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

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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{s_NN} = 39 GeV. The vertical bars represent the statistical uncertainties, and the shaded boxes denote the systematic uncertainties.

Figure 3. \Delta \sigma^2(N₁₂₀) vs N in 0--5% Au+Au collisions at six beam energies from STAR (black circles), AMPT (red area), default MUSIC+FIST (blue area), and MUSIC+FIST with an excluded-volume effect (purple area). The horizontal dashed lines represent the weighted averages of each data set, with the bands about the lines representing statistical uncertainties.

Figure 4. <\Delta \sigma^2  (N₁₂₀) > vs Reference Multiplicity for AMPT (left) and STAR (right) data. For each energy, all centrality classes are plotted with the average refmult as the x-axis value. On both plots, a dashed black line representing a reasonable fit to all AMPT data is included to guide the eye in comparison of the two data sets.

Figure 5. <\Delta \sigma^2> after subtracting the 62.4 GeV fit to remove the common trend for AMPT (left) and STAR (right).

Figure 6. Average of the values in Figure 5 over centrality to show the energy dependence of the deviation from the 62.4 GeV fit.

Figure 7. <\Delta \sigma^2> as a function of w in 0--5% Au+Au collisions at various beam energies from STAR (black circles), AMPT (red), default MUSIC+FIST (blue), and MUSIC+FIST with an excluded-volume effect (purple).

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