  We present a comparative study of various approaches for modelling of the
$e^+ \nu_e \mu^- \bar{\nu}_\mu b\bar{b} \gamma$ final state in $t\bar{t}\gamma$
production at the LHC. Working at the NLO in QCD we compare the fully realistic
description of the top quark decay chain with the one provided by the
narrow-width-approximation. The former approach comprises all double, single
and non-resonant diagrams, interferences, and off-shell effects of the top
quarks. The latter incorporates only double resonant contributions and
restricts the unstable top quarks to on-shell states. We confirm that for the
integrated cross sections the finite top quark width effects are small and of
the order of ${\cal O}(\Gamma_t/m_t)$. We show, however, that they are strongly
enhanced for more exclusive observables. In addition, we investigate fractions
of events where the photon is radiated either in the production or in the decay
stage. We find that large fraction of isolated photons comes from radiative
decays of top quarks. Based on our findings, selection criteria might be
developed to reduce such contributions, that constitute a background for the
measurement of the anomalous couplings in the $t\bar{t}\gamma$ vertex.

High Energy Physics - Phenomenology