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We use the Linear Sigma Model with quarks to study the magnetic field-inducedmodifications on the longitudinal screening mass for the neutral pion atone-loop level. The effects of the magnetic field are introduced into theself-energy which contains the contributions from all the model particles. Wefind that to obtain a reasonable description for the behavior with the fieldstrength, the magnetic field dependence of the particle masses need to beaccounted for. We also find that the couplings need to decrease fast enoughwith the field strength to then reach constant and smaller values as comparedto their vacuum ones. The results illustrate the need to treat the magneticcorrections to the particle masses and couplings in a self-consistent manner,accounting for the back reaction of the field effects for the magnetic fielddependence of the rest of the particle species and couplings in the model.

Magnetic field dependence of the neutral pion longitudinal screening mass in the linear sigma model with quarks