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A bstract We report on the first measurement of the Central Exclusive Production process in proton-proton collisions: pp → ph + h − p (where h = π , K , p ) at the center-of-mass energy $$\sqrt{s}=510$$ GeV with the STAR experiment at RHIC. At this energy, the process is dominated by a double Pomeron exchange mechanism. Hence, it provides a clean environment for investigating Pomeron interactions by measuring fully reconstructed final states involving only two hadrons and two forward scattered protons. The oppositely charged hadron pairs are measured within the central detector of STAR. The forward scattered protons are measured in the Roman Pot system allowing the verification of the event’s exclusivity. Differential fiducial cross sections within the STAR acceptance are presented as a function of the difference in the azimuthal angle between the outgoing protons. The invariant masses of the charged hadron pairs are measured up to approximately 3 GeV and the square of the four-momentum transfer ( t 1 and t 2 ) of the two forward-scattered protons in the range 0.3 GeV 2 < − t 1 , − t 2 < 1.6 GeV 2 . The differential fiducial cross sections of the forward protons as a function of the | t 1 + t 2 | are also presented. All results for the π + π − pair are presented in three mass ranges. A comparison with GRANIITTI Monte Carlo predictions are also presented, where the spectra include continuum and resonant contributions. The observed spectra are consistent with double Pomeron exchange, including resonances seen in previous studies.