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Paper Proposal: Search for Proton Clustering in Au+Au collisions from the RHIC Beam Energy Scan I

Updated on Wed, 2025-07-16 15:59 by dneff. Originally created by yunshancheng on 2025-01-26 23:31.

Paper title: Search for Proton Clustering in Au+Au collisions at \sqrt{sNN} = 7.7, 11.5, 19.6, 27, 39, and 62.4 GeV at RHIC

PAs: Yunshan Cheng, Huan Huang, Dylan Neff, Gang Wang
Target Journal: PRC

Paper Draft: ver2 
Analysis Note: ver1

Comments & Discussions
Comments from PWG Paper Proposal 5/8/25
Comments from PWGC Paper Preview 7/11/25

Abstract:
Proton clustering in high-energy heavy-ion collisions may serve as an experimental probe of a first-order phase transition in the Quantum Chromodynamics phase diagram. In this work, we report STAR measurements of the novel \Delta\sigma^2 observable to search for proton clustering using data from the first phase of the Beam Energy Scan program at the Relativistic Heavy Ion Collider. The \Delta\sigma^2 observable quantifies azimuthal correlations among protons by comparing their variance in localized partitions to a binomial baseline. We analyze Au+Au collision data at \sqrt{sNN} = 7.7, 11.5, 19.6, 27, 39, and 62.4 GeV and compare the results with model predictions from AMPT and MUSIC+FIST. Our findings reveal significantly negative \Delta\sigma^2 values, suggesting a repulsive correlation among protons that strongly depends on event multiplicity and qualitatively resembles the effects of global transverse momentum conservation. While correlation strengths versus multiplicity in AMPT simulations follow an energy-independent universal curve, STAR data exhibit an energy-dependent trend. Additionally, we extract the correlation range among protons by examining the partition width dependence of \Delta\sigma^2.

Figures for the paper:


Figure 1. Example event with six total protons, including three within a 120° (shaded area). Red arrows represent the directions of the proton momenta.


Figure 2. \Delta \sigma^2 with w = 120° vs the total proton multiplicity (N) from the same events (circle), the mixed events (square), and the difference (star) in the most central 0--5% Au+Au collisions at \sqrt{sNN} = 39 GeV. The vertical bars represent the statistical uncertainties, and the shaded boxes denote the systematic uncertainties.


Figure 3. The dependence of \Delta \sigma^2(w = 120°) on Np is shown for three levels of correction: uncorrected (circles), corrected using mixed events (squares), and further corrected for v2 (stars), for 30-40% Au+Au collisions at \sqrt{sNN} = 39 GeV.

The vertical bars represent the statistical uncertainties, and the shaded boxes denote the systematic uncertainties. Some points are slightly shifted horizontally to improve clarity.


Figure 4. Event plane resolution < cos[2(\Psi2f -\Psi2b )] > as a function of centrality in Au+Au collisions at \sqrt{sNN} = 7.7-62.4 GeV. Only the statistical uncertainties are shown. Some points are slightly shifted horizontally to improve clarity.


Figure 5. Proton v2{\eta-sub} as a function of centrality in Au+Au collisions at \sqrt{sNN} = 7.7-62.4 GeV. Only the statistical uncertainties are shown. Some points are slightly shifted horizontally to improve clarity.


Figure 6. \Delta \sigma^2 (w=120°) vs Np in 0--5% Au+Au collisions at six beam energies from STAR data (red circles). The vertical bars represent the statistical uncertainties, and the shaded boxes denote the systematic uncertainties. For comparison, we also plot simulations from AMPT (blue bands), default MUSIC+FIST (black bands), and MUSIC+FIST with an excluded-volume effect (gray bands). The horizontal dashed lines represent the weighted averages <\Delta \sigma^2>  of each data set, obtained with Eq. 9.


Figure 7. (a) < \Delta \sigma^2  (w=120°) > vs Npart from STAR data (open markers) and AMPT simulations (dashed lines) at the beam energies under study. The solid curve represents the universal fit using Eq. 11. (b) STAR data after subtraction of the universal fit curve. Some points are slightly shifted horizontally to improve clarity.


Figure 8. Same as Fig. 7, but as a function of RefMult.


Figure 9. <\Delta \sigma^2 > as a function of w in 0--5% Au+Au collisions at various beam energies from STAR (red circles). The vertical bars represent the statistical uncertainties, and the shaded boxes denote the systematic uncertainties. For comparison, we also plot simulations from AMPT (blue bands), default MUSIC+FIST (black bands), and MUSIC+FIST with an excluded-volume effect (gray bands). The STAR points are fit using a quadratic function described in Eq. 12.

Figure 10. The baseline b as a function of RefMult from STAR data. b is extracted using the quadratic fit to < \Delta \sigma^2(w) >, as defined in Eq. 12. The vertical bars represent the statistical uncertainties, and the shaded boxes denote the systematic uncertainties. The solid curves represent the fits using Eq. 11. For comparison, we also plot AMPT simulations (dashed lines).

Figure 11. Fit parameters (a) C0, (b) C1, and (c) n as a function of collision energy from Fig. 10  using Eq. 11. The vertical bars represent the statistical uncertainties, and the shaded boxes denote the systematic uncertainties. For comparison, the AMPT resutls are shown with open circles.


Figure 12. The inverse curvature z as a function of RefMult from (a) STAR data and (b) AMPT simulations. z is extracted using the quadratic fit to < \Delta \sigma^2 (w)) >, as defined in Eq. 12. The vertical bars represent the statistical uncertainties, and the shaded boxes denote the systematic uncertainties. The solid curve represents a second-order polynomial fit.

Conclusion:

We report the STAR measurements of the novel \Delta \sigma^2 observable for protons using RHIC BES-I data at six energies ranging from \sqrt{sNN}= 7.7 to 62.4 GeV. This observable is sensitive to azimuthal correlations among protons, with potential implications for proton clustering in the presence of a first-order phase transition. Our results reveal significantly negative < \Delta \sigma^2 > values in STAR data, indicating a repulsive interaction between protons. The strength of this repulsion increases at lower event multiplicities, qualitatively consistent with the effects of global transverse momentum conservation.
At a fixed partition of w=120°, the STAR data from all examined energies seem to follow a universal trend of < \Delta \sigma^2 > vs Npart, whereas the AMPT calculations predict a scaling with RefMult.
We further investigate the dependence of <\Delta \sigma^2 > on partition width and extract the general scale b and the inverse curvature z of proton correlations. While b exhibits behavior akin to <\Delta \sigma^2(w=120°) >, the z values as a monotonic function of RefMult from all energies fall on a unversal cruve. Conversely, AMPT shows minimal dependence of z on RefMult. 
We have also made an initial attempt to correct for the momentum conservation effect. By decomposing <\Delta \sigma^2 > or b into two components---a constant C0 and a momentum-conservation-inspired term as defined in Eq. 11---we project the measurements to the high-multiplicity limit, where the effect of momentum conservation diminishes. The C0 thus obtained remains positive, indicating clustering behavior, and exhibits a monotonic trend decreasing at lower energies, except for a potential disruption at 7.7 GeV. The current precision of the data prevents a firm conclusion and warrants further investigation with much higher statistics and a finer energy scan from the RHIC BES-II program. During data taking at BES-II, the STAR Event Plane Detector was available, providing forward event planes that help improve elliptic flow measurements by suppressing nonflow contributions.
 

Previous Presentations:

Related Method paper: https://journals.aps.org/prc/abstract/10.1103/PhysRevC.110.064905

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