Vector interaction strength in Polyakov-Nambu-Jona-Lasinio models from hadron-quark phase diagrams

We estimate the vector interaction strength of the Polyakov-Nambu-Jona-Lasinio (PNJL) parametrizations, assuming that its transition curves should be as close as possible to the recently studied RMF-PNJL hadron-quark phase diagrams. Such diagrams are obtained matching relativistic mean-field hadronic models and the PNJL quark ones. By using this method we found for the magnitude of the vector interaction, often treated as a free parameter, a range of 7.66 GeV-2 less than or similar to G(V) less than or similar to 16.13 GeV-2, or equivalently, 1.52 less than or similar to G(V)/G(s) less than or similar to 3.2, with G(s) being the scalar coupling constant of the model. These values are compatible but restrict the range of 4 GeV-2 less than or similar to G(V) less than or similar to 19 GeV-2, recently obtained from lattice QCD data through a different mean-field model approach.