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

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${}^{-1}$.