Self-consistent interpretations of the multi-wavelength gamma-ray spectrum of LHAASO J0621$+$3755.

LHAASO J0621$+$3755 is a TeV gamma-ray halo newly identified by LHAASO-KM2A. It is likely to be generated by electrons trapped in a slow-diffusion zone around PSR J0622$+$3749 through inverse Compton scattering. When the gamma-ray spectrum of LHAASO-KM2A is fitted, the GeV fluxes derived by the commonly used one-zone normal diffusion model for electron propagation are significantly higher than the upper limits (ULs) of Fermi-LAT. In this work, we respectively adopt the one-zone superdiffusion and two-zone normal diffusion models to solve this conflict. For the superdiffusion scenario, we find that a model with superdiffusion index $\alpha\lesssim1.2$ can meet the constraints of Fermi-LAT observation. For the two-zone diffusion scenario, the size of the slow-diffusion zone is required to be smaller than $\sim50$ pc, which is consistent with theoretical expectations. Future precise measurements of the Geminga halo may further distinguish between these two scenarios for the electron propagation in pulsar halos.