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We use the linear sigma model with quarks to find the magnetic field-inducedmodifications to the neutral pion mass at one-loop level. The magnetic fieldeffects are introduced by using charged particle propagators in the presence ofa magnetic background in the strong field regime. We show that when accountingfor the effects of the magnetic field on the model couplings, the vacuum sigmafield and the neutral pion self-energy, the neutral pion mass decreasesmonotonically as a function of the field strength. We find an excellentqualitative and quantitative agreement with recent lattice QCD calculations,reproducing the monotonically decreasing trend with the field strength as wellas the decrease when lattice data approaches the physical vacuum pion mass fromlarger values.

Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case