A measurement of $b$-hadron pair production is presented, based on a dataset corresponding to an integrated luminosity of 11.4 fb${}^{-1}$ of proton--proton collisions recorded at $\sqrt{s}=8$ TeV with the ATLAS detector at the LHC. Events are selected in which both a $b$-hadron $\to J/\psi(\to\mu\mu)+X$ and $b$-hadron $\to \mu + X$ were identified, and results are presented in a fiducial volume defined by kinematic requirements on three muons based on those used in the analysis. The fiducial cross section is measured to be $17.7\pm 0.1$(stat.)$\pm2.0$(syst.) nb. A number of normalised differential cross sections are i also measured, and compared to predictions from the Pythia8, Herwig++, MadGraph5\_aMC@NLO+Pythia8 and Sherpa event generators, providing constraints on heavy flavour production.
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