transitions. The findings suggest that future experimental analyses in this energy region must account for these spectral distortions to avoid biased interpretations of the QCD phase diagram.