Phase diagram for strongly interacting matter in the presence of a magnetic field using the Polyakov-Nambu-Jona-Lasinio model with magnetic field dependent coupling strengths

We study the phase diagram for strongly interacting matter using the 't Hooft determinant extended Nambu--Jona-Lasinio model with a Polyakov loop in the light and strange quark sectors (\emph{up}, \emph{down} and \emph{strange}) focusing on the effect of a magnetic field dependence of the coupling strengths of these interactions. This dependence was obtained so as to reproduce recent lattice QCD results for the magnetic field dependence of the quarks dynamical masses. A finite magnetic field is known to induce several additional first-order phase transition lines with the respective Critical End Points (CEP) in the temperature-quark chemical potential phase diagram when compared to the zero magnetic field case. A study of the magnetic field dependence in the range $eB=0-0.6~\mathrm{GeV}^2$ of the location of these CEPs reveals that the initial one as well as several of the new ones only survive up to a critical magnetic field. Only two remain in the upper limit of the studied magnetic field strength. A comparison of the results obtained with versions of the model with and without Polyakov loop is also done. We also found that the inclusion of the magnetic field dependence on the coupling strengths, while not changing the qualitative features of the phase diagram, affects the location of these CEPs. The comparison of results with and without a regularization cutoff in the medium part of the integrals does not show a significant change.