NLO matching for $t\bar{t}b\bar{b}$ production with massive $b$ quarks

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 QCD $t\bar{t}+b$-jet background. We introduce a new $pp\to t\bar{t}b\bar{b}$ POWHEG generator in the 4F scheme based on POWHEG-BOX-RES and on OpenLoops for fast evaluation of the scattering amplitudes. We present predictions and uncertainties for $t\bar{t}+b$-jet observables at the 13 TeV LHC. We also consider theoretical uncertainties related to the POWHEG matching method and to the parton shower (PS) 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 by a consistent comparison against SHERPA+OpenLoops.