Average phase factor in the Polyakov-loop extended Nambu-Jona-Lasinio model

The average phase factor ⟨e^2iθ⟩ of the QCD determinant is evaluated at the finite quark chemical potential (μ_q) with the two-flavor version of the Polyakov-loop extended Nambu-Jona-Lasinio model with the scalar-type eight-quark interaction. For μ_q larger than half the pion mass m_π at vacuum, ⟨e^2iθ⟩ 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 end point lies in the region of ⟨e^2iθ⟩=0. The scalar-type eight-quark interaction makes it shorter a relative distance of the critical end point to the boundary of the region. For μ_q<m_π/2, the Polyakov-loop extended Nambu-Jona-Lasinio model with dynamical mesonic fluctuations can reproduce lattice QCD data below the critical temperature.