  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.
