Two-loop QCD amplitudes for tt̄γ production at hadron colliders

The associated production of a photon and a top-antitop quark pair (tt̄γ) is important for measuring the top-quark charge and probing the top-photon interaction, and it requires improved theoretical predictions. We focus on the calculation of two-loop amplitudes for tt̄γ production at hadron colliders. The infrared singularities with full top-quark mass dependence are derived from universal anomalous dimensions combined with one-loop massive amplitudes expanded to higher orders in the dimensional regulator $ε$. The finite remainders are approximated in the high-energy boosted limit using the mass-factorization formula. To validate our approach, we compare approximate one-loop amplitudes up to O(ε²), as well as the two-loop infrared poles, against our exact results. The results in this paper serve as an important step toward next-to-next-to-leading order predictions for tt̄γ production.