B-hadron hadro-production in NNLO QCD: application to LHC $t\bar{t}$ events with leptonic decays

We calculate, for the first time, the NNLO QCD corrections to identified heavy hadron production at hadron colliders. The calculation is based on a flexible numeric framework which allows the calculation of any distribution of a single identified heavy hadron plus jets and non-QCD particles. As a first application we provide NNLO QCD predictions for several differential distributions of $B$ hadrons in $t\bar t$ events at the LHC. Among others, these predictions are needed for the precise determination of the top quark mass. The extension of our results to other processes, like open or associated $B$ and charm production is straightforward. We also explore the prospects for extracting heavy flavor fragmentation functions from LHC data.