Topological $b$-hadron decay reconstruction and identification of $b$-jets with the JetFitter package in the ATLAS experiment at the LHC

The identification of jets containing heavy flavour hadron decays, in particular $b$ jets, plays a major role in the LHC physics program. The topology of $b \rightarrow c \rightarrow s$ decays with two detached vertices corresponding to the $b$- and $c$-flavoured hadron decays, sizeable secondary and tertiary decay multiplicities and relatively large invariant mass gives a very distinctive signature for the identification of $b$-jets. This note discusses the algorithm developed for the topological reconstruction of $b$-flavoured hadron decays in ATLAS, its implementation and performance.