Probing deconfinement in a chiral effective model with Polyakov loop at imaginary chemical potential

The phase structure of the two-flavor Polyakov-loop extended Nambu-Jona-Lashinio model is explored at finite temperature and imaginary chemical potential with a particular emphasis on the confinement-deconfinement transition. We point out that the confined phase is characterized by a $\cos 3{\mu }_I\mathrm{/}T$ dependence of the chiral condensate on the imaginary chemical potential while in the deconfined phase this dependence is given by $\cos {\mu }_I\mathrm{/}T$ and accompanied by a cusp structure induced by the Z(3) transition. We demonstrate that the phase structure of the model strongly depends on the choice of the Polyakov loop potential $\mathcal{U}$. Furthermore, we find that by changing the four fermion coupling constant $G_s$, the location of the critical endpoint of the deconfinement transition can be moved into the real chemical potential region. We propose a new parameter characterizing the confinement-deconfinement transition.