$D^0$ Reconstruction in $b$-jets for Events with $Z^0\rightarrow \mu^+\mu^-$ + $b$-jet

A Monte Carlo study on $b$-jet heavy quark fragmentation in ATLAS using fully reconstructed hadronic $D$ mesons is presented. Events with a $Z^0\rightarrow \mu^+\mu^-$ and a $b$-jet where $b\rightarrow D+X$ were studied. Several charmed hadronic modes were reconstructed. Presented here are the decay channels $D^0\rightarrow K^-\pi^+$ and D$^{*+}\rightarrow D^0\pi^+, D^0\rightarrow K^- \pi^+ $. The mass resolution of the $D^0$ and $D^{*+}$ is reported as well as the yield and reconstruction efficiencies for each species and the shape of the $b$-jet in terms of the $p_{\mathrm{T}}$ distribution of the $D$ meson with respect to the jet axis. When these measurements are repeated with and compared to real LHC data, they will provide important information on the $b$-quark parton distribution inside the proton, and on the $b$-quark fragmentation distribution. Moreover, the analysis, when applied to real data, will give a better understanding of QCD backgrounds and provide an additional tool to constrain the $b$-jet energy scale.