  We use the linear sigma model with quarks to study the magnetic-field-induced
modifications on the longitudinal screening mass for the neutral pion at
one-loop level. The effects of the magnetic field are introduced into the
self-energy, which contains the contributions from all the model particles. We
find that, to obtain a reasonable description for the behavior with the field
strength, we need to account for the magnetic field dependence of the particle
masses. We also find that the couplings need to decrease fast enough with the
field strength to then reach constant and smaller values as compared to their
vacuum ones. The results illustrate the need to treat the magnetic corrections
to the particle masses and couplings in a self-consistent manner, accounting
for the backreaction of the field effects for the magnetic field dependence of
the rest of the particle species and couplings in the model.
