Complete NLO corrections to full off-shell $t\bar{t}$ production in the $\ell + j$ decay channel

TL;DR

This work delivers the first complete NLO predictions for full off-shell $t\bar{t}$ production in the $\ell+j$ decay channel, including all resonant and non-resonant contributions with finite-width effects and interference, across all partonic initial states. The authors implement robust IR-safe techniques by combining democratic clustering with parton-to-photon fragmentation and photon-to-jet conversion functions, enabling a consistent treatment of photons and jets in the presence of QCD and EW corrections. They show that a resonance-enhancing cut on light-jet pairs substantially improves perturbative stability, while differential results reveal significant NLO effects in high-$p_T$ tails and notable photon-initiated contributions, underscoring the necessity of complete NLO modeling. The methodology and findings provide a benchmark for precise SM predictions in the top-quark sector and pave the way for applying the framework to related processes such as $pp\to t\bar{t}H$, $t\bar{t}Z$, and $t\bar{t}W$ at the LHC.

Abstract

We present the calculation of the complete NLO corrections to the full off-shell top-quark pair production in the lepton+jets decay channel, denoted as $pp \to \ell^- \barν_{\ell} j_b j_b jj + X$, where $\ell^- = e^-, μ^-$. The calculation consistently preserves the finite-width effects of the top quarks and $W$ and $Z$ gauge bosons, and takes into account all doubly-, singly-, and non-resonant contributions along with their interference effects. All Born-level contributions, at the perturbative orders from ${\mathcal O}(α_s^4 α^2)$ to ${\mathcal O}(α_s^0 α^6)$, are included and corrected by both NLO QCD and NLO EW effects. We consider all possible partonic initial states and decay channels. Particular attention is paid to the infrared safety in the presence of photons and jets. This requires the use of the so-called parton-to-photon fragmentation function and the photon-to-jet conversion function, which makes the democratic photon-parton clustering and the $γ\to q \bar q$ splittings finite. We present our findings at the integrated and differential fiducial cross-section levels for the LHC Run III centre-of-mass energy of $\sqrt{s} = 13.6$ TeV. In addition, we quantify the impact of subleading NLO effects, in particular electroweak Sudakov logarithms and non-resonant QCD backgrounds. Two analysis strategies are employed and compared, namely with and without the resonance-enhancing requirement on the invariant mass of the two light jets, $|M_{jj} - m_W| < Q_{\text{cut}} = 20$ GeV, illustrating the relationship between QCD background suppression, off-shell effects, interferences, and complete NLO corrections.

Figures (13)

• Figure 1: Examples of Feynman diagrams with two (left), one (middle) and no top-quark resonances (right) contributing to the $pp \to \ell^-\bar{\nu}_\ell\,j_b j_b\, jj +X$ process at $\text{LO}_3$.
• Figure 2: Examples of Feynman diagrams contributing to the $pp \to \ell^-\bar{\nu}_\ell\,j_b j_b jj +X$ process at $\text{LO}_2$ (left) and $\text{LO}_4$ (right) via interference effects. Left: interference effects between $\text{LO$_1$}$ and $\text{LO$_3$}$. Right: interference effects between $\text{LO$_3$}$ and $\text{LO$_5$}$.
• Figure 3: Graphical representation of all LO contributions and their NLO corrections for the $pp \to \ell^-\bar{\nu}_\ell\,j_b j_b jj +X$ process.
• Figure 4: Examples of one-loop Feynman diagrams contributing to the $pp \to \ell^-\bar{\nu}_\ell\,j_b j_b jj+X$ process. The diagram on the left contributes at $\mathcal{O}(g_s^6 g^2)$, the one in the middle at $\mathcal{O}(g_s^2 g^6)$ and the one on the right at $\mathcal{O}(g_s^4 g^4)$.
• Figure 5: Examples of real-emission Feynman diagrams contributing to the $pp \to \ell^-\bar{\nu}_\ell\,j_b j_b jj+X$ process at $\text{NLO$_3$}$.