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

Hard Photons in Hadroproduction of Top Quarks with Realistic Final States