Inverse magnetic catalysis in the linear sigma model: a beyond mean field approach

We explore the restoration of chiral symmetry in the linear sigma model coupled to quarks under the influence of strong magnetic fields and finite temperature, incorporating screening effects through ring diagrams. While previous studies using tree-level thermal masses lead to magnetic catalysis across all temperature ranges, in tension with lattice QCD results, we go beyond this limitation by computing the bosonic masses self-consistently within the lowest Landau level (LLL) approximation. The self-consistent approach modifies the effective potential and allows us to accurately track the thermal evolution of the order parameter. Our results reveal the emergence of a critical end point (CEP) in the T-|eB| phase diagram and, notably, exhibit inverse magnetic catalysis (IMC) behavior: the (pseudo) critical temperature decreases with increasing magnetic field strength. This is in contrast to the magnetic catalysis behavior found when non-self-consistent masses are used. To the best of our knowledge, this is the first time that self-consistent boson masses have been implemented in this context, offering a new framework for exploring the QCD phase diagram using effective models.