Off-shell Top Quarks with One Jet at the LHC: A comprehensive analysis at NLO QCD

TL;DR

This work delivers a first-principles NLO QCD analysis of off-shell top-quark pair production in association with a jet, in the dilepton decay channel, at LHC Run II energies. Using the Helac-NLO framework, it includes all resonant and non-resonant contributions at ${\cal O}(\alpha_s^4 \alpha^4)$, with full off-shell effects and interference, and evaluates theoretical uncertainties from scales and PDFs. A key finding is that dynamical scales such as $E_T/2$ and $H_T/2$ greatly improve perturbative stability for differential distributions, with $H_T/2$ typically yielding the smallest uncertainties; PDF uncertainties remain subdominant but non-negligible in tails. The results have direct implications for precision top-quark measurements and new-physics searches that rely on accurate modelling of $t\bar{t}+j$ backgrounds.

Abstract

We present a comprehensive study of the production of top quark pairs in association with one hard jet in the di-lepton decay channel at the LHC. Our predictions, accurate at NLO in QCD, focus on the LHC Run II with a center-of-mass energy of 13 TeV. All resonant and non-resonant contributions at the perturbative order ${\cal O}(α_s^4 α^4)$ are taken into account, including irreducible backgrounds to $t\bar{t}j$ production, interferences and off-shell effects of the top quark and the $W$ gauge boson. We extensively investigate the dependence of our results upon variation of renormalisation and factorisation scales and parton distribution functions in the quest for an accurate estimate of the theoretical uncertainties. Additionally, we explore a few possibilities for a dynamical scale choice with the goal of stabilizing the perturbative convergence of the differential cross sections far away from the $t\bar{t}$ threshold. Results presented here are particularly relevant for searches of new physics as well as for precise measurements of the top-quark fiducial cross sections and top-quark properties at the LHC.

Figures (36)

• Figure 1: A representative set of Feynman diagrams, involving two (a), one (b) and no top-quark resonances (c), contributing to the leading order $pp \to e^+\nu_e \mu^- \bar{\nu}_\mu b\bar{b}j+X$ process at ${\cal O}(\alpha_s^3 \alpha^4)$. The last diagram (d) with a single $W$ boson resonance contributes to the off-shell effects of the $W$ gauge boson.
• Figure 2: A representative set of Feynman diagrams, involving heptagons (a and d), hexagons (e and f), the pentagon diagram (b) and the box diagram (c) contributing to virtual corrections to the $pp \to e^+\nu_e \mu^- \bar{\nu}_\mu b\bar{b}j+X$ process at ${\cal O}(\alpha_s^4 \alpha^4)$.
• Figure 3: A representative set of Feynman diagrams involving two (a), one (b) and no top-quark resonances (c and d) contributing to the real emission corrections to the $pp \to e^+\nu_e \mu^- \bar{\nu}_\mu b\bar{b}j+X$ process at ${\cal O}(\alpha_s^4\alpha^4)$.
• Figure 4: Differential cross section distribution as a function of $E_T$ and $H_T$ at LO (left panel) and at NLO (right panel) for the $pp\to e^+ \nu_e \mu^- \bar{\nu}_\mu b\bar{b}j +X$ process at the LHC run II with $\sqrt{s} = 13$ TeV. Renormalisation and factorisation scales are set to the common value $\mu_R=\mu_F=\mu_0=m_t$. The LO and the NLO CT14 PDF sets are employed. Also shown is the $E_T/H_T$ ratio.
• Figure 5: Scale dependence of the LO cross section with the individual contributions of the partonic channels (left panel) and scale dependence of the LO and NLO cross sections (right panel) for the $pp\to e^+ \nu_e \mu^- \bar{\nu}_\mu b\bar{b}j +X$ process at the LHC run II with $\sqrt{s} = 13$ TeV. Renormalisation and factorisation scales are set to the common value $\mu_R=\mu_F=\mu_0$ with $\mu_0=m_t$, $\mu_0=H_T/2$ and $\mu_0=E_T/2$. The LO and the NLO CT14 PDF sets are employed.