We present a complete description of top quark pair production in association with a hard photon in the di-lepton decay channel. The calculation is performed at NLO QCD and includes all resonant and non-resonant Feynman diagrams, interferences, and finite-width effects of the top quarks and W ±/Z gauge bosons. We provide the results for the pp → \( {e}^{+}{\nu}_e\ {\mu}^{-}\ \overline{\nu}\ b\overline{b}\ \gamma \) + X process using the fixed-cone, smooth-cone and hybrid-photon isolation criteria. The fixed-cone isolation criterion allows contributions from collinear photon radiation off QCD partons, which requires the inclusion of parton-to-photon fragmention processes. To this end, we include the latter contributions into our computational framework. We quantify the impact of different photon-isolation prescriptions on the integrated and differential cross-section predictions for the LHC at a centre-of-mass energy of \( \sqrt{s} \) = 13.6 TeV. Our state-of-the-art NLO QCD results with the fixed-cone criterion allow us to reproduce the photon-isolation prescription employed in ATLAS and CMS. This will help to improve future comparisons with the LHC data.
