Multi-peak structure of meson spectral function in magnetic field

We investigate the spectral functions of neutral and charged mesons in a hot dense medium under a external magnetic field using the two-flavor quark-meson model within the functional renormalization group (FRG) framework. Our results show that the spectral functions of {\sigma} and {\pi}0 mesons develop new structures due to decay channels into quarks occupying different Landau levels. By consistently incorporating the momentum relations at vertices for charged particles in a magnetic field, we further show that the {\pi}+ spectral function develops a multi-peak structure at finite temperatures, resulting from the various annihilation and decay channels available to {\pi}+ in the magnetic environment. This multi-peak structure is further enhanced in a finite-density medium, causing the {\pi}+ meson to become a broad resonance at lower temperatures and densities compared to neutral mesons. Such a multi-peak pattern is expected to be universal for charged mesons under magnetic fields and carries significant implications for understanding transport properties in magnetized strongly interacting fluids