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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 UrQMDmodel. We found that high order proton cumulants show suppressions at largeacceptance. By decomposing the proton cumulants into linear combination ofmulti-proton correlation functions, we observed the two-proton correlationfunctions always show negative values due to the effects of baryon numberconservations. The three and four-proton correlation functions are close tozero and show negligible acceptance dependence. We further observed that theproton cumulants and correlation functions follow similar trends and show ascaling behavior when plotting the results versus mean number of protons. Thecomparisons between experimental data and the UrQMD calculations show that thenon-monotonic energy dependence of proton correlation functions measured bySTAR experiment cannot be described by the UrQMD model. The UrQMD calculationscan provide us baselines for the experimental studies of the proton cumulantsand correlation functions. Finally, we propose to measure the rapiditydependence of the reduced proton correlation functions to search for the QCDcritical point in heavy-ion collisions.

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