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The $\pi_0$ neutral meson pole mass is calculated in a strongly magnetizedmedium using the SU(2) Nambu-Jona-Lasinio model within the random phaseapproximation (RPA) at zero temperature and zero baryonic density. We employ amagnetic field dependent coupling, $G(eB)$, fitted to reproduce lattice QCDresults for the quark condensates. Divergent quantities are handled with amagnetic field independent regularization scheme in order to avoid unphysicaloscillations. A comparison between the running and the fixed couplings revealsthat the former produces results much closer to the predictions from recentlattice calculations. In particular, we find that the $\pi_0$ meson masssystematically decreases when the magnetic field increases while the scalarmass remains almost constant. We also investigate how the magnetic backgroundinfluences other mesonic properties such as $f_{{\pi}_0}$ and $g_{\pi_0 q q}$.

$\pi_0$ pole mass calculation in a strong magnetic field and lattice constraints