We studied the effects of centrality fluctuation and deuteron formation on the cumulants ($C_n$) and correlation functions ($kappa_n$) of protons up to sixth order in most central ($b<3$ fm) Au+Au collisions at $sqrt{s_mathrm{NN}}$ = 3 GeV from a microscopic transport model (JAM). The results are presented as a function of rapidity acceptance within transverse momentum $0.4<p_{T}<2 $ GeV/$c$. We compared the results obtained by centrality bin width correction (CBWC) using charged reference particle multiplicity with CBWC done using impact parameter bins. It was found that at low energies the centrality resolution for determining the collision centrality using charged particle multiplicities is not good enough to reduce the initial volume fluctuations effect for higher-order cumulant analysis. New methods need to be developed to classify events with high centrality resolution for heavy-ion collisions at low energies. Finally, we observed that the formation of deuteron will suppress the higher-order cumulants and correlation functions of protons and is found to be similar to the efficiency effect. This work can serve as a noncritical baseline for the QCD critical point search at the high baryon density region.
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