Complete NLO corrections to $tar{t}γ$ and $tar{t}γγ$

In this contribution we discuss recent progress in associated top-quark pair production with one or two isolated photons, $pp\to t\bar{t}γ(γ)$. The focus is the simultaneous inclusion of higher-order effects and photon radiation in the production of the top-quark pair and in the decay processes. This allows us to quantify the importance of photon radiation in decay processes and the size of the so-called complete NLO corrections in realistic final states.

💡 Research Summary

In this paper the authors present a comprehensive next‑to‑leading order (NLO) study of top‑quark pair production in association with one or two isolated photons at the LHC, i.e. the processes pp → tt̄γ and pp → tt̄γγ. The novelty of the work lies in the “complete NLO” approach: all leading‑order (LO) and NLO contributions are included not only for the production of the top‑quark pair but also for the subsequent decays of the top quarks and the intermediate W bosons. The authors work in the narrow‑width approximation and focus on the dileptonic decay channel, which allows a clean separation of the full amplitude into three resonant classes according to the origin of the photons: (i) production‑only (Prod.), (ii) mixed production‑and‑decay (Mixed), and (iii) decay‑only (Decay).

The LO contributions are split into a dominant QCD term (LO₁ ∼ α_s²α⁴⁺ⁿγ) and two sub‑leading electroweak (EW) pieces (LO₂ ∼ α_sα⁵⁺ⁿγ and LO₃ ∼ α⁶⁺ⁿγ) that arise from photon‑initiated channels and pure EW top‑pair production. At NLO the authors compute the QCD correction to LO₁ (NLO₁ ∼ α_s³α⁴⁺ⁿγ) and three additional sub‑leading pieces (NLO₂, NLO₃, NLO₄) which correspond to QCD/EW corrections to LO₂ and LO₃. The full NLO prediction, denoted NLO, is the sum of all LO and NLO pieces. For practical purposes they also define an approximation, NLO_prd, in which only the production‑stage corrections are retained while photon radiation and higher‑order effects in the decays are omitted.

The calculation is performed with state‑of‑the‑art automated tools: RECOLA for one‑loop amplitudes, the Collier library for scalar and tensor integrals, CutTools (OPP reduction) and OneLOop for cross‑checks, and the Nagy‑Soper subtraction scheme as implemented in HELAC‑DIPOLES for real radiation. Phase‑space integration is handled by PARNI and Kaleu.

Results for pp → tt̄γγ
In the dileptonic channel the authors find that the production‑only contribution accounts for only about 40 % of the total fiducial cross section. The Mixed and Decay contributions together provide roughly 60 %, leading to an overall increase of the cross section by a factor of ≈2.5 when photon radiation in the decays is consistently included. Differential distributions illustrate this effect clearly: the transverse momentum of the photon pair (p_T,γ₁γ₂) is dominated by Decay photons at low p_T, while at high p_T the Prod. component rises to ≈80 % of the total. The angular separation ΔR_{ℓ+γ₂} shows distinct peaks for each component; the Mixed and Decay terms peak at small ΔR due to photons emitted in the top‑quark decay, a feature absent in the pure production contribution.

Results for pp → tt̄γ
Table 1 shows an LO cross section of 55.60 fb, which grows to 59.05 fb after the NLO QCD correction (≈+5 %). The complete NLO result (including all sub‑leading pieces) is 59.59 fb, i.e. only a 0.9 % increase over NLO QCD. The sub‑leading LO₂, LO₃ and NLO₂‑NLO₄ contributions are each below 1 % of the total at the integrated level, confirming that the NLO QCD prediction (NLO QCD) already captures the bulk of the physics. However, in the high‑energy tails of observables such as the photon transverse momentum (p_T,γ₁) and the invariant mass of the two b‑jets (p_T,b₁b₂), the EW Sudakov logarithms in NLO₂ become sizable, reaching 5‑10 % relative to the LO₁ baseline. This leads to a modest reduction of the full NLO prediction with respect to NLO QCD in the photon p_T spectrum. The NLO₃ term (real QCD radiation) shows an opposite trend, partially cancelling the NLO₂ effect, especially in the b‑jet observable. Consequently, the difference between the full NLO and the production‑only approximation NLO_prd never exceeds ≈2 %, well within the typical scale uncertainties of 6‑8 %.

Conclusions
The study demonstrates that for processes involving multiple isolated photons, such as tt̄γγ, photon radiation from top‑quark decays is indispensable for a realistic description; neglecting it would severely underestimate both total rates and shape of key observables. For tt̄γ, sub‑leading contributions are numerically small overall but can affect differential distributions in the high‑p_T regime through EW Sudakov effects. The production‑only approximation provides a computationally cheaper alternative with only a percent‑level loss of accuracy, making it attractive for matching to parton showers. The work thus supplies the most precise fixed‑order predictions currently available for tt̄γ and tt̄γγ, which are essential for background modeling in tt̄H (H→γγ) analyses and for probing the top‑photon coupling at the LHC. Future extensions could include other decay channels, NNLO QCD/EW corrections, and a systematic study of photon isolation criteria.