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

This note presents a feasibility study and the technical details of the implementation of a measurement $in\ situ$ of the energy scale of jets reconstructed from the hadronisation of $b$-quarks ($b$-jets) and passing flavour-tagging requirements in the ATLAS experiment. The measurement uses 139 fb$^{-1}$ of proton$-$proton collisions collected in 2015$-$2018 during the second data-taking period of the Large Hadron Collider at CERN. 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 $b$-tagged jets are reconstructed with the anti-$k_t$ $R=0.4$ algorithm based on calorimeter information and have pseudorapidity $|\eta|<2.5$. The measurement relies on the measured value of the top-quark mass and is based on a template method applied to the distribution of the difference $m_{qqb} - m_{qq}$ between the three-body invariant mass of the two non $b$-tagged jets and one $b$-tagged jet ($m_{qqb}$) and the two-body invariant mass ($m_{qq}$) of the two non $b$-tagged jets in four-jet events. The measurement is both performed inclusively for $b$-tagged jets transverse momenta above 20 GeV, and for the first time, thanks to the large size of the control sample under study, differentially as a function of the $b$-tagged jet transverse momentum between 30 and 500 GeV. The specific $b$-tagged jet energy correction in data 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.