  We investigate the QCD phase diagram and the location of the critical end
point (CEP) in the SU(2) Polyakov$-$Nambu$-$Jona-Lasinio model with
entanglement interaction giving special attention to the $\pi$ and
$\sigma$-mesons properties, namely the decay widths $\sigma\rightarrow\pi\pi$,
for several conditions around the CEP: we focus on the possible
$\sigma\rightarrow\pi\pi$ decay along the isentropic trajectories close to the
CEP since the hydrodynamical expansion of a heavy-ion collision fireball nearly
follows trajectories of constant entropy. It is expected that the type of
transition the dense medium goes through as it expands after the thermalization
determines the behavior of this decay. It is shown that no pions are produced
from the sigma decay in the chirally symmetric phase if the isentropic lines
approach the first order line from chemical potentials above it. Near the CEP
or above the $\sigma\rightarrow\pi\pi$ decay is possible with a high decay
width.
