NLO QCD predictions for $\boldsymbol{t\bar{t}\gamma}$ with realistic photon isolation

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 $W^\pm/Z$ gauge bosons. We provide the results for the $pp\to e^+\nu_e \,\mu^- \bar{\nu}\, b\bar{b}\,\gamma+X$ 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.