Average phase factor in the PNJL model

The average phase factor of the QCD determinant is evaluated at finite quark chemical potential ({\mu}_q) with the two-flavor version of the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with the scalar-type eight-quark interaction. For {\mu}_q larger than half the pion mass at vacuum m_{\pi}, the average phase factor is finite only when the Polyakov loop is larger than 0.5, indicating that lattice QCD is feasible only in the deconfinement phase. A critical endpoint (CEP) lies in the region of the zero average phase factor. The scalar-type eight-quark interaction makes it shorter a relative distance of the CEP to the boundary of the region. For {\mu}_q < m_{\pi}/2, the PNJL model with dynamical mesonic fluctuations can reproduce lattice QCD data below the critical temperature.