Light charged pion in ultra-strong magnetic field

In this work, the mass of charged pions is investigated in the presence of background magnetic fields stronger than the energy scale of QCD. We introduce an anomaly magnetic momentum term in the Dirac equation and obtain the quark propagator as consequence. We find a novel finite Landau level, denoted as $tl$LL, becoming dominant rather than the conventional lowest Landau level. We examine that, due to the shifting of Landau level, it drives a mass decreasing around $eB\sim 0.8~\mathrm{GeV}^2$ for charged pions and their masses drastically limit to the neutral one at ultra-strong magnetic field, $eB\sim 1.6~\mathrm{GeV}^2$, which is consistent with the recent lattice simulation.