Bottom-quark mass effects in associated production with $Z$ and $H$ bosons

In this study, predictions obtained in the four and in the five flavour schemes are compared for two important processes involving heavy flavours at the LHC: the production of a $Z$ or a Higgs boson in association with $b$ quarks. In particular we obtain predictions with \Sherpa's \MCatNLO implementation for the four--flavour scheme, treating the $b$'s as massive, and with multijet merging at leading and next-to leading order for the five--flavour scheme. While differences between the two schemes, at the inclusive level, are well understood from resummation of possibly large logs into the $b$-PDFs, differences in shape present a major problem for experimental measurements. We make use of data for $Z+b(\bar{b})$ production at the $7$ TeV LHC to exhibit strengths and weaknesses of the different approaches and we use these results to validate predictions for $b$-associated Higgs-boson production at the 13 TeV Run II.