Acceptance dependence of factorial cumulants, long-range correlations, and the antiproton puzzle

Abstract

We analyze joint factorial cumulants of protons and antiprotons in relativistic heavy-ion collisions and point out that they obey the scaling ${\hat{C}}_{nm}^{p,\bar{p}}\propto ⟨N_p{⟩}^n⟨N_{\bar{p}}{⟩}^m$ as a function of acceptance when only long-range correlations are present in the system, such as global baryon conservation and volume fluctuations. This hypothesis can be directly tested experimentally without the need for corrections for volume fluctuations. We show that if correlations among protons and antiprotons are driven by global baryon conservation and volume fluctuations only, the equality ${\hat{C}}_2^p/⟨N_p{⟩}^2={\hat{C}}_2^{\bar{p}}/⟨N_{\bar{p}}{⟩}^2$ holds for large systems created in central collisions. We point out that the experimental data of the STAR Collaboration from phase I of RHIC beam energy scan are approximately consistent with the scaling ${\hat{C}}_{nm}^{p,\bar{p}}\propto ⟨N_p{⟩}^n⟨N_{\bar{p}}{⟩}^m$, but the normalized antiproton correlations are stronger than that of protons, $-{\hat{C}}_2^{\bar{p}}/⟨N_{\bar{p}}{⟩}^2>-{\hat{C}}_2^p/⟨N_p{⟩}^2$. Existing theoretical baselines, based on global baryon conservation and volume fluctuations, cannot explain the data, to which we refer as the antiproton puzzle. We also discuss high-order factorial cumulants which can be measured with sufficient precision within phase II of RHIC-BES.

10 pages, 3 figures, published version

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• Accessing proton number fluctuations in limited regions of phase space