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The recent HAWC observations of very-high-energy $\gamma$-ray halo aroundGeminga and Monogem indicate a very slow diffusion of cosmic rays, whichresults in tiny contribution of positrons from these two pulsars to the localflux. This makes the cosmic positron excess anomaly observed by PAMELA andAMS-02 even more puzzling. However, from the Boron-to-Carbon ratio data one caninfer that the average diffusion coefficient in the Galaxy should be muchlarger. In this work we propose a two-zone diffusion model that the diffusionis slow only in a small region around the source, outside of which thepropagation is as fast as usual. We find that such a scenario can naturallyexplain the positron excess data with parameters even more reasonable than thatin the conventional one-zone diffusion model. The reason is that during thelife time of Geminga ($\sim 300$ kyr) the electrons/positrons have propagatedtoo far away with a fast diffusion and lead to a low local flux. The slowdiffusion region in the two-zone model helps to confine the electrons/positronsfor a long time and lead to an enhancement of the local flux. So under theconstraint of the HAWC observations, pulsars are still the probable origin ofthe cosmic-ray positron excess.

Two-zone diffusion of electrons and positrons from Geminga explains the positron anomaly