The dark photon is widely predicted in many new physics beyond the Standard Model. In this work, we propose to utilize the polarized lepton cross section and single-spin asymmetry in neutral current DIS process at the HERA and upcoming Electron-Ion Collider (EIC) to probe the properties of the dark photon. It shows that we can constrain the mixing parameter ϵ<0.02 when the dark photon mass mAD<10GeV at the HERA with polarized lepton beam and this bound is comparable to the limit from the unpolarized data of HERA I and II. With the help of high integrated luminosity and high electron beam polarization of the EIC, the upper limit of the ϵ could be further improved. Depending on the assumption of the systematic error of the cross section measurements, we obtain ϵ<0.01∼0.02 for the mass region mAD<10GeV under the integrated luminosity of 300fb−1. A similar and robust upper limit for the ϵ could be obtained from the single-spin asymmetry measurement, which is not depending on the assumption of the systematic errors.
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