Theoretical uncertainties in the simulation of production represent one of the main obstacles that still hamper the observation of Higgs-boson production in association with top-quark pairs in the channel. In this Letter we present a next-to-leading order (NLO) simulation of production with massive b-quarks matched to the Sherpa parton shower. This allows one to extend NLO predictions to arbitrary kinematics, including the case where one or both b-jets arise from collinear splittings. We find that this splitting mechanism plays an important role for the analysis.
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