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We report a search for a dark photon using ~fb of annihilation data taken at center-of-mass energies from 4.13 to 4.60~GeV with the BESIII detector operated at the BEPCII storage ring. The dark photon is assumed to be produced in the radiative annihilation process of and to predominantly decay into light dark matter particles, which escape from the detector undetected. The mass range from 1.5 to 2.9~GeV is scanned for the dark photon candidate, and no significant signal is observed. The mass dependent upper limits at the 90 confidence level on the coupling strength parameter for a dark photon coupling with an ordinary photon vary between and .

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