We present a complete description of top quark pair production in association with a hard photon in the dilepton channel. Our calculation is accurate to NLO in QCD. It is based on matrix elements for $e^+ u_e mu^-bar{ u}_mu b bar{b}gamma$ production and includes all resonant and non-resonant diagrams, interferences, and off-shell effects of the top quarks and the $W$ gauge bosons. This calculation constitutes the first full computation for top quark pair production with a final state photon in hadronic collisions at NLO in QCD. Numerical results for total and differential cross sections are presented for the LHC at a centre-of-mass energy of $sqrt{s}=13$ TeV. For a few observables relevant for new physics searches, beyond some kinematic bounds, we observe shape distortions of more than $100%$. In addition, we confirm that the size of the top quark off-shell effects for the total cross section is consistent with the expected uncertainties of the narrow width approximation. Results presented here are not only relevant for beyond the Standard Model physics searches but also important for precise measurements of the top-quark fiducial cross sections and top-quark properties at the LHC.
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