# Proton Cumulants and Correlation Functions in Au + Au Collisions at $\sqrt{s_\mathrm{NN}}$=7.7-200 GeV from UrQMD Model

## TL;DR

This study uses the UrQMD model to analyze proton cumulants and correlation functions in central Au+Au collisions across a range of energies, revealing suppression effects, correlation behaviors, and limitations of the model in describing experimental non-monotonic energy dependencies.

## Contribution

It provides a detailed analysis of proton cumulants and correlation functions dependence on acceptance and energy, establishing UrQMD as a baseline and proposing new measurements for QCD critical point searches.

## Key findings

- High order proton cumulants show suppression at large acceptance.
- Two-proton correlation functions are consistently negative due to baryon number conservation.
- UrQMD fails to reproduce the non-monotonic energy dependence observed in experimental data.

## Abstract

We studied the acceptance dependence of proton cumulants (up to fourth order) and correlation functions in 0--5\% most central Au+Au collisions at $\sqrt{s_\text{NN}}$=7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV from UrQMD model. We found that high order proton cumulants show suppressions at large acceptance. By decomposing the proton cumulants into linear combination of multi-proton correlation functions, we observed the two-proton correlation functions always show negative values due to the effects of baryon number conservations. The three and four-proton correlation functions are close to zero and show negligible acceptance dependence. We further observed that the proton cumulants and correlation functions follow similar trends and show a scaling behavior when plotting the results versus mean number of protons. The comparisons between experimental data and the UrQMD calculations show that the non-monotonic energy dependence of proton correlation functions measured by STAR experiment cannot be described by the UrQMD model. The UrQMD calculations can provide us baselines for the experimental studies of the proton cumulants and correlation functions. Finally, we propose to measure the rapidity dependence of the reduced proton correlation functions to search for the QCD critical point in heavy-ion collisions.