A thermo-magnetic bag model for the quark-gluon plasma

In this work we study the pressure of the quark-gluon plasma (QGP) in the presence of a weak magnetic field, using a minimally enhanced model of a weakly interacting gas of quasi-particles in a thermal bath. We include the magnetic field effects through the quark mass that has been modified using a recently proposed thermo-magnetic coupling. This thermo-magnetic coupling emerges form the quark-gluon vertex in the HTL approximation 1. We use Lattice QCD 2 data, to constrain the thermo-magnetic bag function of the quasi-particle model and provide an estimate of the thermo-magnetic vacuum energy density. We then compute the transverse pressure of the system and compare with similar results from the literature. We find that the inverse magnetic catalysis already built within this thermo-magnetic coupling allows a robust description of this Lattice QCD data for the pressure of the QGP in the presence of a weak magnetic field. The extension to the thermal quasi-particle model we have introduced here, makes it easier to pursue further phenomenological studies that require simulations with an EoS that has integrable quasi-particle thermodynamic variables which have the general features of lattice data in the weak magnetic field regime.