New NLOPS predictions for $\boldsymbol{t\bar{t}+b}$-jet production at the LHC.

Measurements of $t\bar{t} H$ production in the $H\to b\bar{b}$ channel depend in a critical way on the theoretical uncertainty associated with the irreducible $t\bar{t}+b$-jet background. In this paper, analysing the various topologies that account for $b$-jet production in association with a $t\bar{t}$ pair, we demonstrate that the process at hand is largely driven by final-state $g\to b\bar{b}$ splittings. We also show that in five-flavour simulations based on $t\bar{t}+$multi-jet merging $b$-jet production is mostly driven by the parton shower, while matrix elements play only a marginal role in the description of $g\to b\bar{b}$ splittings. Based on these observations we advocate the use of NLOPS simulations of $pp\to t\bar{t}b\bar{b}$ in the four-flavour scheme, and we present a new POWHEG generator of this kind. Predictions and uncertainties for $t\bar{t}+b$-jet observables at the 13 TeV LHC are presented both for the case of stable top quarks and with spin-correlated top decays. Besides QCD scale variations we consider also theoretical uncertainties related to the POWHEG matching method and to the parton shower modelling, with emphasis on $g\to b\bar{b}$ splittings. In general, matching and shower uncertainties turn out to be remarkably small. This is confirmed also by a tuned comparison against Sherpa+OpenLoops.