Measurement of the integrated luminosity of data samples collected during 2019-2022 by the Belle II experiment

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A series of data samples was collected with the Belle~II detector at the SuperKEKB collider from March 2019 to June 2022. We determine the integrated luminosities of these data samples using three distinct methodologies involving Bhabha ($e^+e^- \to e^+e^-(n\gamma)$), digamma ($e^+e^- \to \gamma\gamma(n\gamma)$), and dimuon ($e^+e^- \to \mu^+ \mu^- (n\gamma)$) events. The total integrated luminosity obtained with Bhabha, digamma, and dimuon events is ({426.88}$\pm$ 0.03 $\pm${2.61})~fb$^{-1}$, ({429.28}$\pm$ 0.03 $\pm${2.62})~fb$^{-1}$, and ({423.99}$\pm$ 0.04 $\pm${3.83})~fb$^{-1}$, where the first uncertainties are statistical and the second are systematic. The resulting total integrated luminosity obtained from the combination of the three methods is ({427.87 $\pm$ 2.01})~fb$^{-1}$.

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