Functional renormalization group study of neutral and charged pions in magnetic fields in the quark-meson model
Rui Wen, Shi Yin, Wei‐jie Fu, Mei Huang
Abstract
We calculated the masses of neutral and charged pions and pion decay constants in magnetic fields at zero temperature. The quantum fluctuations are integrated through the functional renormalization group. We consider the quark and meson propagators in the Landau level representation and weak-field expansion, respectively. The neutral pion mass monotonically decreases with the magnetic field, while the charged pion mass monotonically increases with the magnetic field. The pion decay constant and the quark mass show the magnetic catalysis behavior at vanishing temperature. The neutral pion mass and pion decay constant are quantitatively in agreement with the lattice QCD results in the region of $eB<1.2\text{ }\text{ }{\mathrm{GeV}}^{2}$, and no nonmonotonic mass behavior for charged pions has been observed in this framework.