The OLYMPUS experiment measured the cross-section ratio of positron-proton elastic scattering relative to electron-proton elastic scattering to look for evidence of hard two-photon exchange. To make this measurement, the experiment alternated between electron beam and positron beam running modes, with the relative integrated luminosities of the two running modes providing the crucial normalization. For this reason, OLYMPUS had several redundant luminosity monitoring systems, including a pair of electromagnetic calorimeters positioned downstream from the target to detect symmetric M{o} ller and Bhabha scattering from atomic electrons in the hydrogen gas target. Though this system was designed to monitor the rate of events with single M{o} ller/Bhabha interactions, we found that a more accurate determination of relative luminosity could be made by additionally considering the rate of events with both a M{o} ller/Bhabha interaction and a concurrent elastic $ep$ interaction. This method was improved by small corrections for the variance of the current within bunches in the storage ring and for the probability of three interactions occurring within a bunch. After accounting for systematic effects, we estimate that the method is accurate in determining the relative luminosity to within 0.36%. This precise technique can be employed in future electron-proton and positron-proton scattering experiments to monitor relative luminosity between different running modes.
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