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Several observables sensitive to the fragmentation of $b$-quarks into$b$-hadrons are measured using 36 fb${}^{-1}$ of $\sqrt s = 13$ TeVproton-proton collision data collected with the ATLAS detector at the LHC. Jetscontaining $b$-hadrons are obtained from a sample of dileptonic $t\bar{t}$events, and the associated set of charged-particle tracks is separated intothose from the primary $pp$ interaction vertex and those from the displaced$b$-decay secondary vertex. This division is used to construct observables thatcharacterize the longitudinal and transverse momentum distributions of the$b$-hadron within the jet. The measurements have been corrected for detectoreffects and provide a test of heavy-quark-fragmentation modeling at the LHC ina system where the top-quark decay products are color-connected to the protonbeam remnants. The unfolded distributions are compared with the predictions ofseveral modern Monte Carlo parton-shower generators and generator tunes, and awide range of agreement with the data is observed, with $p$-values varying from$5 \times 10^{-4}$ to 0.98. These measurements complement similar measurementsfrom $e^+e^-$ collider experiments in which the $b$-quarks originate from acolor-singlet $Z/\gamma^*$.

Measurements of jet observables sensitive to $b$-quark fragmentation in $t\bar{t}$ events at the LHC with the ATLAS detector