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Impacts of (inverse) magnetic catalysis on screening masses of neutral pions and sigma mesons in hot and magnetized quark matter

We investigate the screening masses of neutral pions and sigma mesons in hot and magnetized quark matter in the framework of a two-flavor lattice-improved Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling constant, which is determined by utilizing the results from lattice QCD simulations. Since such model can well reproduce inverse magnetic catalysis (IMC), by comparing with the standard NJL model, we systemically analyze the impacts of IMC on the temperature and magnetic field dependences of the longitudinal and transverse screening masses of the chiral partners, i.e. π^0 and σ mesons, as well as the screening mass differences between them. Particularly, it is found that the eB dependences of two alternative (pseudo)critical temperatures for the chiral transition defined by σ-π^0 meson screening mass differences are consistent with that defined by the quark condensate.