Energy scale calibration of $b$-tagged jets with ATLAS Run 2 data using $t\bar{t}$ lepton+jets events

A feasibility study is presented for an in situ measurement of the energy scale of jets reconstructed from the hadronisation of $b$-quarks ($b$-jets) and passing flavour-tagging requirements in the ATLAS experiment. Proton--proton ($pp$) collisions collected in 2015--2018 during the second data-taking period of the Large Hadron Collider (LHC) at CERN are used. A sample enriched in $b$-jets is selected in events with a $t\bar{t}$ lepton+jets signature consistent with the process $pp\to t\bar{t} \to \ell\nu q\bar{q}b\bar{b}$ ($\ell=e,\mu$). The measurement is both performed inclusively for $b$-tagged jets transverse momenta above 20 GeV, and for the first time, differentially as a function of the $b$-tagged jet transverse momentum between 30 and 500~GeV. The $b$-tagged jet energy correction is consistent with unity, with an uncertainty of 2.5% for the inclusive measurement, and decreasing from 4% to 1.9% for $b$-tagged jet transverse momenta increasing between 30 and 500 GeV for the differential measurement.