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We study the phase diagram for strongly interacting matter using the 't Hooftdeterminant extended Nambu--Jona-Lasinio model with a Polyakov loop in thelight and strange quark sectors (\emph{up}, \emph{down} and \emph{strange})focusing on the effect of a magnetic field dependence of the coupling strengthsof these interactions. This dependence was obtained so as to reproduce recentlattice QCD results for the magnetic field dependence of the quarks dynamicalmasses.  A finite magnetic field is known to induce several additional first-orderphase transition lines with the respective Critical End Points (CEP) in thetemperature-quark chemical potential phase diagram when compared to the zeromagnetic 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 theinitial one as well as several of the new ones only survive up to a criticalmagnetic field. Only two remain in the upper limit of the studied magneticfield strength. A comparison of the results obtained with versions of the modelwith and without Polyakov loop is also done.  We also found that the inclusion of the magnetic field dependence on thecoupling strengths, while not changing the qualitative features of the phasediagram, affects the location of these CEPs. The comparison of results with andwithout a regularization cutoff in the medium part of the integrals does notshow a significant change.

european physical journal. a, hadrons and nuclei

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