  Theoretical predictions for ttbb production are of crucial importance for ttH
measurements in the H->bb channel at the LHC. To address the large
uncertainties associated with the modelling of extra QCD radiation in ttbb
events, in this paper we present a calculation of pp->ttbbj at NLO QCD. The
behaviour of NLO corrections is analysed in a variety of observables, and to
assess theoretical uncertainties we use factor-two rescalings as well as
different dynamic scales. In this context, we propose a systematic alignment of
dynamic scales that makes it possible to disentangle normalisation and shape
uncertainties in a transparent way. Scale uncertainties at NLO are typically at
the level of 20-30% in fiducial cross sections, and below 10% for the shapes of
distributions. The kinematics of QCD radiation is investigated in detail,
including the effects of its recoil on the objects of the ttbb system. In
particular, we discuss various azimuthal correlations that allow one to
charaterise the QCD recoil pattern in a precise and transparent way. In
general, the calculation at hand provides a variety of precise benchmarks that
can be used to validate the modelling of QCD radiation in ttbb generators.
Moreover, as we will argue, pp->ttbbj at NLO entails information that can be
used to gain insights into the perturbative convergence of the inclusive ttbb
cross section beyond NLO. Based on this idea, we address the issue of the large
NLO K-factor observed in the ttbb cross section, and we provide evidence that
supports the reduction of this K-factor through a mild adjustment of the QCD
scales that are conventionally used for this process. The presented 2->5 NLO
calculations have been carried out using OpenLoops 2 in combination with Sherpa
and Munich.
