π0 pole mass calculation in a strong magnetic field and lattice constraints

The π0 neutral meson pole mass is calculated in a strongly magnetized medium using the SU(2) Nambu-Jona-Lasinio model within the random phase approximation (RPA) at zero temperature and zero baryonic density. We employ a magnetic field dependent coupling, G(eB), fitted to reproduce lattice QCD results for the quark condensates. Divergent quantities are handled with a magnetic field independent regularization scheme in order to avoid unphysical oscillations. A comparison between the running and the fixed couplings reveals that the former produces results much closer to the predictions from recent lattice calculations. In particular, we find that the π0 meson mass systematically decreases when the magnetic field increases while the scalar mass remains almost constant. We also investigate how the magnetic background influences other mesonic properties such as fπ0 and gπ0qq.