${\pi }_0$ pole mass calculation in a strong magnetic field and lattice constraints

Abstract

The ${\pi }_0$ 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 ${\pi }_0$ 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 $f_{{\pi }_0}$ and $g_{{\pi }_{0}qq}$.

Comments: 7 pages, 5 figures, v2 PLB version