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Reconcile the AMS-02 positron fraction and Fermi-LAT/HESS total $e^{\pm}$ spectra by the primary electron spectrum hardening

The recently reported positron fraction up to $\sim 350$ GeV by AMS-02 seems to have tension with the total electron/positron spectra detected by Fermi and HESS, for either pulsar or dark matter annihilation/decay scenario as the primary positron sources. In this work we will show that the tension will be removed by an adjustment of the primary electron spectrum. If the primary electron spectrum becomes harder above $\sim50$ GeV, similar as the cosmic ray nuclei spectrum, the AMS-02 positron fraction and Fermi/HESS data can be well fitted by both the pulsar and dark matter models. This result indicates that there should be a common origin of the cosmic ray nuclei and the primary electrons. Furthermore, this study also implies that the properties of the extra sources derived from the fitting to the AMS-02 data should depend on the form of background.