Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC

Abstract: We report the beam energy (\sqrt s_{NN} = 7.7 - 200 GeV) and collision centrality dependence of the mean (M), standard deviation (\sigma), skewness (S), and kurtosis (\kappa) of the net-proton multiplicity distributions in Au+Au collisions. The measurements are carried out by the STAR experiment at midrapidity (|y| < 0.5) and within the transverse momentum range 0.4 < pT < 0.8 GeV/c in the first phase of the Beam Energy Scan program at the Relativistic Heavy Ion Collider. These measurements are important for understanding the Quantum Chromodynamic (QCD) phase diagram. The products of the moments, S\sigma and \kappa\sigma^{2}, are sensitive to the correlation length of the hot and dense medium created in the collisions and are related to the ratios of baryon number susceptibilities of corresponding orders. The products of moments are found to have values significantly below the Skellam expectation and close to expectations based on independent proton and anti-proton production. The measurements are compared to a transport model calculation to understand the effect of acceptance and baryon number conservation, and also to a hadron resonance gas model.

• The paper presents an analysis of net-proton moments (M, σ, S, κ) using energy-dependent heavy-ion collisions to probe QCD phase structures.
• The paper finds significant deviations from Skellam expectations, indicating potential signatures of critical phenomena near the QCD critical point.
• The paper compares experimental data with UrQMD and HRG models, providing insights into baryon number susceptibilities and the QCD phase diagram.

Analysis of the Energy Dependence of Net-Proton Multiplicity Distributions at RHIC

The article investigates the energy and centrality dependence of moments in net-proton multiplicity distributions within the context of high-energy heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC). Conducted by the STAR Collaboration, this study utilizes the Beam Energy Scan (BES) program to explore Quantum Chromodynamics (QCD) phase structures across a range of beam energies, specifically focusing on the quantum phase transitions and critical points important in the study of QCD matter. Quantifying fluctuations in net-proton distributions through mean (M), standard deviation (σ), skewness (S), and kurtosis (κ), the authors attempt to elucidate the behavior of strongly interacting matter, integral to understanding the QCD phase diagram.

Key Findings

1. Energy and Centrality Dependence: The work reveals that higher moments such as skewness and kurtosis, and their products with standard deviation, display energy-dependent trends across a variety of collision centralities. These moments are particularly sensitive to the correlation length of the QCD medium.
2. Deviation from Skellam Expectations: Importantly, the measurements diverge from Skellam distributions, often employed as a baseline to assume independent random particle production, instead reflecting effects akin to those predicted by QCD-based calculations that consider a phase critical point (CP).
3. Comparison with Models: To comprehend these deviations, the study juxtaposes empirical results with theoretical models such as the UrQMD transport model (lacking a critical point) and a hadron resonance gas (HRG) model, assessing consistency and highlighting potential signatures of critical phenomena in QCD.
4. Observations on Baryon Number Susceptibilities: The second-order and fourth-order net-baryon susceptibilities, essential in evaluating critical phenomena, are scrutinized. The study links deviations in moment products, specifically $S\sigma$ and $\kappa\sigma^2$, to the experimental signature of the QCD critical point.

Implications and Future Directions

The paper provides substantial insights into the experimental search for the QCD critical point, bolstered by accurate measurements of moment fluctuations over a vast energy range (corresponding to varying baryonic chemical potentials, $\mu_B$). The findings bolster the hypothesis that signs of critical phenomena may manifest in non-monotonic behaviors within moment products, warranting further exploration both experimentally and through advanced theoretical models. Enhancements to experimental techniques and more sophisticated calculations incorporating dynamic evolution and finite-size effects may better elucidate transition dynamics and critical behaviors inherent in QCD.

In conclusion, the study of net-proton multiplicity distributions and moment analyses stands crucial in refining our comprehension of the QCD phase diagram. This research contributes valuable data for ongoing theoretical-experimental synergy aimed at pinpointing the QCD critical point and further understanding the nature of strongly interacting matter under extreme conditions.