  Firstly we qualitatively analyze the formation of the dip and peak structures
of the kurtosis $\kappa \sigma^2$ of net baryon number fluctuation along
imagined freeze-out lines and discuss the signature of the existence of the QCD
critical end point (CEP) in the Nambu--Jona-Lasinio (NJL) model, Polyakov-NJL
(PNJL) model as well as $\mu$-dependent PNJL($\mu$ PNJL) model with different
parameter sets, and then we apply a realistic PNJL model with parameters fixed
by lattice data at zero chemical potential, and quantitatively investigate its
$\kappa \sigma^2$ along the real freeze-out line extracted from experiments.
The important contribution from gluodynamics to the baryon number fluctuations
is discussed. The peak structure of $\kappa \sigma^2$ along the freeze-out line
is solely determined by the existence of the CEP mountain and can be used as a
clean signature for the existence of CEP. The formation of the dip structure is
sensitive to the relation between the freeze-out line and the phase boundary,
and the freeze-out line starts from the back-ridge of the phase boundary is
required. To our surprise, the kurtosis $\kappa \sigma^2$ produced from the
realistic PNJL model along the experimental freeze-out line agrees with BES-I
data well, which indicates that equilibrium result can explain the experimental
data. It is worth to point out that the extracted freeze-out temperatures from
beam energy scan measurement are indeed higher than the critical temperatures
at small chemical potentials, which supports our qualitative analysis.
