Chiral dynamics in a magnetic field from the functional renormalization group

We investigate the quark-meson model in a magnetic field using the functional renormalization group equation beyond the local-potential approximation. Our truncation of the effective action involves anisotropic wave function renormalization for mesons, which allows us to investigate how the magnetic field distorts the propagation of neutral mesons. Solving the flow equation numerically, we find that the transverse velocity of mesons decreases with the magnetic field at all temperatures, which is most prominent at zero temperature. The meson screening masses and the pion decay constants are also computed. The constituent quark mass is found to increase with magnetic field at all temperatures, resulting in the crossover temperature that increases monotonically with the magnetic field. This tendency is consistent with most model calculations but not with the lattice simulation performed at the physical point. Our work suggests that the strong anisotropy of meson propagation may not be the fundamental origin of the inverse magnetic catalysis.