Off-shell vs on-shell modelling of top quarks in photon associated production

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.